From bc74f03d247a8b044dd524b365bf1de7bc32c9b0 Mon Sep 17 00:00:00 2001 From: Ruge Lin Date: Fri, 9 Oct 2026 00:13:02 +0800 Subject: [PATCH] Consolidate reader documentation around results and reproduction --- AGENTS.md | 6 +- CHANGELOG.md | 50 +--- README.md | 53 ++-- WORKSPACES.md | 27 +- audits/README.md | 5 +- audits/quantitative_contribution_verdict.md | 100 +++---- docs/ARCHIVE.md | 17 +- docs/CALIBRATION_PRECISION.md | 25 +- docs/QUANTITATIVE_CORE.md | 5 +- docs/RELEASE.md | 41 +-- docs/REPRODUCIBILITY.md | 25 +- docs/RESEARCH_STATUS.md | 54 ++-- docs/background_claims.md | 122 ++++---- docs/learn/01_correlations.md | 10 +- docs/learn/03_ising.md | 4 +- docs/learn/04_rounding.md | 6 +- docs/learn/05_worked_certificate.md | 10 +- docs/learn/README.md | 18 +- docs/learn/assumptions_and_sources.md | 20 +- llms.txt | 56 ++-- research/sharpness_and_calibration.md | 34 +-- research/uniform_extraction_core.md | 25 +- results/release_preparation.json | 305 +++++++++++++++----- snapshot_manifest.json | 2 +- work_orders/CURRENT.md | 22 +- work_orders/INDEPENDENT_AUDIT.md | 44 +-- 26 files changed, 550 insertions(+), 536 deletions(-) diff --git a/AGENTS.md b/AGENTS.md index 00d0bec..58abd38 100644 --- a/AGENTS.md +++ b/AGENTS.md @@ -1,10 +1,10 @@ # Workspace instructions -Read README.md, STATUS.md, and work_orders/CURRENT.md before extending the project. +Read README.md, docs/RESEARCH_STATUS.md, and work_orders/CURRENT.md before extending the project. ## Fixed boundaries -- The project belongs to Ruge Lin and develops the Monster-related idea behind arXiv:2209.15025. It is a new research direction, not a defense of the old embedding observation. +- The project belongs to Ruge Lin. Its active result is the quantitative moonshine correlation criterion in research/uniform_extraction_core.md. - Preserve the owner's LICENSE. The MIT LICENSE from initial commit 40cbbbe04247c1f816cc2c7f8106264ecff2b253 must remain byte-identical. - Preserve all files under provenance/*.zip and the historical research notes 01–05 byte-for-byte. New work may correct them through an explicit erratum, never through a silent archival rewrite. - Never present scalar or toy verification as a full Monster simulation, proof assistant verification, novelty audit, or independent expert review. @@ -20,4 +20,4 @@ Work on one claim or audit obligation at a time. Record the mathematical change External references and mathematical data retain their source attribution. Do not bundle downloaded papers or font files. Do not publish a manuscript or contact researchers without the user's instruction. -If another workspace is active, use separate branches and small commits. Do not force-push or overwrite another workspace's unmerged work. The canonical remote is https://github.com/GoGoKo699/Monster-Correlation-Rigidity. Read WORKSPACES.md and use work_orders/INDEPENDENT_AUDIT.md for the first second-workspace assignment. A second assistant workspace is not independent human or expert review. +If another workspace is active, use separate branches and small commits. Do not force-push or overwrite another workspace's unmerged work. The canonical remote is https://github.com/GoGoKo699/Monster-Correlation-Rigidity. Use WORKSPACES.md for contribution workflow and work_orders/INDEPENDENT_AUDIT.md for proof-review procedure. Describe assistant reviews accurately. diff --git a/CHANGELOG.md b/CHANGELOG.md index 7cac2cb..3a52c6c 100644 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -1,45 +1,13 @@ # Changelog -## Unreleased — research-backlog disposition, 28 September 2026 +## Unreleased -Recorded individual dispositions and immutable source links for PRs #12–27: -PR12 is rejected as written, PR23 is superseded by the consolidated core, and -the other fourteen proposals are archived as separate research. Added the -normalization counterexample warning and retained PR26’s latest checker -correction. Branches and commits are preserved; the selected proofs, checkers, -scientific outputs and numerical tolerances are unchanged. +- Quantitative moonshine correlation criterion with unequal coupling deficits and an explicit overlap-error budget. +- Sharp square-root field-distance exponent and seven-scalar interval calibration. +- Five physics lessons anchored in Gaberdiel, with selected Yamauchi material and worked exercises. +- Scale-aware exact square-root enclosures and an explicit precision-limit outcome for calibration. +- Reproducible exact certificates, historical report replay, and mathematical-rendering checks. +- Consolidated reader navigation and concise result, source, and implementation documentation. -## Unreleased — release preparation, 27 September 2026 - -The final reader cleanup removes repeated reproduction and status prose, repairs -the audit index and worked-certificate command, and marks the earlier review's -implementation findings as dated. The core's “multiplicity-free” wording is -corrected to an eigenspace statement; all equations, assumptions, thresholds, -checker sources and scientific report fingerprints are unchanged by this cleanup. - -Corrected a small-scale interval-calibration exception without changing the -analytic theorem, exact premises, or sufficient error tolerances. Added adaptive -exact square-root enclosures, an explicit precision-work-limit outcome, and -scale/interval regression checks. Current report fingerprints are separate from -preserved historical outputs. - -Added `verify_current.py`, a pinned reproduction requirements file, a -reproduction guide, current release integrity checks, and a clear distinction -between exact certification, historical strict replay, and bounded portability. - -Clarified current versus historical status, indexed preserved and pending work, -and replaced ambiguous missing-file references with pinned destinations. Added -citation metadata, a scope-accurate LLM source map, and release-scope notes. -The Gaberdiel-first physics teaching path and approved native mathematics remain. - -No manuscript, DOI, tagged release, or merge of unrelated research branches is -included. Protected historical notes, provenance archives, the original license, -and existing recorded evidence are retained. - -## Prior integrated research and presentation - -The selected quantitative core, calibration/sharpness results, and bounded -review were integrated before this release-preparation pass. Five physics -lessons and subsequent math-rendering improvements form the current teaching -path. Consult the [archive index](docs/ARCHIVE.md) and Git history for exact -historical commits rather than interpreting those integrations as formal releases. +[Package contents](docs/RELEASE.md) · [Reproduction](docs/REPRODUCIBILITY.md) · +[Archive](docs/ARCHIVE.md) diff --git a/README.md b/README.md index 8bcbfdc..65c25e0 100644 --- a/README.md +++ b/README.md @@ -6,17 +6,13 @@ Quantitative identification of the moonshine vertex operator algebra from near-e This repository serves as a record of the work and a guide for the author’s self-directed learning. For discussion or potential collaboration, please contact Ruge Lin at [gogoko699@gmail.com](mailto:gogoko699@gmail.com). -This repository contains research proofs, source comparisons, scope controls and reproducible certificates, not a drafted paper. The [current scientific status](docs/RESEARCH_STATUS.md) records the reviewed scope and remaining boundaries. - ## Start here: a physicist's reading path Can nearly extremal interaction coefficients identify an exact chiral theory within a specified class? Begin with [the five-lesson learning path](docs/learn/README.md): correlation functions, weight-two geometry, internal Ising structure, quantitative rounding, and a worked certificate. No prior VOA or Monster-group expertise is assumed. The primary anchor is **Gaberdiel, _An Introduction to Conformal Field Theory_**. Selected parts of **Yamauchi, _3-transposition groups arising in VOA theory_**, provide the secondary algebraic anchor. The [reading map](docs/learn/README.md) interleaves short source selections with local explanations, calculations, and self-checks; it does not require two complete courses. [Assumptions and source roles](docs/learn/assumptions_and_sources.md) separates the physical language, exact premises, imported theorems, and project estimates. -For direct proof checking, start with the selected result below and the research documents that follow. The teaching path does not enlarge the theorem's scope. - -## The selected result +## The result Work in an **exact** simple unitary, rational, $C_2$-cofinite, holomorphic vertex operator algebra of CFT type, with central charge 24 and no weight-one states. Let $x$ and $y$ be real unit weight-two primaries, and let $f(x)$ be the normalized self-three-point coefficient. Put @@ -33,7 +29,7 @@ f(x),f(y)\ge M-\frac1{32768},\qquad then the underlying VOA is isomorphic to the moonshine VOA. -The proof extracts nearby exact Ising directions, uses Sakuma's discrete overlap gap to force an orthogonal pair, and then applies the **prior classification theorem of Abe–Lam–Yamada**. The quantitative criterion does not assume a Monster action, its multiplication table, or a preidentified nearby exact axis. It also does not prove uniqueness of the bare ambient class: actual fields satisfying the inequalities are additional input. +The proof extracts nearby exact Ising directions, uses Sakuma's discrete overlap gap to force an orthogonal pair, and then applies the **prior classification theorem of Abe–Lam–Yamada**. The inputs are the specified fields and their coefficients; a Monster action or a preidentified nearby exact axis is unnecessary. The criterion is sufficient: fields satisfying its inequalities identify the VOA within the stated exact class. The general version allows unequal self-coupling deficits and an explicit overlap-error budget. The square-root field-distance exponent is sharp. For actual real fields of exact weight two, seven scalar intervals can be used to correct stress contamination and normalization before applying the criterion. @@ -43,45 +39,30 @@ The general version allows unequal self-coupling deficits and an explicit overla |---|---| | [Self-contained core proof](research/uniform_extraction_core.md) | Exact hypotheses, uniform localization, pair rounding and attributed classification endpoint. | | [Sharpness and calibration](research/sharpness_and_calibration.md) | Optimal extraction exponent and certified scalar preprocessing. | -| [Final bounded review](audits/final_quantitative_review.md) | Adversarial proof/source/implementation checks and their limits. | | [Contribution comparison](audits/quantitative_contribution_verdict.md) | Closest inspected prior results, attribution and a scoped priority judgment. | -| [Background evidence](docs/background_claims.md) | Scientific support for eventual framing, without manuscript prose. | +| [Scientific context and sources](docs/background_claims.md) | Physical interpretation and primary-source roles. | +| [Results and assumptions](docs/RESEARCH_STATUS.md) | Result map and input requirements. | -Finite coefficient tolerances are not approximate VOA axioms or a device-independent experiment. Exact grading, real structure, the known stress tensor and the ambient class remain hypotheses. No practical field-finding algorithm, sample complexity, optimal numerical decision region, or explicit implemented isomorphism is claimed. +Coefficient errors are allowed within the stated bounds; the ambient axioms, field grades, and real structure are exact premises. Calibration additionally uses a known stress tensor. The numerical tolerances are sufficient bounds, while the field-distance exponent is sharp. -## Reproduce the selected certificates +## Reproduce the certificates -The current exact checks and documentation checks use Python's standard library: +The exact certificates and documentation checks use Python's standard library: ```sh python verify_current.py ``` -The command runs the selected checks in normal, `-O`, and `-OO` modes and -compares current fingerprints. The [reproduction guide](docs/REPRODUCIBILITY.md) -provides the complete inventory, pinned environment, and `--all` command. -It reports historical strict byte replay and bounded portability separately: -a floating-point mismatch remains a strict failure even if the bounded check passes. -See [calibration precision](docs/CALIBRATION_PRECISION.md) for the current -implementation and its explicit precision limit. - -No full Monster tensor is simulated. Finite checks do not verify the imported -classification theorems or constitute independent human review. - -## Earlier research and preservation - -Use [the archive and research index](docs/ARCHIVE.md) for older gate-testing, -circuit, and readout records. It identifies the dated ledgers, including the -unchanged import-era `STATUS.md`. Their older “current” labels do not supersede -[the current scientific status](docs/RESEARCH_STATUS.md). Protected source notes, -provenance archives, and saved evidence remain available unchanged; legacy -mathematics may not render correctly in every GitHub viewer. - -[Release scope](docs/RELEASE.md), [the changelog](CHANGELOG.md), and -[citation metadata](CITATION.cff) describe the current research package without -claiming a manuscript, publication, DOI, or tagged release. For LLM-assisted -research, [the source map](llms.txt) points questions to the theorem, its exact -assumptions, teaching anchors, verification, and historical boundaries. +The command runs the exact certificates, implementation checks, and documentation +checks in normal, `-O`, and `-OO` modes. The [reproduction guide](docs/REPRODUCIBILITY.md) +contains the full suite, pinned environment, and interpretation of the results. +See [calibration precision](docs/CALIBRATION_PRECISION.md) for the input contract +and precision limit. + +## Reference + +[Package contents](docs/RELEASE.md) · [Additional research and archive](docs/ARCHIVE.md) · +[Citation metadata](CITATION.cff) · [AI source guide](llms.txt) Original code and documentation retain the owner's [MIT license](LICENSE). Imported mathematical results remain attributed to their authors. diff --git a/WORKSPACES.md b/WORKSPACES.md index a3aa47f..87331e2 100644 --- a/WORKSPACES.md +++ b/WORKSPACES.md @@ -1,23 +1,10 @@ -# Workspace coordination +# Maintainer workflow -Canonical repository: https://github.com/GoGoKo699/Monster-Correlation-Rigidity +Repository: https://github.com/GoGoKo699/Monster-Correlation-Rigidity -## Roles +Use a separate branch and a focused pull request for each change. Check existing +branches before starting overlapping work, review the diff, and merge after the +required checks pass. Preserve other contributors' work and avoid force-pushes. -The main conversation is the integration workspace. It maintains the current claim ledger, checks compatibility of corrections, and integrates reviewed changes. The repository is the shared source of truth; conversation summaries are not a substitute for reading the current branch. - -The first additional workspace is a proof auditor. Its assignment is [INDEPENDENT_AUDIT.md](work_orders/INDEPENDENT_AUDIT.md). This means a fresh reconstruction of the argument, not a claim of independent human, expert, or formal review. No additional workspace is assumed to be running merely because this file exists. - -## Branch and file ownership - -Start the audit on `audit/voa-extrema` from the latest main. Check existing branches and pull requests before creating it; never reset someone else's branch. Record the exact base commit in the audit report. Put new findings in `audits/` and small new checks in `checks/audit_*`. Keep patches to shared front-door files separate for integration. - -Do not change LICENSE, the five research notes, original check scripts/data/results, or provenance ZIPs. Correct historical statements through a separately named erratum and update affected claims explicitly. Do not force-push. Use a small pull request to main rather than direct simultaneous edits of main. - -## Evidence rules - -A passing arithmetic or toy test is not a proof audit. Each audit outcome must identify the exact statement, source or proof, missing assumption or correction, and affected claim IDs. Use PASS, ERROR, or UNRESOLVED with that evidence; do not use PASS merely because a script ran. - -Before proposing integration, run `python verify.py`; hash changes must be intentional and documented. New checks should emit their report to stdout and remain effective under `-O` and `-OO`. Do not overwrite recorded reports to hide a mismatch. Include the largest tested dimension and whether full Monster data were used (the existing work uses no full Monster simulation). - -Manuscript writing, release creation, DOI registration, researcher outreach, claims of established novelty, and claims of practical implementation are outside this work order. +Follow [AGENTS.md](AGENTS.md) for scientific and preservation rules and +[the reproduction guide](docs/REPRODUCIBILITY.md) for validation commands. diff --git a/audits/README.md b/audits/README.md index 7dd1655..5aaa7a8 100644 --- a/audits/README.md +++ b/audits/README.md @@ -1,6 +1,6 @@ # Audit record -Start with [current scientific status](../docs/RESEARCH_STATUS.md). These are +Start with [results and assumptions](../docs/RESEARCH_STATUS.md). These are assistant reconstructions and finite checks, not independent human review or formal verification of the imported theorems. @@ -13,8 +13,7 @@ formal verification of the imported theorems. | [Calibration erratum](calibration_scale_erratum.md) | Subsequent small-scale implementation repair, precision limit and preserved historical evidence. | Use [current reproduction](../docs/REPRODUCIBILITY.md) for commands and report -fingerprints. The [maintenance work order](../work_orders/CURRENT.md) governs -new work on this selected result. +fingerprints. ## Earlier gate-rigidity audits diff --git a/audits/quantitative_contribution_verdict.md b/audits/quantitative_contribution_verdict.md index de78600..b0a6514 100644 --- a/audits/quantitative_contribution_verdict.md +++ b/audits/quantitative_contribution_verdict.md @@ -1,81 +1,63 @@ -# Contribution verdict and direct prior-theorem comparison +# Correlation criterion and prior theorems -Research assessment, 26 September 2026. This is not an abstract, introduction, conclusion, or submission document. It contains no private publication planning. The comparison concerns the bounded quantitative identification theorem, not unrestricted moonshine uniqueness. +This comparison concerns the quantitative identification criterion in the [core proof](../research/uniform_extraction_core.md). Among the primary-source statements listed below, no result was identified with both the same finite-coefficient input and the same exact structural output. This conclusion is limited to the inspected statements and is revisable if a closer source is supplied. -## 1. Decision after the directed comparison - -**Retain the uniform coefficient-to-structure criterion as the principal bounded contribution. Attribute its exact classification endpoint and general variational geometry to prior work. Do not open another special-subtheory campaign merely to avoid deciding the current result's scope.** - -Within the primary sources and theorem statements inspected below, no result was found with the same input (arbitrary actual near-extremal normalized primary fields, with uniform coefficient bounds) and the same output (exact orthogonal Ising subalgebras and ambient moonshine identification). This is a scoped comparison, not a certification that no equivalent statement exists anywhere or a claim of being first. - -The defensible contribution is a **quantitative, source-based identification theorem**. It is not a new Ising-pair classification, a new general theorem about extrema of metrized algebras, a new generic Morse lemma, or a solution of bare-class uniqueness. Its proof is comparatively short because it uses deep established inputs. That can be useful, but it also creates a significance risk: a specialist may judge the result a modest corollary rather than a major structural advance. Adding more recorded constants or unrelated applications does not resolve that judgment. - -The bounded priority obligation is closed at the evidence level represented by this dossier: the nearest inspected statements have been compared by hypotheses and conclusions, generic ingredients have been credited, and no direct overlap has been identified in that corpus. Scholarly priority always remains revisable if a closer source is supplied. It is not appropriate to repeat the same indefinite keyword search as a substitute for a contribution decision. - -## 2. Exact object of comparison +## 1. The criterion and its inputs Fix an exact simple unitary rational C2-cofinite holomorphic VOA of CFT type with c=24 and V1=0. Given two real normalized weight-two primaries, their two self-three-point coefficients and one cross-two-point coefficient satisfy explicit sufficient inequalities. These force nearby exact Ising directions, then an exact orthogonal pair, and finally the ambient VOA isomorphism type by the prior theorem of Abe–Lam–Yamada. -Uniformity means the constants do not depend on unknown multiplication coordinates or on an already supplied nearby exact axis. It does not mean the class axioms are inferred from the coefficients. Failure of the sufficient inequalities is not an exclusion test. In particular, the theorem has meaningful conditional content without proving existence of a hypothetical competitor to moonshine. +Uniformity means the constants do not depend on unknown multiplication coordinates or on an already supplied nearby exact axis. The exact ambient class is a hypothesis. Failure of the sufficient inequalities is inconclusive. -## 3. Direct comparison matrix +The quantitative step replaces an exact orthogonal-pair premise by sufficient coefficient bounds. The exact classification endpoint, critical-point-to-idempotent mechanism, and general variational geometry come from prior work. -| Primary source / inspected statement | Its input and output | Relationship to our claim | -|---|---|---| -| Tkachev, Proposition 2.1, *On an extremal property of Jordan algebras of Clifford type* | A positive metrized commutative algebra; extremizing a cubic on a unit sphere gives an idempotent with a tangent spectral inequality. | The general critical-point-to-idempotent and second-variation mechanism is prior work. It does not give the unitary Virasoro charge gap, the exact Ising interpretation, or the ambient classification from approximate coefficients. | -| Tkachev, Proposition 2.7 | A unital positive metrized algebra; complementary nonzero idempotents exist. | These are not automatically two charge-1/2 Virasoro vectors. A complementary stress component can have large charge. This result does not close the original pair-existence problem. | -| Sakuma, Theorem 4.4 | Two exact Ising vectors in a positive-real current-free VOA; discrete pair possibilities and overlaps. | It is the overlap quantization input. Exact vectors are assumed, not extracted from finite self-coupling deficits. | -| Hall–Rehren–Shpectorov, Theorems 1.1–1.2 | Exact primitive semisimple idempotents obeying specified fusion rules; a universal axial construction and the nine two-generated Norton–Sakuma types. | A broader algebraic form of exact pair classification, not an approximate-axis extraction theorem or the identification of an arbitrary ambient holomorphic VOA. Their axis/product normalization differs from ours and is not copied numerically. | -| Khasraw–McInroy–Shpectorov, introductory stability definition and structural theorems | Exact generating axes; stability means invariance under replacing a set of axes by another set with the same group closure. | This use of “stable” is not metric robustness under errors. It cannot be cited as either proving or refuting our finite-tolerance claim. | -| Lam–Yamauchi, Theorem 1.1, framed characterization | A holomorphic c24 VOA with V1=0 and an exact Virasoro frame; moonshine identification. | An earlier exact structural route requiring a complete frame. No finite-error premise on two arbitrary fields. | -| Abe–Lam–Yamada, Theorem A.1 | Exact orthogonal Ising pair, rationality, C2-cofiniteness, holomorphicity, CFT type, c24 and V1=0; ambient moonshine identification. | This supplies the full exact endpoint. We replace its pair premise by sufficient coefficient inequalities; we do not claim its conclusion or proof as new. | -| Jiao–Zheng, introduction/main pair-generation result | Exact Ising pair with fixed overlap and appropriate exact involution data; identification of the generated subVOA, notably the 6A case. | Different input and generally a smaller endpoint. It is not uniform extraction of approximate fields. | -| Loi–Phien, Lemma 2.11 and Theorem 3.1 | Local nondegenerate matrix data or a smooth function with derivative control and permission to perturb it; quantitative normal forms and Morse properties. | Quantitative geometry is prior work. Their perturbation of a function is not an allowed modification of an exact VOA cubic. The compact localization lemma used here is elementary, not a new general Morse result. | -| Carpi–Codogni, Conjecture 1.3, Theorem 1.4 and section 14 | Genus-dependent partition data and reconstruction structure; a distinction between reconstructing the partition-function subalgebra/module and the full VOA. | Current background on spectral versus product data. Our statement does not solve the conjectural full-reconstruction or bare moonshine-uniqueness question. | +## 2. Direct comparison -Exact pair, exact idempotent, and exact fusion-law assumptions must not be paraphrased as approximate correlation hypotheses. Conversely, replacing exact hypotheses by inequalities does not automatically make a corollary a major new theorem. Both parts of that assessment are necessary. - -## 4. What the new completion work adds - -Two auxiliary issues are settled in `research/sharpness_and_calibration.md`: - -* The exponent 1/2 in value-to-nearest-axis distance is optimal, using an explicit curve inside the actual moonshine theory. This is the familiar quadratic-loss phenomenon realized in the relevant class, not a new generic exponent law. -* Seven scalar coefficients for two exact real weight-two fields determine their primary-projected normalized inputs. Certified interval arithmetic can propagate uncertainty in these coefficients. The identities are algebraic and do not relax the ambient axioms or grade/reality assumptions. - -These strengthen the precision and usability of the bounded statement. They should be presented as proof-completion and scope results, not as separate breakthroughs intended to inflate the central claim. The old dyadic thresholds are sufficient constants, not optimal ones. The optimality result concerns field-distance extraction, not the optimal possible decision region for identifying a VOA. +| Primary source / inspected statement | Its input and output | Relationship to the criterion | +|---|---|---| +| Tkachev, Proposition 2.1, *On an extremal property of Jordan algebras of Clifford type* | A positive metrized commutative algebra; extremizing a cubic on a unit sphere gives an idempotent with a tangent spectral inequality. | Supplies the general critical-point-to-idempotent and second-variation mechanism. The unitary Virasoro charge gap, exact Ising interpretation, and ambient classification require further inputs. | +| Tkachev, Proposition 2.7 | A unital positive metrized algebra; complementary nonzero idempotents exist. | A complementary stress component can have large charge. These idempotents therefore do not automatically supply two charge-1/2 Virasoro vectors. | +| Sakuma, Theorem 4.4 | Two exact Ising vectors in a positive-real current-free VOA; discrete pair possibilities and overlaps. | Supplies overlap quantization after the finite self-coupling deficits have been used to extract exact vectors. | +| Hall–Rehren–Shpectorov, Theorems 1.1–1.2 | Exact primitive semisimple idempotents obeying specified fusion rules; a universal axial construction and the nine two-generated Norton–Sakuma types. | Provides an algebraic exact-pair classification. Its axis/product normalization differs from that in the core proof and requires conversion before comparing numerical values. | +| Khasraw–McInroy–Shpectorov, introductory stability definition and structural theorems | Exact generating axes; stability means invariance under replacing a set of axes by another set with the same group closure. | “Stable” here concerns equivalent generating sets. It is a different property from metric robustness under coefficient errors. | +| Lam–Yamauchi, Theorem 1.1, framed characterization | A holomorphic c24 VOA with V1=0 and an exact Virasoro frame; moonshine identification. | An exact structural route requiring a complete frame. The correlation criterion instead takes two arbitrary fields satisfying finite-error bounds. | +| Abe–Lam–Yamada, Theorem A.1 | Exact orthogonal Ising pair, rationality, C2-cofiniteness, holomorphicity, CFT type, c24 and V1=0; ambient moonshine identification. | Supplies the full exact endpoint. The correlation criterion replaces its pair premise by sufficient coefficient inequalities. | +| Jiao–Zheng, introduction/main pair-generation result | Exact Ising pair with fixed overlap and appropriate exact involution data; identification of the generated subVOA, notably the 6A case. | The exact-pair input and generated-subVOA endpoint differ from extraction from arbitrary supplied fields and identification of the ambient VOA. | +| Loi–Phien, Lemma 2.11 and Theorem 3.1 | Local nondegenerate matrix data or a smooth function with derivative control and permission to perturb it; quantitative normal forms and Morse properties. | Quantitative geometry is prior work. Their permitted perturbation of a function changes the comparison: the core proof must work with the fixed exact VOA cubic. | +| Carpi–Codogni, Conjecture 1.3, Theorem 1.4 and section 14 | Genus-dependent partition data and reconstruction structure; a distinction between reconstructing the partition-function subalgebra/module and the full VOA. | Gives context for the distinction between spectral and product data. The correlation criterion assumes actual fields satisfying coefficient bounds, whereas full reconstruction and bare moonshine uniqueness are stronger questions. | -## 5. Search procedure and its limitations +Exact pair, exact idempotent, and exact fusion-law assumptions are substantive premises. Comparing theorems requires preserving those distinctions, together with whether the conclusion identifies a generated subalgebra or the entire ambient VOA. -The search was directed from the exact source inputs and their reference chains, not only from numerical constants. Starting points were Sakuma and ALY. The variational/idempotent search led to Tkachev, whose references led to the universal axial-algebra work. Exact-pair successors and framed-characterization predecessors were inspected, and the terminology match “stable axial algebras” was checked against its actual definition. The current reconstruction paper was read for background and whether the broader claim had already changed. +## 3. Sharpness and calibrated inputs -Additional combinations of “Griess,” “Ising vectors,” “near-extremal,” “quantitative,” “approximate idempotents,” and “axial” returned many unrelated lattice-spin, computational optimization, and chemical-reagent results. Those are not evidence for originality. An unmatched query is not a proof that no source exists. This is not a bibliometric census, a complete crawl of all citing papers, or a claim to have read every source's entire proof. +[Sharpness and calibration](../research/sharpness_and_calibration.md) supplies two precision results: -## 6. Scientific gap assessment +* The exponent 1/2 in value-to-nearest-axis distance is optimal, using an explicit curve inside the actual moonshine theory. It realizes the quadratic-loss phenomenon in the relevant class. +* Seven scalar coefficients for two exact real weight-two fields determine their primary-projected normalized inputs. Certified interval arithmetic propagates uncertainty in these coefficients while retaining the exact ambient axioms and grade/reality assumptions. -No new blocking error was found in the core Q1–Q4 proof at this pass's interface depth. The important points checked were: the positive-energy cyclic Virasoro module; the distinction between exact Ising highest weights and their ambient descendants; uniform local growth without Monster multiplicities; global entry without compactness of a moduli space; singular-product orthogonality; and the exact ambient hypotheses at ALY. +The exponent result concerns field-distance extraction. The numerical thresholds remain sufficient constants, and the optimality statement does not determine an optimal decision region for identifying a VOA. -The added calibration theorem explicitly handles stress contamination without claiming uncertain grade or uncertain PCT reality. The sharpness example has an actual known-theory embedding; it is not a three-dimensional algebra asserted to be an alternative full CFT. +## 4. Mathematical interfaces -The imported classification proofs have not been independently re-proved here. Importing correctly stated mathematics is part of a mathematical proof, not an unfinished obligation to reproduce all foundational papers. Source misapplication would be a blocking gap; the source interface matrix records what was checked and what remains an inherited theorem. +The core argument uses a positive-energy cyclic Virasoro module, the distinction between exact Ising highest weights and their ambient descendants, uniform local growth without Monster multiplicities, global entry without compactness of a moduli space, singular-product orthogonality, and the exact ambient hypotheses of Abe–Lam–Yamada. -The next stage for the chosen bounded contribution is integrated reproducibility and an adversarial read of this assembled chain. Automatic first-Ising existence, extendability in every unknown candidate, and approximate-VOA axioms are not required lemmas for the stated conditional result. They should not be silently demanded, nor silently claimed solved. +Calibration handles stress contamination within exact grade two and PCT reality. The sharpness curve is embedded in the known moonshine theory; its three-dimensional algebra describes that family within the ambient VOA. Orthogonality means commuting Virasoro subalgebras and vanishing singular OPE, while regular products can be nonzero. -## 7. Citation-level reading record +The representation and classification theorems are imported through the source interfaces listed below. The finite certificates check the accompanying arithmetic and explicit examples. -* **Tkachev [T]**, arXiv:1801.05724, Proposition 2.1 and its variational proof; Proposition 2.7; introduction and relevant references. Publisher full text and arXiv text were inspected; a later repeat publisher request returned 403. The arXiv printed-page screenshot attempt failed. Published DOI: 10.1080/00927872.2018.1499924. No claim of a full proof audit of its Jordan-algebra classification. -* **Hall–Rehren–Shpectorov [HRS]**, arXiv:1311.0217, introduction, Theorems 1.1–1.2, definitions of axes and normalization. Parsed PDF inspected; page-2 screenshot failed. The entire universal-algebra construction was not re-proved. The apparent c>=1 rationality statement in the parsed preliminary text is not used. -* **Khasraw–McInroy–Shpectorov [KMS]**, arXiv:1809.10132v2, introduction and definition of stable under equivalent generating axes. Parsed text inspected to disambiguate terminology; no perturbation theorem is attributed to it. -* **Sakuma [S]**, arXiv:math/0608709, exact hypotheses, Ising modules, Theorem 4.4 and reference trail. Parsed statement read; page-14 screenshot failed. Its full classification proof is imported. -* **Abe–Lam–Yamada [ALY]**, arXiv:1705.09022v4, Theorem A.1 and the Appendix endpoint. Printed page 10 (PDF index 9) visually inspected successfully. The orbifold and simple-current-extension machinery are imported, not independently reconstructed. -* **Lam–Yamauchi [LY]**, arXiv:math/0609718, Theorem 1.1 and introduction. Parsed exact frame hypothesis and endpoint inspected; not used as an additional premise of our theorem. -* **Jiao–Zheng [JZ]**, arXiv:2201.11359, introduction and main exact-pair result. Parsed text inspected; screenshot request failed. Full generated-subVOA classification proof not re-audited. -* **Loi–Phien [LP]**, arXiv:1305.3352, Lemma 2.11 and Theorem 3.1 including the permitted perturbation. Parsed statements read; screenshot failed. Our elementary localization proof does not depend on this paper. -* **Carpi–Codogni [CC]**, arXiv:2605.26972v1, introduction, Conjecture 1.3, Theorem 1.4 and section 14 in HTML. Used only for current background and reconstruction distinctions, not to import a proved solution of bare moonshine uniqueness. -* **Dong–Lin [DL]**, arXiv:1308.2361, Definitions 2.1–2.2. Printed page 3 visually inspected successfully for positive Hermitian/PCT conventions. -* **Wassermann [W]**, arXiv:1012.6003, pp.1–2 on the positive-energy unitary series, with original FQS attribution. Parsed statement read; screenshot failed. The original FQS 1986 publisher abstract was obtained but not its full proof. -* **Lam–Shimakura [LS]**, arXiv:0810.5395, Theorem 3.1 and the moonshine lattice inclusion. Printed page 6 visually inspected successfully. The literal all-mode vanishing phrase preceding the theorem is not used; orthogonality is interpreted through commuting Virasoro/singular OPE data. +## 5. Source statements and versions -No papers or fonts are bundled. This is a scoped research record rather than an external expert review or exhaustive priority certificate. +* **Tkachev [T]**, arXiv:1801.05724, *On an extremal property of Jordan algebras of Clifford type*: Proposition 2.1 and its variational proof; Proposition 2.7; introduction and relevant references. Published DOI: 10.1080/00927872.2018.1499924. The comparison concerns the variational statements, rather than the full Jordan-algebra classification. +* **Hall–Rehren–Shpectorov [HRS]**, arXiv:1311.0217: introduction, Theorems 1.1–1.2, definitions of axes and normalization. The comparison uses the exact-axis hypotheses and pair-classification statements. The apparent c>=1 rationality statement in the preliminary text is not an input to the criterion. +* **Khasraw–McInroy–Shpectorov [KMS]**, arXiv:1809.10132v2: introduction and definition of stability under equivalent generating axes. +* **Sakuma [S]**, arXiv:math/0608709: exact hypotheses, Ising modules, Theorem 4.4 and reference trail. The pair classification supplies the discrete overlap possibilities. +* **Abe–Lam–Yamada [ALY]**, arXiv:1705.09022v4: Theorem A.1 and the Appendix endpoint, printed page 10. Its orbifold and simple-current-extension machinery supplies the exact ambient classification. +* **Lam–Yamauchi [LY]**, arXiv:math/0609718: Theorem 1.1 and introduction. The exact-frame characterization is a comparison theorem, rather than an additional premise of the correlation criterion. +* **Jiao–Zheng [JZ]**, arXiv:2201.11359: introduction and main exact-pair generation result. The comparison concerns the input and generated-subVOA conclusion. +* **Loi–Phien [LP]**, arXiv:1305.3352: Lemma 2.11 and Theorem 3.1, including the permitted perturbation. This is a quantitative-geometry comparison; the core proof states and proves its own elementary localization lemma. +* **Carpi–Codogni [CC]**, arXiv:2605.26972v1: introduction, Conjecture 1.3, Theorem 1.4 and section 14. These supply background on reconstruction distinctions. +* **Dong–Lin [DL]**, arXiv:1308.2361: Definitions 2.1–2.2, printed page 3, for positive Hermitian/PCT conventions. +* **Wassermann [W]**, arXiv:1012.6003: pp. 1–2 on the positive-energy unitary series, with attribution to the original FQS classification. The representation-theoretic interface uses this account of the series. +* **Lam–Shimakura [LS]**, arXiv:0810.5395: Theorem 3.1 and the moonshine lattice inclusion, printed page 6. The proof uses commuting Virasoro subalgebras and vanishing singular OPE, rather than the literal all-mode vanishing phrase preceding the source theorem. ### Primary source locations diff --git a/docs/ARCHIVE.md b/docs/ARCHIVE.md index 7b190b8..4e23da1 100644 --- a/docs/ARCHIVE.md +++ b/docs/ARCHIVE.md @@ -2,17 +2,8 @@ [Overview](../README.md) · [Current scientific status](RESEARCH_STATUS.md) · [Reproduction](REPRODUCIBILITY.md) -## The active path - -The released-science scope, when a release is tagged, is the -[quantitative correlation criterion](../research/uniform_extraction_core.md) -and [sharpness/calibration](../research/sharpness_and_calibration.md). -Start learning with [Gaberdiel and the physics lessons](learn/README.md), using -Yamauchi only as the secondary algebraic supplement. - -**Only [Current scientific status](RESEARCH_STATUS.md) is authoritative for the -present project.** The older ledgers below describe earlier research directions. -They are preserved as records, not silently reinterpreted as current claims. +This index collects earlier research, corrections, and fixed source records. +The [result map](RESEARCH_STATUS.md) covers the correlation criterion. ## Historical research on main @@ -83,7 +74,3 @@ The import-era `STATUS.md` is protected by the original seed verifier and remain byte-identical, including its dated headings. Use this index and the current scientific-status page rather than interpreting its old “current” label as a statement about the release candidate. - -## Purpose and contact - -This repository serves as a record of the work and a guide for the author’s self-directed learning. For discussion or potential collaboration, please contact Ruge Lin at [gogoko699@gmail.com](mailto:gogoko699@gmail.com). diff --git a/docs/CALIBRATION_PRECISION.md b/docs/CALIBRATION_PRECISION.md index dc0821f..7d7ffe0 100644 --- a/docs/CALIBRATION_PRECISION.md +++ b/docs/CALIBRATION_PRECISION.md @@ -2,18 +2,15 @@ [Overview](../README.md) · [Calibration identities](../research/sharpness_and_calibration.md) · [Reproduction](REPRODUCIBILITY.md) -## What was repaired +## Scale-aware square-root enclosures -The exact seven-scalar identities do not depend on a field's positive overall -scale. The original square-root implementation nevertheless used a fixed -absolute dyadic grid. For very small positive norms, its lower square-root bound -could become zero and cause division by an interval containing zero. - -The current `sqrt_bounds` chooses the grid from the size of the exact rational -radicand. It never replaces exact interval arithmetic with floating point, and -it never changes the theorem's comparison thresholds. The -[implementation erratum](../audits/calibration_scale_erratum.md) gives the concrete -failing input and separates the code correction from the unchanged theorem. +The normalized coefficients computed by the seven-scalar identities are +invariant under positive rescaling of either field. The `sqrt_bounds` +implementation chooses its dyadic grid from the size of the exact rational radicand, keeping the lower square-root enclosure positive +for every positive input within the work limit. All interval operations use exact +rational arithmetic and the theorem’s stated comparison thresholds. +The [implementation erratum](../audits/calibration_scale_erratum.md) records the +fixed-grid failure case and its correction. ## Why the lower bound stays positive @@ -72,6 +69,6 @@ inconclusive even when the underlying fields happen to be ideal. The scale tests cover tiny and large positive scales, independently scaled fields, stress shifts, finite-width intervals, sign/duplicate/cap controls, and the work-limit return. Exact squared inequalities independently check -outward root containment. These tests do not prove the ambient physical premises, -replace source classification proofs, or guarantee that every valid pair passes -a sufficient criterion. +outward root containment. They verify the arithmetic +implementation under the exact input contract; the mathematical criterion is +sufficient. diff --git a/docs/QUANTITATIVE_CORE.md b/docs/QUANTITATIVE_CORE.md index d6cf0f0..bb4df59 100644 --- a/docs/QUANTITATIVE_CORE.md +++ b/docs/QUANTITATIVE_CORE.md @@ -2,8 +2,5 @@ Read the [self-contained core proof](../research/uniform_extraction_core.md), then [sharpness and calibration](../research/sharpness_and_calibration.md). -For context and verification, use [current scientific status](RESEARCH_STATUS.md), +For context and verification, use [results and assumptions](RESEARCH_STATUS.md), the [physics learning path](learn/README.md), and [reproduction](REPRODUCIBILITY.md). - -The [earlier integration-stage page](https://github.com/GoGoKo699/Monster-Correlation-Rigidity/blob/ecd0623e9de41b49754b6ca16dc23752443143af/docs/QUANTITATIVE_CORE.md) -remains available as a historical record. diff --git a/docs/RELEASE.md b/docs/RELEASE.md index 14a185d..369c111 100644 --- a/docs/RELEASE.md +++ b/docs/RELEASE.md @@ -1,29 +1,18 @@ -# Release scope +# Package contents -[Overview](../README.md) · [Current status](RESEARCH_STATUS.md) · [Changelog](../CHANGELOG.md) +| Material | Entry point | +|---|---| +| Correlation criterion and its hypotheses | [Core proof](../research/uniform_extraction_core.md) | +| Optimal exponent and seven-scalar calibration | [Sharpness and calibration](../research/sharpness_and_calibration.md) | +| Five physics lessons and exercises | [Learning path](learn/README.md) | +| Scientific context and primary-source roles | [Context and sources](background_claims.md) | +| Exact certificates and implementation checks | [Reproduction guide](REPRODUCIBILITY.md) | +| Interval arithmetic and precision limit | [Calibration arithmetic](CALIBRATION_PRECISION.md) | +| Source comparisons and proof reviews | [Review index](../audits/README.md) | +| Further research records | [Archive index](ARCHIVE.md) | -This research package contains the quantitative correlation-identification -proof, sharpness and calibration results, the physics-first tutorial, -finite verification code, attributed source comparisons, and preserved history. -These notes do not create or announce a tag, -DOI, publication, or manuscript. +Cite the repository and the commit used, following [CITATION.cff](../CITATION.cff). +Original code and documentation use the [MIT license](../LICENSE); imported +mathematical results retain their source attribution. -The criterion assumes an exact simple unitary rational C2-cofinite holomorphic -VOA of CFT type, central charge 24, no weight-one states, and actual fields -satisfying the stated inequalities. The classification endpoint is the prior -Abe–Lam–Yamada theorem. The field-distance exponent is sharp; the numerical -tolerances are sufficient, not claimed optimal. No practical field-finding -algorithm, sample complexity, or verification of ambient axioms from measurements -is supplied. - -Consult the [changelog](../CHANGELOG.md) for changes and -[reproduction](REPRODUCIBILITY.md) for exact certificates, historical replay, -and their limits. Finite checks do not verify imported classifications or -constitute independent human review. The [archive index](ARCHIVE.md) identifies -legacy rendering limitations and archived branches outside the selected scope. - -Original code and documentation retain the [MIT license](../LICENSE). - -## Purpose and contact - -This repository serves as a record of the work and a guide for the author’s self-directed learning. For discussion or potential collaboration, please contact Ruge Lin at [gogoko699@gmail.com](mailto:gogoko699@gmail.com). +[Overview and contact](../README.md) diff --git a/docs/REPRODUCIBILITY.md b/docs/REPRODUCIBILITY.md index d5db5b0..53282db 100644 --- a/docs/REPRODUCIBILITY.md +++ b/docs/REPRODUCIBILITY.md @@ -1,8 +1,8 @@ -# Reproduce the current research package +# Reproduce the results -[Overview](../README.md) · [Current status](RESEARCH_STATUS.md) · [Archive index](ARCHIVE.md) +[Overview](../README.md) · [Results and assumptions](RESEARCH_STATUS.md) · [Archive index](ARCHIVE.md) -## The current command +## Exact certificates From the repository root, run: @@ -19,7 +19,7 @@ outputs or a mismatching current exact fingerprint fail the command. The recorded environment is **Python 3.13.5**. A virtual environment is recommended but no third-party package is needed for this default command. -## The complete inventory and the historical comparisons +## Full suite and replay For the original NumPy-based small examples as well: @@ -73,12 +73,6 @@ commits, not assertions that every formatted document or repaired implementation has the same bytes today. The [release manifest](../results/release_preparation.json) records intentional source changes and all preserved files. -The square-root repair refines rational enclosures in the calibration report; -its current output is deliberately recorded separately from the older 74-check -output. The original logical checks remain. The extraction certificate retains -its original fingerprint. [The erratum](../audits/calibration_scale_erratum.md) -explains the change and its regression family. - ## Mathematical rendering The default command checks fenced/inline math extraction, delimiters, local @@ -91,13 +85,12 @@ npm install --prefix ../monster-renderer --ignore-scripts --no-audit --no-fund m NODE_PATH=../monster-renderer/node_modules node checks/render_math.cjs ../monster-math.json ``` -This is syntax checking, not a promise about every GitHub browser, screen size, -or historical page. The [archive index](ARCHIVE.md) identifies legacy rendering -boundaries. No MathJax package, generated website, paper, or font is bundled. +These commands validate mathematical syntax. Rendering of historical pages is +described in the [archive index](ARCHIVE.md). ## Evidence boundary These programs check arithmetic, finite examples, implementation behavior, -source integrity, and documentation. They do not prove the imported VOA -classifications, simulate the full Monster tensor, establish practical -measurement complexity, or constitute independent human review. +source integrity, and documentation. Analytic proofs and the imported VOA +classification theorems are justified in the research notes and their primary +references. diff --git a/docs/RESEARCH_STATUS.md b/docs/RESEARCH_STATUS.md index ce52a81..1f031ec 100644 --- a/docs/RESEARCH_STATUS.md +++ b/docs/RESEARCH_STATUS.md @@ -1,33 +1,41 @@ -# Current scientific status +# Results and assumptions -The selected quantitative result has a complete written proof, sharpness and calibration boundaries, primary-source comparisons, and a final falsification-oriented review with no blocking error found at its documented scope. See [the final review](../audits/final_quantitative_review.md). This status replaces the pre-integration coordination notes, not the historical mathematical record. +The repository develops a quantitative criterion identifying the moonshine VOA +from near-extremal weight-two correlation coefficients. -## Purpose and contact +## Result map -This repository serves as a record of the work and a guide for the author’s self-directed learning. For discussion or potential collaboration, please contact Ruge Lin at [gogoko699@gmail.com](mailto:gogoko699@gmail.com). +| Result | Statement | Proof | +|---|---|---| +| Correlation criterion | Two sufficiently near-extremal self-couplings and a controlled overlap force an orthogonal Ising pair and identify the ambient VOA as moonshine. | [Core, Q0–Q4](../research/uniform_extraction_core.md) | +| Sharp exponent | The square-root rate from coupling deficit to field distance is optimal, already in the moonshine VOA. | [Sharpness, section 3](../research/sharpness_and_calibration.md) | +| Calibration | Seven certified scalar intervals remove stress contamination and normalize two real weight-two fields before applying the criterion. | [Calibration, section 2](../research/sharpness_and_calibration.md) | -No manuscript, submission, DOI, or tagged GitHub release has been created. The repository now includes release-preparation notes and a changelog. Scientific evidence for eventual framing is in [background_claims.md](background_claims.md). +The classification endpoint is Abe–Lam–Yamada's Theorem A.1. The quantitative +step extracts exact Ising directions and uses Sakuma's discrete overlap gap. +The [source comparison](../audits/quantitative_contribution_verdict.md) identifies +the roles of prior variational methods and classification results. -## The bounded contribution +## Input requirements -Within an exact simple unitary rational C2-cofinite holomorphic VOA of CFT type with c=24 and V1=0, sufficiently near-extremal coefficients of two actual real weight-two primaries force exact orthogonal Ising subalgebras and hence the underlying moonshine VOA by the prior Abe–Lam–Yamada theorem. The square-root field-distance exponent is optimal. Seven certified scalar intervals suffice to remove known stress contamination and normalization from actual real weight-two inputs. +The ambient object is an exact simple unitary, rational, C2-cofinite, +holomorphic VOA of CFT type, with central charge 24 and no weight-one states. +The inputs are actual real weight-two fields. The core uses normalized +primaries; calibration also accepts stress-contaminated and unnormalized +fields when the stress tensor is known and projected norms are certified +positive. -The [core](../research/uniform_extraction_core.md), [precision results](../research/sharpness_and_calibration.md), [prior comparison](../audits/quantitative_contribution_verdict.md), and [final review](../audits/final_quantitative_review.md) are the active scientific path. The subsequent [implementation erratum](../audits/calibration_scale_erratum.md) repairs small-scale calibration and documents its precision limit without changing the analytic theorem. +Identification is conditional on fields satisfying the coefficient bounds. +The numerical tolerances are sufficient bounds; an inconclusive certificate +leaves the isomorphism type undecided. The sharpness result concerns the +field-distance exponent. -No additional essential lemma has been identified as missing for this bounded claim. The directed priority assessment is a revisable scholarly judgment, not an exhaustive firstness assertion or a guarantee of importance. The review was conducted by the research assistant, not an independent human referee or proof assistant. +## Verification and learning -## Not claimed or silently postponed +The [reproduction guide](REPRODUCIBILITY.md) describes exact finite certificates +and implementation checks. The [calibration input contract](CALIBRATION_PRECISION.md) +specifies interval inputs and the precision limit. The +[proof and source review](../audits/final_quantitative_review.md) records the +assistant's reconstruction and its source depth. -The theorem does not prove that every member of the bare ambient class is moonshine. It does not find the required fields, verify the exact ambient axioms from measurements, control approximate VOA axioms or uncertain conformal grades, or reconstruct an implemented physical system. These stronger questions are outside the stated claim, not hidden gaps assigned to manuscript drafting. - -The extended-six-sevenths implication, generic readout results, and other archived proposals are separate research records and are not premises of this core. In particular the rejected normalization-dependent condition has not been integrated. This review does not certify every historical research branch. - -## Evidence access - -The [reproduction guide](REPRODUCIBILITY.md) provides current commands, -fingerprints, and separate strict-versus-bounded historical replay outcomes. -Original reports and tolerances are preserved. The [archive index](ARCHIVE.md) -covers older ledgers and archived research; [release scope](RELEASE.md) defines -the research package. - -Future work on the bounded result should respond to a concrete proof objection, source overlap, or documentation defect. Enlarging the theorem or beginning manuscript drafting requires a separate scope decision; an unresolved stronger conjecture is not by itself a reason to keep extending this paper's research indefinitely. +For a guided introduction, use the [physics learning path](learn/README.md). diff --git a/docs/background_claims.md b/docs/background_claims.md index 6421c14..d8389bd 100644 --- a/docs/background_claims.md +++ b/docs/background_claims.md @@ -1,86 +1,96 @@ -# Background and interpretation evidence for the eventual paper +# Scientific context and sources -26 September 2026. This is a research ledger, NOT drafted abstract, introduction, or conclusion text. Each proposed scientific claim has an evidence slot and an explicit boundary. The study concerns exact VOAs and normalized chiral coefficient data. +[Overview](../README.md) · [Core proof](../research/uniform_extraction_core.md) · [Contribution comparison](../audits/quantitative_contribution_verdict.md) -## 1. Abstract-level claim slots +The correlation criterion identifies an underlying VOA from normalized chiral +coefficient data within an exact class. The tables connect its claims and +interpretation to the proofs and primary sources. -| ID | Claim permitted by the present proof | Evidence | Boundary that must accompany it | -|---|---|---|---| -| A01 | In the fixed unitary rational holomorphic current-free c24 class, explicit inequalities on two real normalized primary self-couplings and one overlap imply moonshine VOA isomorphism. | `research/uniform_extraction_core.md`, Q0–Q4. | Exact ambient axioms, primarity, reality, and normalization are premises. This does not prove that the bare class is a singleton. | -| A02 | The error thresholds are uniform over unknown admissible candidates and do not start from a supplied nearby Ising vector. | Q1–Q3; same gap, radius, and quadratic-growth constants in every candidate. | No compactness of the moduli space of VOAs, construction of an isomorphism, or efficient field search is asserted. | -| A03 | The exact orthogonal-Ising-pair classification is an imported final step. | Abe–Lam–Yamada, Theorem A.1 [ALY]. | The exact classification must be attributed; it is not the new theorem. | -| A04 | The rounding proof combines a discrete critical-value gap, a local quadratic estimate, global compactness, and a discrete overlap gap. | Q1–Q4; [W,S]. | Quadratic growth and compactness are standard tools; the fractions alone do not establish novelty. | - -Do not use unqualified wording such as “three measurements identify a physical theory,” “robust under arbitrary CFT errors,” “self-testing the Monster,” “first characterization,” or “proves moonshine uniqueness.” Those assertions exceed the present evidence. A failed sufficient test does not exclude moonshine. +## 1. Quantitative identification -## 2. Introduction-level background slots - -| ID | Background fact or motivation | Primary source / derivation | Permitted use | +| ID | Result | Evidence | Assumptions and interpretation | |---|---|---|---| -| B01 | The normalized genus-one character contains graded dimensions; reconstructing the state-field product is a distinct question. | Carpi–Codogni 2026, introduction and Conjecture 1.3 [CC]. | Motivate interaction-sensitive identification. Do not claim equality of characters determines a VOA. | -| B02 | The known moonshine VOA has c24, V1=0, and Monster automorphisms. The bare uniqueness statement remains formulated as a conjecture in the inspected 2026 source. | [CC], introduction and section 14; construction attributed there to Frenkel–Lepowsky–Meurman. | Locate the conditional theorem relative to the broader problem. The project does not claim that broader problem is solved or use its status as a reason not to attempt research. | -| B03 | Exact Ising data give strong structural restrictions. | Sakuma's positive-real hypotheses and Theorem 4.4 [S]; ALY Theorem A.1 [ALY]. | State the exact prior route before introducing finite tolerances. Neither theorem begins with arbitrary nearly extremal fields. | -| B04 | A positive unitary form and real involution supply mode adjoints and a real sphere on which the cubic is bounded. | Dong–Lin, Definitions 2.1–2.2 [DL]. | Define the physical inner-product convention. Distinguish the author's first-linear Hermitian convention from alternative notation; the present proof stays on the real subspace. | -| B05 | Normalized two- and three-point coefficients are genuinely interaction-sensitive inputs. | Invariant metric and mode/state-field definitions [M, section 1]; Q0 gives the actual coefficient convention. | Explain the observables mathematically. Do not infer an apparatus, noise model, or number of statistical samples. | -| B06 | Quantitative Morse/near-critical-point methods predate this project. | Loi–Phien, Lemma 2.11 and Theorem 3.1 [LP]. | Credit the general geometry. Their main theorem perturbs a smooth function to obtain Morse properties; that is not a physically allowed modification of an exact VOA's product. | -| B07 | Other exact two-Ising results classify the subVOA generated by a specified exact pair. | Jiao–Zheng [JZ], introduction and main result. | Compare the actual hypotheses and endpoint, not just the word “two.” Local subVOA identification is different from the ALY ambient conclusion. | - -The current paper's theorem may take c24 and V1=0 as explicit assumptions. Re-proving the broader minimum-central-charge characterization is unnecessary for that bounded theorem. If a future framing promotes that minimization to a physical-selection principle, its source and assumption audit becomes part of the required core, not an unstated motivation. +| A01 | In the fixed unitary rational holomorphic current-free c24 class, explicit inequalities on two real normalized primary self-couplings and one overlap imply moonshine VOA isomorphism. | `research/uniform_extraction_core.md`, Q0–Q4. | The full exact ambient class is specified in Q0. Primarity, reality, and normalization are premises, and actual fields satisfying the inequalities are supplied. | +| A02 | The error thresholds are uniform over admissible candidates and require no preidentified nearby Ising vector. | Q1–Q3; the same gap, radius, and quadratic-growth constants apply in every candidate. | Compactness is applied separately within each finite-dimensional primary sphere. | +| A03 | An exact orthogonal Ising pair identifies the ambient VOA in the stated class. | Abe–Lam–Yamada, Theorem A.1 [ALY]. | This exact classification is the imported endpoint of the quantitative criterion. | +| A04 | Rounding combines a discrete critical-value gap, a local quadratic estimate, global compactness, and a discrete overlap gap. | Q1–Q4; [W,S]. | Quadratic growth and compactness are standard tools; the project composes them with the attributed classification inputs. | -A common source of overclaim is the word “finite”: a finite list of coefficient inequalities is not the same as a finite experimentally validated theory description. The class assumptions and exact field identification carry substantial information. +These are sufficient inequalities on coefficients of supplied fields. Failure +of the test is inconclusive: broad input intervals or unsuitable fields can fail +even in the moonshine VOA. The exact class and field assumptions are part of the +criterion, rather than conclusions of the coefficient test. -## 3. Conclusion-level implications and exclusions +## 2. Interaction data and prior structure -| ID | Justified implication | Not justified | -|---|---|---| -| C01 | Near-boundary coefficient data can force exact internal subalgebras and, through an existing theorem, the underlying VOA isomorphism type. | Small changes in arbitrary VOA axioms or all OPE coefficients yield a nearby conformal net. | -| C02 | The proof does not require a chosen Monster matrix representation or its multiplication table as input. | The background class itself is established by those three coefficients, or the theorem is device independent. | -| C03 | The result supplies a sufficient correlation criterion with an attained region in the known example. | A hypothetical non-moonshine candidate exists; finite separation proves that such a competitor has been constructed. | -| C04 | The geometric extraction method and its discrete classification inputs have distinct roles. | A new general Morse theorem, an independently proved FQS/Sakuma/ALY classification, or optimal constants. | -| C06 | Automatic existence of a pair and robustness to approximate axioms are legitimate future questions. | Either is a missing lemma required to prove the stated conditional theorem. They become required only if the advertised claim is enlarged. | - -The research-completion boundary is not “every stronger theorem is proved.” It is that every scientific assertion needed by the CHOSEN contribution and its framing has proof or accurately scoped primary evidence. No essential reasoning is to be left for the manuscript-writing stage. +| ID | Background fact | Primary source / derivation | Role in the argument | +|---|---|---|---| +| B01 | The normalized genus-one character contains graded dimensions; reconstructing the state-field product is a distinct question. | Carpi–Codogni, introduction and Conjecture 1.3 [CC]. | Motivates identification through interaction data. | +| B02 | The moonshine VOA has c24, vanishing weight-one space, and Monster automorphisms. | [CC], introduction and section 14; construction attributed there to Frenkel–Lepowsky–Meurman. | Supplies the known example. The criterion adds coefficient hypotheses to this ambient class. | +| B03 | Exact Ising data impose structural restrictions. | Sakuma's positive-real hypotheses and Theorem 4.4 [S]; ALY Theorem A.1 [ALY]. | The quantitative bounds recover the exact hypotheses required by these prior results. | +| B04 | A positive unitary form and real involution supply mode adjoints and a real sphere on which the cubic is bounded. | Dong–Lin, Definitions 2.1–2.2 [DL]. | Defines the inner-product convention. Dong–Lin use a first-linear Hermitian form; the quantitative geometry is on its real subspace. | +| B05 | Normalized two- and three-point coefficients encode interaction data. | Invariant metric and mode/state-field definitions [M, section 1]; Q0 gives the coefficient convention. | Specifies the mathematical inputs to the criterion. | +| B06 | Quantitative Morse and near-critical-point methods predate this project. | Loi–Phien, Lemma 2.11 and Theorem 3.1 [LP]. | Their theorem perturbs a smooth function to obtain Morse properties. Q1 instead proves the needed localization directly for the fixed VOA cubic. | +| B07 | Exact two-Ising results can classify the subVOA generated by a specified pair. | Jiao–Zheng [JZ], introduction and main result. | Distinguishes the generated-subalgebra endpoint from the ambient-VOA identification in ALY. | -## Archived separate work, not evidence for the selected release +The central charge and vanishing weight-one space are explicit assumptions of +the criterion. A finite list of coefficient inequalities carries its force +together with these exact structural assumptions and identified fields. -The following entries are deliberately outside the active tables. They are not -premises of the correlation criterion and have not been merged or certified as -part of this release-preparation pass. IDs are retained to make older references -interpretable; their presence is not an endorsement of the archived claims. +## 3. Interpretation -| Earlier ID | Pinned record | Role and boundary | +| ID | Consequence | Precise meaning | |---|---|---| -| A05 / C05 | [Extended-six-sevenths proposal, PR27](https://github.com/GoGoKo699/Monster-Correlation-Rigidity/blob/576fd31b53862d0b7667a723330ae27c859cc774/research/extended_six_sevenths_forces_ising.md) | Separate proposed existence implication with additional module/trace inputs; not released evidence or a premise of the selected theorem. | -| B08 | [Readout-scope audit, PR22](https://github.com/GoGoKo699/Monster-Correlation-Rigidity/blob/d2b85266d4273ae7c6ce32d87e0b6060a881b87e/audits/readout_scope_audit.md) | Separate general-readout comparison; not part of the selected release proof. | - -The [archive index](ARCHIVE.md) distinguishes historical provenance, archived -branches, and the authoritative current path. Do not merge unrelated results -merely to resolve a file reference. +| C01 | Near-extremal coefficient data can force exact internal subalgebras and the underlying VOA isomorphism type. | The estimates recover an orthogonal Ising pair; the prior ALY theorem supplies the ambient conclusion. | +| C02 | The criterion can be applied without a chosen Monster matrix representation or multiplication table. | Its inputs are the exact ambient class, specified fields, and their coefficient bounds. | +| C03 | The sufficient criterion has an attained region in the known example. | Moonshine supplies an exact orthogonal Ising pair satisfying the bounds. | +| C04 | Geometric extraction and classification have distinct roles. | The quantitative estimates use the imported FQS and Sakuma structure and lead to the ALY classification endpoint. The field-distance exponent is sharp, while the numerical tolerances are sufficient bounds. | -## 4. Source reading in this continuation +## 4. Sources and theorem interfaces -[ALY] T. Abe, C. H. Lam, H. Yamada, arXiv:1705.09022v4, Appendix A, Theorem A.1 and A.6–A.8. The exact theorem and its role were rechecked; PDF index9 (printed10) was visually inspected. Orbifold and extension-uniqueness proofs are imported, not independently reconstructed. +[ALY] T. Abe, C. H. Lam, H. Yamada, arXiv:1705.09022v4, +Appendix A, Theorem A.1 and A.6–A.8. The exact orthogonal-pair theorem supplies +the ambient identification; its orbifold and extension-uniqueness arguments +are imported. https://arxiv.org/abs/1705.09022 -[S] S. Sakuma, arXiv:math/0608709v1, general real-positive hypotheses, Ising module decomposition, Theorems4.3–4.4. Parsed theorem text was read. Screenshot of PDF index13 failed; the formula set comes from the theorem text, not a claimed successful table image. +[S] S. Sakuma, arXiv:math/0608709v1, general real-positive hypotheses, +Ising module decomposition, Theorems 4.3–4.4. These supply the exact spectral +and discrete-overlap inputs. https://arxiv.org/abs/math/0608709 -[DL] C. Dong, X. Lin, arXiv:1308.2361v1, Definitions2.1–2.2 and the normalization convention. Parsed text inspected; no new full-paper proof audit is claimed. +[DL] C. Dong, X. Lin, arXiv:1308.2361v1, Definitions 2.1–2.2 +and the normalization convention. These specify unitarity and the mode adjoints. https://arxiv.org/abs/1308.2361 -[W] A. Wassermann, arXiv:1012.6003v1, introduction pp.1–2. The exact positive-energy unitary series is explicitly attributed to Friedan–Qiu–Shenker. Parsed statement read; page2 screenshot failed. The original FQS proof remains an imported interface. +[W] A. Wassermann, arXiv:1012.6003v1, introduction pp. 1–2. +The positive-energy unitary Virasoro series is explicitly attributed there +to Friedan–Qiu–Shenker and is used as an imported classification theorem. https://arxiv.org/abs/1012.6003 -[M] A. Matsuo, arXiv:math/0007169v1, mode conventions and Ising spectral interface. Parsed passages rechecked; neither mixed fifth-order coefficient nor the large-Aut trace hypothesis is used to prove Q1–Q4. +[M] A. Matsuo, arXiv:math/0007169v1, section 1 and the Ising spectral +interface. These provide mode conventions and the weight-two algebraic language. +The Q1–Q4 argument uses the stated identities independently of the mixed +fifth-order coefficient and large-automorphism trace hypotheses. https://arxiv.org/abs/math/0007169 -[LP] T. L. Loi, P. Phien, *The Quantitative Morse Theorem*, arXiv:1305.3352v1, Lemma2.11 and Theorem3.1. The hypotheses, perturbed output f=f0+h, and explicit conclusions were read in parsed text. Screenshot of PDF index4 failed. The proof is not a premise of Q1, which is supplied directly. +[LP] T. L. Loi, P. Phien, *The Quantitative Morse Theorem*, +arXiv:1305.3352v1, Lemma 2.11 and Theorem 3.1. The perturbed output f=f0+h +provides the comparison with established quantitative geometry. Q1 has a direct +proof and does not depend on this theorem. https://arxiv.org/abs/1305.3352 -[JZ] X. Jiao, W. Zheng, *Vertex operator algebras generated by two Ising vectors*, arXiv:2201.11359v1. Abstract, introduction, exact-pair hypotheses and main identification inspected in parsed text. The whole 6A classification proof was not independently audited and is not a dependency. +[JZ] X. Jiao, W. Zheng, *Vertex operator algebras generated by two Ising vectors*, +arXiv:2201.11359v1. The introduction, exact-pair hypotheses, and main +identification supply the generated-subVOA comparison. https://arxiv.org/abs/2201.11359 -[CC] S. Carpi, G. Codogni, *Vertex operator algebras, partition functions and Teichmüller modular forms*, arXiv:2605.26972v1. Introduction, Conjecture1.3, Theorem1.4 and section14 framing inspected in HTML. Used only for background and the distinction between partition data and reconstruction. No numerical character coefficient is copied from its introductory HTML, which contains an apparent extra digit in that example. Its classification theorems are not premises of Q1–Q4. +[CC] S. Carpi, G. Codogni, *Vertex operator algebras, partition functions and +Teichmüller modular forms*, arXiv:2605.26972v1, introduction, Conjecture 1.3, +Theorem 1.4, and section 14. This is background for the distinction between +partition data and reconstruction; its classification results are separate +from the proof of Q1–Q4. https://arxiv.org/abs/2605.26972 -Read-depth reporting is evidence discipline, not a claim that finite excerpts audit all foundational mathematics. No papers are bundled. Bibliographic details and theorem attribution remain separate from any private submission planning. +The [contribution comparison](../audits/quantitative_contribution_verdict.md) +and [proof review](../audits/final_quantitative_review.md) record the scope of +the source checks and the comparison with prior work. diff --git a/docs/learn/01_correlations.md b/docs/learn/01_correlations.md index 629bd84..7922503 100644 --- a/docs/learn/01_correlations.md +++ b/docs/learn/01_correlations.md @@ -8,7 +8,7 @@ Read Gaberdiel Sections 2.1, 3.1, 3.4, and 3.5 for the state, amplitude, OPE, an ## A state and its field are two descriptions of the same input -Write a chiral state as $x$ and its field as $\phi_x(z)$. The state–field correspondence makes the field depend linearly on the state. A linear combination of states therefore specifies a linear combination of fields. We are not choosing an arbitrary classical function of position. +Write a chiral state as $x$ and its field as $\phi_x(z)$. The state–field correspondence makes the field depend linearly on the state. A linear combination of states therefore specifies a linear combination of fields. The chiral conformal weight is the eigenvalue of $L_0$. In this project, the supplied fields have **exact weight two**: @@ -16,7 +16,7 @@ The chiral conformal weight is the eigenvalue of $L_0$. In this project, the sup L_0x=2x. ``` -“Low energy” refers here to a low conformal grade. It is not a numerical energy in joules, an experimental bandwidth, or a claim that a laboratory can isolate that grade. +“Low energy” refers here to a low conformal grade. A primary state also obeys $L_nx=0$ for every positive integer $n$. This is stronger than merely having weight two. The ambient stress tensor has weight two but is not primary at nonzero central charge. @@ -46,7 +46,7 @@ For a unit vector $x$, define its self-three-point coefficient by f(x)=C(x,x,x). ``` -The normalized theorem takes $f(x)$, $f(y)$, and $\langle x,y\rangle$ as input. “Three coefficients” does not mean three individual measurement shots; the theorem does not specify a measurement protocol or sample complexity. +The normalized theorem takes $f(x)$, $f(y)$, and $\langle x,y\rangle$ as input. These inputs are certified coefficient values. ## Why normalization cannot be skipped @@ -60,13 +60,13 @@ For a nonzero real primary $w$, the scale-corrected quantity is It is invariant under positive rescaling. Under a negative rescaling, its sign changes. Flipping only $x$ also changes the sign of $\langle x,y\rangle$, so the two signs cannot be chosen independently just to make each inequality look favorable. -Throughout the proof, “real” means fixed by the theory's specified unitary conjugation, often called its PCT involution. On this subspace the metric is positive definite and the cubic is real. Real does not mean merely writing coordinates that look real in an arbitrary complex basis. No choice of a complex phase is silently absorbed into the hypotheses. +Throughout the proof, “real” means fixed by the theory's specified unitary conjugation, often called its PCT involution. On this subspace the metric is positive definite and the cubic is real. Real does not mean merely writing coordinates that look real in an arbitrary complex basis. ## The physical question Suppose an exact candidate theory and two appropriate fields are supplied. Can unusually large normalized self-couplings, together with their mutual overlap, force that theory to have a particular algebraic identity? -This is a conditional identification question, not a procedure for discovering the fields. It also does not reconstruct a full nonchiral theory or an apparatus from correlator samples. The [assumptions page](assumptions_and_sources.md) separates what is assumed from what is concluded. +The [assumptions page](assumptions_and_sources.md) states the exact class, supplied-field requirements, and conditional identification conclusion. ## Check your understanding diff --git a/docs/learn/03_ising.md b/docs/learn/03_ising.md index 225fc10..9bf0062 100644 --- a/docs/learn/03_ising.md +++ b/docs/learn/03_ising.md @@ -8,7 +8,7 @@ Gaberdiel Sections 3.7.3 and 4.4 introduce the relevant Virasoro and Ising backg ## An Ising vector is an internal stress tensor -Do not picture a spin variable on a lattice. Here an **Ising vector** $e$ is a weight-two state whose field generates an internal unitary Virasoro theory with central charge $1/2$. It is that subtheory's stress tensor. It is not the Ising spin primary of weight $1/16$. +Here an **Ising vector** $e$ is a weight-two state whose field generates an internal unitary Virasoro theory with central charge $1/2$. It is that subtheory's stress tensor. It is not the Ising spin primary of weight $1/16$. In the product convention of Lesson 2, @@ -59,7 +59,7 @@ The core constructs $r$ for every stationary $\lambda$ and proves that this is a \lambda'(r)=-\frac{1}{2[r(24-r)/48]^{3/2}}<0. ``` -Thus smaller allowed internal charge means larger stationary self-coupling. This is an algebraic relation, not an RG flow or a dynamical relaxation law. +Thus smaller allowed internal charge means larger stationary self-coupling. diff --git a/docs/learn/04_rounding.md b/docs/learn/04_rounding.md index 0fa8d75..42a652f 100644 --- a/docs/learn/04_rounding.md +++ b/docs/learn/04_rounding.md @@ -4,7 +4,7 @@ **Question:** how can inequalities with finite errors imply an exact algebraic conclusion? -This lesson follows [core Q1–Q4](../../research/uniform_extraction_core.md). No additional chapter of Gaberdiel is needed. Yamauchi Section 4, Theorem 4.6, is the secondary guide to the discrete pair structure; the proof's primary citation is Sakuma's Theorem 4.4. +This lesson follows [core Q1–Q4](../../research/uniform_extraction_core.md). Yamauchi Section 4, Theorem 4.6, is the secondary guide to the discrete pair structure; the proof's primary citation is Sakuma's Theorem 4.4. ## First control the field direction @@ -37,7 +37,7 @@ f(x)\ge M-\epsilon,\quad 0\le\epsilon<\frac1{50} for some exact maximizing direction $a$. The core also supplies the separation and finiteness details used in this compactness argument. -The same constants apply in every admissible candidate. We are not assuming the collection of all VOAs is compact, running gradient ascent, or providing an algorithm that finds $a$. +The same constants apply in every admissible candidate. Compactness is used within each candidate’s primary sphere to establish the existence of $a$. ## Then control the pair @@ -90,7 +90,7 @@ The inequality is strict because the boundary corresponds to the first nonzero a Abe–Lam–Yamada's Theorem A.1 identifies the **ambient VOA** as moonshine from an orthogonal Ising pair in its stated class. It does not merely identify the subalgebra generated by the pair. The full exact ambient assumptions are given on the [assumptions page](assumptions_and_sources.md). -The project supplies a sufficient quantitative route into that theorem. It does not prove bare uniqueness of the ambient class, construct the isomorphism, or establish the axioms from measurements. +The coefficient inequalities supply a sufficient quantitative route into that theorem. ## Check your understanding diff --git a/docs/learn/05_worked_certificate.md b/docs/learn/05_worked_certificate.md index 363a68e..7d810b0 100644 --- a/docs/learn/05_worked_certificate.md +++ b/docs/learn/05_worked_certificate.md @@ -4,7 +4,7 @@ **Question:** can we apply the sufficient criterion without confusing its conclusion with its assumptions? -Everything below is arithmetic or explanation of [core Q4–Q5](../../research/uniform_extraction_core.md) and [sharpness and calibration](../../research/sharpness_and_calibration.md). It is not a simulated experiment. +This worked example applies [core Q4–Q5](../../research/uniform_extraction_core.md) and [sharpness and calibration](../../research/sharpness_and_calibration.md). ## An example using the repository's stated thresholds @@ -35,7 +35,7 @@ The corresponding exact Ising-stress overlap therefore has magnitude at most <\frac{48}{12288}=\frac1{256}. ``` -The gap forces zero overlap. The prior classification theorem now identifies the ambient VOA as moonshine. The spare margin is $1/12288$ in the Ising-stress overlap; it is not an optimal tolerance or an experimental resolution requirement. +The gap forces zero overlap. The prior classification theorem now identifies the ambient VOA as moonshine. The spare margin is $1/12288$ in the Ising-stress overlap for this sufficient certificate. ## A failed test is not a different theory @@ -76,13 +76,13 @@ f(x_i)=\frac{q_i-\tau_i n_i/2+\tau_i^3/36}{N_i^{3/2}}, Since $N=4$, division by $N^{3/2}=8$ returns $F$. The apparently large raw cubic contained known stress contributions, not a stronger primary signal. -With intervals rather than exact scalars, every operation must enclose all permitted exact values. In particular, require a strictly positive lower bound for each projected norm and use conservative upper bounds for the error budget. The existing calibration checker performs outward interval arithmetic. This does not certify uncertain conformal grade, non-real inputs, unknown stress tensor, or empirical coverage of measurement errors. +With intervals rather than exact scalars, every operation must enclose all permitted exact values. In particular, require a strictly positive lower bound for each projected norm and use conservative upper bounds for the error budget. The existing calibration checker performs outward interval arithmetic. The exact grade, real structure, known stress tensor, and certified input intervals remain assumptions. ## Why the square root is natural—and sharp here A small displacement along a unit-sphere curve through a smooth nondegenerate maximum changes the value quadratically but changes the field direction linearly. Thus a loss of order $t^2$ naturally controls distance of order $|t|$, or the square root of the loss. -The project does not rely only on this picture: its sharpness note constructs such a curve inside the actual moonshine VOA and shows that the nearest maximizing direction remains the selected one. Hence no larger uniform exponent can replace $1/2$ near that example. This does not prove the numerical constants or the whole identification region are optimal. +The project does not rely only on this picture: its sharpness note constructs such a curve inside the actual moonshine VOA and shows that the nearest maximizing direction remains the selected one. Hence no larger uniform exponent can replace $1/2$ near that example. The numerical tolerances remain sufficient bounds. ## Check your understanding @@ -109,4 +109,4 @@ To run the current certificates and documentation checks, use the repository roo python verify_current.py ``` -The [reproduction guide](../REPRODUCIBILITY.md) distinguishes current fingerprints from historical reports. These are finite arithmetic and implementation checks, not proofs of the imported VOA classifications. No full Monster tensor is simulated. +The [reproduction guide](../REPRODUCIBILITY.md) describes the finite arithmetic and implementation checks, their fingerprints, and the separate historical replay. diff --git a/docs/learn/README.md b/docs/learn/README.md index 9fe1996..71c3213 100644 --- a/docs/learn/README.md +++ b/docs/learn/README.md @@ -1,6 +1,6 @@ # A physicist's route to Monster correlation rigidity -**Start with correlation functions, not the Monster group.** The question is whether a small amount of interaction data can identify an exact chiral theory within a specified class. The result is conditional: the class is assumed, and suitable fields must actually be supplied. Their existence is not inferred from the spectrum alone. +**Start with correlation functions.** The question is whether a small amount of interaction data can identify an exact chiral theory within a specified class. The result is conditional: the class is assumed, and suitable fields must actually be supplied. Their existence is not inferred from the spectrum alone. This path assumes quantum-mechanical states and inner products, elementary linear algebra, differentiation, and some familiarity with complex coordinates. It does not assume prior VOA, finite-group, or moonshine expertise. Complex mode notation is introduced when needed; the quantitative geometry takes place in a real finite-dimensional inner-product space. @@ -8,7 +8,7 @@ This path assumes quantum-mechanical states and inner products, elementary linea **Primary anchor:** Matthias R. Gaberdiel, [*An Introduction to Conformal Field Theory*, arXiv:hep-th/9910156v2](https://arxiv.org/html/hep-th/9910156v2). Read it in small selections alongside the lessons below, rather than finishing the whole review first. -**Secondary anchor:** Hiroshi Yamauchi, [*3-transposition groups arising in VOA theory*, arXiv:2201.06887v1](https://arxiv.org/html/2201.06887v1), selected parts of Section 4. This is a guided supplement for the special weight-two and Ising structure, not a second prerequisite course. The local lessons explain the facts needed to follow the argument. Proof-level source checking is a separate route. +**Secondary anchor:** Hiroshi Yamauchi, [*3-transposition groups arising in VOA theory*, arXiv:2201.06887v1](https://arxiv.org/html/2201.06887v1), selected parts of Section 4. This guided supplement covers the special weight-two and Ising structure used in the local lessons; it is not a second prerequisite course. | Local lesson | Primary reading in Gaberdiel | Question to answer before moving on | |---|---|---| @@ -18,9 +18,9 @@ This path assumes quantum-mechanical states and inner products, elementary linea | [4. From nearly extremal to exact](04_rounding.md) | No new chapter required | How do continuous error bounds force a discrete exact structure? | | [5. Work through the certificate](05_worked_certificate.md) | Use the earlier sections as needed | Can I propagate the three error budgets and explain a failed test? | -For Lesson 3, Yamauchi Section 4, equation (4.2), Lemma 4.3, and equations (4.8)–(4.9) provide the algebraic supplement. For Lesson 4, consult Theorem 4.6 and its overlap table. Group presentations, conjugacy-class calculations, and the later 3-transposition constructions are not prerequisites for this result. +For Lesson 3, Yamauchi Section 4, equation (4.2), Lemma 4.3, and equations (4.8)–(4.9) provide the algebraic supplement. For Lesson 4, consult Theorem 4.6 and its overlap table. -Gaberdiel Sections 3.2–3.3 support the underlying OPE construction and can be read on a second pass. Section 3.9 supplies orbifold and moonshine context, not a necessary calculation in our quantitative argument. Appendix A discusses rationality terminology. A full course on modular forms, Zhu's algebra, or fusion categories is not required before starting these lessons. +Gaberdiel Sections 3.2–3.3 support the underlying OPE construction and can be read on a second pass. Section 3.9 supplies orbifold and moonshine context, not a necessary calculation in our quantitative argument. Appendix A discusses rationality terminology. ## The result before the notation @@ -32,14 +32,8 @@ The new quantitative step and the old classification have different jobs. The cl ## How to use the lessons -Each lesson has one central question, a calculation, and two self-checks with expandable answers. Read the physical explanation first. Details marked as a second pass can be postponed without losing the main argument. The exercises test understanding; they are not an assessment of mathematical background. +Each lesson has one central question, a calculation, and two self-checks with expandable answers. Read the physical explanation first. Details marked as a second pass can be postponed without losing the main argument. At the end, you should be able to explain why normalization matters, why a nearly maximal coefficient locates an exact Ising direction, why the overlap gap forces orthogonality, and why a finite list of coefficients does not certify all the ambient axioms. -Then read the [core proof](../../research/uniform_extraction_core.md), followed by [sharpness and calibration](../../research/sharpness_and_calibration.md). The [research status](../RESEARCH_STATUS.md), [contribution comparison](../../audits/quantitative_contribution_verdict.md), and [final bounded review](../../audits/final_quantitative_review.md) belong to the research-checking route, not the first lesson. - -The teaching notes explain the existing theorem. They do not replace its exact hypotheses or re-prove its imported classification theorems. - -## Purpose and contact - -This repository serves as a record of the work and a guide for the author’s self-directed learning. For discussion or potential collaboration, please contact Ruge Lin at [gogoko699@gmail.com](mailto:gogoko699@gmail.com). +Then read the [core proof](../../research/uniform_extraction_core.md), followed by [sharpness and calibration](../../research/sharpness_and_calibration.md). The [results and assumptions](../RESEARCH_STATUS.md), [contribution comparison](../../audits/quantitative_contribution_verdict.md), and [proof review](../../audits/final_quantitative_review.md) support closer research checking. diff --git a/docs/learn/assumptions_and_sources.md b/docs/learn/assumptions_and_sources.md index 36e1d67..2b87f96 100644 --- a/docs/learn/assumptions_and_sources.md +++ b/docs/learn/assumptions_and_sources.md @@ -2,9 +2,9 @@ [Learning path](README.md) · [Canonical proof](../../research/uniform_extraction_core.md) -## The exact class is supplied, not measured by the criterion +## Exact assumptions -The ambient object is an **exact simple unitary, rational, C2-cofinite, holomorphic bosonic VOA of CFT type**, with central charge 24, no weight-one states, and finite-dimensional grades. The following explanations orient a physics reader; they do not replace the formal hypotheses of [core Q0](../../research/uniform_extraction_core.md). +The ambient object is an **exact simple unitary, rational, C2-cofinite, holomorphic bosonic VOA of CFT type**, with central charge 24, no weight-one states, and finite-dimensional grades. The following explanations orient a physics reader to the formal hypotheses of [core Q0](../../research/uniform_extraction_core.md). | Term | Meaning needed for this reading path | |---|---| @@ -20,7 +20,7 @@ The ambient object is an **exact simple unitary, rational, C2-cofinite, holomorp Gaberdiel's “meromorphic” terminology should not silently be replaced by the stronger holomorphic-module condition above. His Section 2.1 explicitly flags a terminology distinction, and Appendix A discusses differing rationality definitions. Yamauchi's OZ-type setting means one-dimensional grade zero and vanishing grade one, with the positive-real assumptions relevant to Section 4. Those low-grade conditions alone do not supply all the ambient classification hypotheses. -The normalized criterion additionally assumes two actual real unit weight-two primaries. The calibration extension begins with two actual real weight-two fields and a known stress tensor, then removes their stress components and normalizes them. Neither version tests approximate VOA axioms or identifies conformal grades from noisy data. +The normalized criterion additionally assumes two actual real unit weight-two primaries. The calibration extension begins with two actual real weight-two fields and a known stress tensor, then removes their stress components and normalizes them. Both versions retain the exact ambient class, conformal grade, and real structure as assumptions. ## A compact translation dictionary @@ -43,16 +43,12 @@ The mathematical formulas, rather than these plain-text table labels, define the **Imported proof inputs.** The core attributes unitary conventions to [Dong–Lin, 1308.2361](https://arxiv.org/abs/1308.2361), and mode/product conventions to [Matsuo, math/0007169](https://arxiv.org/abs/math/0007169). The unitary Virasoro necessity theorem is attributed to Friedan–Qiu–Shenker via its explicit statement in [Wassermann, 1012.6003, pp. 1–2](https://arxiv.org/abs/1012.6003). The discrete Ising overlaps come from [Sakuma, math/0608709, Theorem 4.4](https://arxiv.org/abs/math/0608709). The ambient identification is [Abe–Lam–Yamada, 1705.09022v4, Theorem A.1](https://arxiv.org/abs/1705.09022v4). -These are research references for verifying the imported interfaces, not extra tutorial assignments. The two anchors are not substitutes for primary-source attribution. +These research references supply the imported theorem statements; the anchors provide the teaching route. -**Project argument.** [Uniform extraction](../../research/uniform_extraction_core.md) supplies the quantitative localization, overlap propagation, and composition with the prior endpoint. [Sharpness and calibration](../../research/sharpness_and_calibration.md) gives the additional bounds. The teaching notes provide a route into those records, not a new scientific result or an independent source-proof audit. +**Project argument.** [Uniform extraction](../../research/uniform_extraction_core.md) supplies the quantitative localization, overlap propagation, and composition with the prior endpoint. [Sharpness and calibration](../../research/sharpness_and_calibration.md) gives the additional bounds. -## What the conclusion does not say +## Conclusion -The conclusion is an isomorphism of the **underlying VOA** to the moonshine VOA. It does not supply an implemented isomorphism, identify an experimental device, or reconstruct a full nonchiral CFT. It does not infer the existence of the required input fields from the ambient assumptions alone. The numerical test is sufficient, not necessary, and its constants are not claimed optimal. +The conclusion is an isomorphism of the **underlying VOA** to the moonshine VOA, conditional on the supplied fields satisfying the coefficient bounds. The numerical criterion is sufficient. Its field-distance exponent is sharp; its numerical tolerances are sufficient bounds. -For the complete boundaries and reviewed status, see [Current scientific status](../RESEARCH_STATUS.md). - -## Purpose and contact - -This repository serves as a record of the work and a guide for the author’s self-directed learning. For discussion or potential collaboration, please contact Ruge Lin at [gogoko699@gmail.com](mailto:gogoko699@gmail.com). +See [results and assumptions](../RESEARCH_STATUS.md) for the theorem and supporting results. diff --git a/llms.txt b/llms.txt index b183556..c9001b1 100644 --- a/llms.txt +++ b/llms.txt @@ -1,41 +1,39 @@ # Monster Correlation Rigidity > Quantitative conditional identification of the moonshine vertex operator -> algebra from near-extremal low-weight correlation coefficients. Research by -> Ruge Lin. No tagged release is implied. +> algebra from near-extremal weight-two correlation coefficients. Research by +> Ruge Lin. -## When this repository is relevant +## Retrieval topics -Use it for a uniform value-to-Ising-direction estimate, a sufficient two-field -correlation criterion, the sharp square-root field-distance exponent, or -certified stress subtraction and normalization from seven exact scalar intervals. -It is not a source for device-independent self-testing, automatic first-Ising -existence, bare-class uniqueness, optimal numerical tolerances, or a practical -Monster-tensor simulation. +Use this repository for uniform value-to-Ising-direction estimates, a sufficient +two-field correlation criterion, the sharp square-root field-distance exponent, +and certified stress subtraction and normalization from seven scalar intervals. -## Authoritative sources +The criterion applies to actual real weight-two fields in an exact simple +unitary, rational, C2-cofinite, holomorphic VOA of CFT type, with central charge +24 and no weight-one states. Attribute the exact classification endpoint to +Abe–Lam–Yamada and the Ising overlap gap to Sakuma. -- [Current status](docs/RESEARCH_STATUS.md): exact claim scope and what is not asserted. -- [Core proof](research/uniform_extraction_core.md): hypotheses, normalization, local-to-global localization, discrete overlap rounding, and the prior Abe–Lam–Yamada endpoint. -- [Sharpness and calibration](research/sharpness_and_calibration.md): analytic precision results, not a reconstruction of the imported classifications. -- [Current arithmetic](docs/CALIBRATION_PRECISION.md): scale-safe interval implementation and its work-limit boundary. -- [Reproduction](docs/REPRODUCIBILITY.md): current command, pinned numerical environment, current versus historical report fingerprints, and strict versus bounded replay. +## Research and implementation -## Teaching and attribution +- [Results and assumptions](docs/RESEARCH_STATUS.md): result map, exact input requirements, and interpretation of a sufficient certificate. +- [Core proof](research/uniform_extraction_core.md): normalization, uniform localization, and discrete overlap rounding. +- [Sharpness and calibration](research/sharpness_and_calibration.md): optimal field-distance exponent and seven-scalar reduction. +- [Calibration arithmetic](docs/CALIBRATION_PRECISION.md): scale-safe interval implementation and precision limit. +- [Reproduction](docs/REPRODUCIBILITY.md): commands, environment, and exact versus bounded replay. -- [Physics learning path](docs/learn/README.md): Gaberdiel, An Introduction to Conformal Field Theory, is the primary anchor; Yamauchi Section 4 is a guided secondary supplement. -- [Assumptions and source roles](docs/learn/assumptions_and_sources.md): tutorial sources are not substitutes for primary theorem attribution. -- [Contribution comparison](audits/quantitative_contribution_verdict.md): bounded source comparison, not exhaustive novelty certification. -- [Final bounded review](audits/final_quantitative_review.md): dated assistant review and its explicit source depth. -- [Calibration erratum](audits/calibration_scale_erratum.md): implementation correction and preserved old evidence. +## Teaching and sources -## Historical and release boundaries +- [Physics learning path](docs/learn/README.md): Gaberdiel, An Introduction to Conformal Field Theory, is the primary anchor; Yamauchi Section 4 is the secondary supplement. +- [Assumptions and source roles](docs/learn/assumptions_and_sources.md): physical language, exact premises, and imported theorems. +- [Scientific context](docs/background_claims.md): claim-to-source mapping and primary references. +- [Contribution comparison](audits/quantitative_contribution_verdict.md): detailed comparison with inspected prior results. -- [Archive index](docs/ARCHIVE.md): older status ledgers and archived branches do not supersede the active status or supply silently imported release dependencies. -- [Release scope](docs/RELEASE.md): research package and exact assumptions, not a paper or release announcement. -- [Citation](CITATION.cff): cite the repository and exact commit used; do not invent a paper, DOI, external review, or proof-assistant certificate. -- [License](LICENSE): original MIT license for repository code and documentation, with imported results attributed to their authors. +## Reference -## Purpose and contact - -This repository serves as a record of the work and a guide for the author’s self-directed learning. For discussion or potential collaboration, please contact Ruge Lin at [gogoko699@gmail.com](mailto:gogoko699@gmail.com). +- [Package contents](docs/RELEASE.md): file navigation. +- [Additional research and archive](docs/ARCHIVE.md): earlier investigations, corrections, and fixed source records. +- [Citation](CITATION.cff): cite the repository and exact commit used. +- [License](LICENSE): MIT license for original code and documentation. +- [Purpose and contact](README.md#purpose-and-contact): repository purpose and Ruge Lin's email. diff --git a/research/sharpness_and_calibration.md b/research/sharpness_and_calibration.md index 81727a5..0b59295 100644 --- a/research/sharpness_and_calibration.md +++ b/research/sharpness_and_calibration.md @@ -2,10 +2,9 @@ [← Core proof](uniform_extraction_core.md) · [Learning path](../docs/learn/README.md) · [Overview](../README.md) -Research record, 26 September 2026. Read main: `09e3f98ad79034eefab43f4fb9ea432368fc19e7`. -No manuscript section is being drafted. The imported exact classification remains credited to Abe–Lam–Yamada; the estimates below supplement the self-contained [core](uniform_extraction_core.md). +These estimates supplement the [correlation criterion](uniform_extraction_core.md), whose exact classification endpoint is due to Abe–Lam–Yamada. -## 1. The two remaining precision questions +## 1. Sharpness and calibration The core proves the following sufficient criterion in an exact simple unitary rational $C_2$-cofinite holomorphic VOA of CFT type, central charge 24, and $V_1=0$. For two real unit weight-two primaries $x,y$, put $M=46/\sqrt{141}$. If @@ -22,12 +21,12 @@ with $0\le\epsilon_x,\epsilon_y<1/50$ and then the underlying VOA is moonshine. The proof first locates an exact Ising primary within $\sqrt{\epsilon/2}$ of each field, then applies Sakuma's discrete overlap theorem and the prior ambient classification theorem. All class, reality, grading, and norm hypotheses are exact. -Two questions about that statement can now be settled without another special-subtheory campaign: +Two precision results accompany this criterion: * The square-root exponent in value-to-field localization cannot be improved, even in the known moonshine theory. This is an optimal exponent, not an optimal numerical tolerance region for theory identification. * Exact normalization and exact stress subtraction need not be supplied as preprocessed data. Seven scalar intervals for two actual real weight-two fields suffice to conservatively compute the quantities in the criterion. Exact ambient axioms, reality, grade two, and the known stress tensor remain hypotheses. -The first conclusion is an explicit realization of the familiar quadratic-loss mechanism at a nondegenerate maximum. The second is exact invariant-metric algebra and interval arithmetic. Neither auxiliary statement is advertised as a new general optimization or calibration theorem. +The first conclusion is an explicit realization of the familiar quadratic-loss mechanism at a nondegenerate maximum. The second is exact invariant-metric algebra and interval arithmetic. ## 2. Calibrating arbitrary real weight-two fields @@ -76,7 +75,7 @@ Solving for $q(z)$ gives $q-\tau n/2+\tau^3/36$. The bilinear projection identit This argument needs no multiplication table and no chosen Ising vector in the unknown candidate. It does not alter the field signs: a negative primary self-coupling remains negative unless a sign change and the accompanying overlap change are explicitly made. -The current implementation uses scale-aware outward square-root bounds. The [calibration precision note](../docs/CALIBRATION_PRECISION.md) proves the arithmetic enclosure and explains its explicit work limit; the [implementation erratum](../audits/calibration_scale_erratum.md) records the earlier small-scale exception. The identities and physical premises above are unchanged. +The implementation uses scale-aware outward square-root bounds. The [calibration precision note](../docs/CALIBRATION_PRECISION.md) proves the enclosure and specifies the work limit and input contract. ### Certified scalar intervals @@ -84,7 +83,7 @@ Suppose each of the seven exact numbers lies in a supplied rational interval. Ev The checker uses only fractions and integer square roots. It encloses $\sqrt{s}$ between adjacent dyadic numbers and propagates both endpoints. It rejects a primary norm interval reaching zero, a certified lower self-coupling above the unitary cap, and other inconsistent conditions. Failure to establish the sufficient inequality is **inconclusive**, not proof that the theory is different from moonshine. Broad intervals can fail even for the known example. -This is robustness with respect to uncertainties in specified coefficients in an exact model. It is NOT robustness to violations of the VOA axioms, uncertain conformal weight, non-real fields, unknown stress tensor, leakage to other weights, or unknown empirical error coverage. No statistical sample count, field-finding algorithm, measurement architecture, or efficient normalization protocol is inferred. +The uncertainty bounds apply to the seven supplied coefficients. The ambient VOA axioms, grade, real structure, known stress tensor, and validity of the input enclosures are premises. The three exact controls use differently scaled and stress-shifted orthogonal Ising vectors. A separate seven-interval example of radius $10^{-12}$ around the uncentered exact pair also passes with a strictly positive margin. That radius is a test case for the arithmetic, not a claim about required experimental precision or an optimal allowance. @@ -170,26 +169,13 @@ The same curve obeys The cross-overlap changes linearly at zero, while the self-coupling deficit changes quadratically. Therefore, from self-coupling losses alone, one cannot replace the generic square-root field and overlap control by a uniform linear-in-deficit estimate. This is not a necessity theorem for the whole-theory identification region: additional correlations can provide additional information, and an already known moonshine theory remains moonshine at all $t$. -## 4. Where this leaves the selected contribution +## 4. Verification and references -The bounded core is now a quantitative conditional identification theorem with two useful boundary results: +`checks/verify_calibration_and_sharpness.py` emits 74 labelled exact checks. They include algebraic projection identities, rescaling/stress-shift examples, certified interval operations and negative inputs, the full polynomial curve, and the Taylor coefficients used in the analytic sharpness proof. The largest coefficient vector has length three. The continuum limit follows from the displayed analytic functions of $t$. -1. the field-distance exponent is sharp in an actual admissible theory; -2. the normalized-primary assumptions can be implemented algebraically from seven calibrated coefficients of real weight-two fields, while retaining all exact ambient hypotheses. +For comparison with prior variational methods and classification results, see [the source comparison](../audits/quantitative_contribution_verdict.md). -Neither auxiliary result should be advertised as a separate foundational advance. The candidate contribution remains the uniform replacement of exact internal-subalgebra hypotheses by controlled correlation coefficients and the resulting ambient identification through the prior theorem. - -The proof does not claim that the original holomorphic/current-free class is a singleton, that the coefficient test must pass for arbitrary supplied fields, or that the spectrum alone finds those fields. General approximate-VOA stability and first-Ising existence are outside this bounded theorem, not missing lemmas being left for manuscript drafting. - -## 5. Evidence and inherited interfaces - -`checks/verify_calibration_and_sharpness.py` emits 74 labelled exact checks. They include algebraic projection identities, rescaling/stress-shift examples, certified interval operations and negative inputs, the full polynomial curve, and the Taylor coefficients used in the analytic sharpness proof. The largest coefficient vector has length three. No matrix or full VOA is constructed. The continuum limit follows from the displayed analytic functions, not from sampling four values of $t$. - -At import, the prior core/checker/report and original license were copied byte-identically from the supplied research-completion packet; its 14 payload hashes and 63-check report were verified under normal/-O/-OO. No private planning or manuscript is included. Imported FQS, Ising-module, Sakuma and ALY theorems remain distinct source dependencies; no independent expert or formal verification of those results is claimed. - -For the directly inspected source history and contribution assessment, see [the comparison record](../audits/quantitative_contribution_verdict.md). The new results do not change the fundamental source attribution: the exact classification belongs to ALY; positive-metric cubic/idempotent variational methods and local quadratic growth are prior mathematics. - -[LS] C.H. Lam, H. Shimakura, *Ising vectors in the vertex operator algebra $V_{\mathrm{Leech}}^+$ associated with the Leech lattice*, arXiv:0810.5395v1, Theorem 3.1. Printed page 6 was visually inspected in this continuation. The lattice inclusion into moonshine and real-unitary convention are inherited from the source construction; this finite stress-algebra check does not reprove the construction. +[LS] C.H. Lam, H. Shimakura, *Ising vectors in the vertex operator algebra $V_{\mathrm{Leech}}^+$ associated with the Leech lattice*, arXiv:0810.5395v1, Theorem 3.1. The lattice inclusion into moonshine and real-unitary convention use this construction. https://arxiv.org/abs/0810.5395 [ALY] T. Abe, C.H. Lam, H. Yamada, *A remark on $\mathbb Z_p$-orbifold constructions of the Moonshine vertex operator algebra*, arXiv:1705.09022v4, Theorem A.1. The exact endpoint is imported. diff --git a/research/uniform_extraction_core.md b/research/uniform_extraction_core.md index 51d24f6..93e2c9e 100644 --- a/research/uniform_extraction_core.md +++ b/research/uniform_extraction_core.md @@ -2,8 +2,7 @@ [← Learning path](../docs/learn/README.md) · [Overview](../README.md) · [Sharpness and calibration →](sharpness_and_calibration.md) -Research proof record, 26 September 2026. Read baseline: `09e3f98ad79034eefab43f4fb9ea432368fc19e7`. -This is a self-contained consolidation of the quantitative part of [the earlier two-field selection note](https://github.com/GoGoKo699/Monster-Correlation-Rigidity/blob/ac5acad7cad4a63f0d879e4ea716f5a27c3bcd61/research/two_field_selection.md) (historical provenance in unmerged PR23, not an omitted prerequisite), not a manuscript or a new exact classification theorem. The geometric argument is elementary quadratic growth plus compactness. Its novelty must not be conflated with the old classification theorems. +The proof combines quadratic growth and compactness with the discrete Ising overlap theorem and the exact ambient classification of Abe–Lam–Yamada. ## Q0. Fixed scope and normalization @@ -24,9 +23,9 @@ C(a,b,c)=\langle a*b,c\rangle,\qquad f(x)=C(x,x,x). Two- and three-point chiral functions of these weight-two primaries have these coefficients times the fixed position factors $z_{12}^{-4}$ and $(z_{12}z_{23}z_{31})^{-2}$, respectively. Thus the inputs are normalized coefficients, not whole unknown functions or arbitrary laboratory readings. All signs refer to the SAME two supplied real fields. Flipping a field to make its cubic positive also flips its overlap and must not be done silently. -An exact VOA and exact primarity, reality, and normalization are premises. Only coefficient inequalities may have finite tolerance. No norm on approximately satisfied VOA axioms, no measurement implementation, and no device-independent conclusion are asserted. +The VOA axioms, primarity, reality, and normalization are exact premises; the coefficient inequalities allow finite tolerance. -Source conventions: Dong–Lin [DL, Definitions 2.1–2.2]; weight-two mode identities [M, section 1]. The final classification conclusion is an isomorphism of underlying VOAs. A stronger claim about an implemented conformal net, a full nonchiral CFT, or an explicitly supplied unitary isomorphism is not part of this statement. +Source conventions: Dong–Lin [DL, Definitions 2.1–2.2]; weight-two mode identities [M, section 1]. The final classification conclusion is an isomorphism of underlying VOAs. ## Q1. Elementary uniform localization lemma @@ -96,7 +95,7 @@ for every non-Ising critical point. Equality $f(a)=M$ is equivalent to $e$ being e_a=\omega/48+(\sqrt{141}/24)a. ``` -This identification uses unitary Virasoro classification, not a known Monster orbit or an axis count. The exact charge classification is imported, not re-proved by the numerical certificate. Source [W] attributes it to FQS; the original FQS full proof was not newly obtained here. +This identification uses unitary Virasoro classification, not a known Monster orbit or an axis count. The exact charge classification is imported, not re-proved by the numerical certificate. Source [W] attributes it to FQS. ## Q3. Uniform local growth without multiplicities @@ -181,23 +180,21 @@ Thus the overlap is zero, and the vectors are distinct. Their singular OPE vanis Now apply Abe–Lam–Yamada [ALY, Theorem A.1]. It identifies the ambient VOA, not just the subalgebra generated by the pair. This exact classification is prior work. End proof. -The symmetric historical tolerances are recovered by $\epsilon_x=\epsilon_y=1/32768$, $\delta=1/128$. The resulting bound is $1/64<3/188$, and the Ising overlap is at most $47/12288$, leaving margin $1/12288$ below $1/256$. These numbers are sufficient, not optimal. +The symmetric tolerances are recovered by $\epsilon_x=\epsilon_y=1/32768$, $\delta=1/128$. The resulting bound is $1/64<3/188$, and the Ising overlap is at most $47/12288$, leaving margin $1/12288$ below $1/256$. These numbers are sufficient, not optimal. -The asymmetric formula is explicit error propagation of the existing proof, not a separate claim of a newly classified family. Failure to satisfy it is failure of this certificate, NOT proof that $V$ differs from moonshine. +The asymmetric formula propagates the two self-coupling errors separately. Failure to satisfy it leaves the certificate inconclusive for $V$. -## Q5. Honest interpretation of approximate inputs +## Q5. Certified coefficient intervals Certified coefficient intervals can be substituted conservatively. If $f(x)\ge f_x^-$ and $f(y)\ge f_y^-$ are established lower bounds, take $\epsilon_x=M-f_x^-$ and $\epsilon_y=M-f_y^-$ when these are nonnegative. If an overlap estimate $\hat c$ has an absolute error bound $\eta$, use $\delta=|\hat c+1/47|+\eta$. Each distance square root can be bounded from above by exact rational interval arithmetic, as in the checker. -A lower bound $f_x^->M$ contradicts the assumed model/normalization; it must not be clipped to zero and presented as a successful physical test. No uncertainty in normalization, primarity, real structure, locality, or holomorphicity is absorbed by this procedure unless separately bounded by a proved theorem. The theorem does not establish sample complexity, field finding, or a method to compute an isomorphism. +A lower bound $f_x^->M$ contradicts the assumed model/normalization; it must not be clipped to zero and presented as a successful physical test. No uncertainty in normalization, primarity, real structure, locality, or holomorphicity is absorbed by this procedure unless separately bounded by a proved theorem. -One may choose far stronger exact structural assumptions and get a prior theorem immediately. The candidate scientific contribution is the uniform replacement by a limited set of coefficient inequalities, not a new exact classification or a general Morse theorem. The exact Ising tensor power outside the holomorphic class passes the local data, so the ambient hypotheses cannot be omitted. The existing explicit lattice pair verifies that the admitted region is attained in the known moonshine example; this consolidation does not re-run a full VOA construction. +The coefficient inequalities replace exact internal-subalgebra input. The exact Ising tensor power outside the holomorphic class passes the local data, so the ambient hypotheses are essential. The explicit lattice pair in the sharpness note shows that the admitted region is attained in moonshine. -## Dependencies, status, and references +## Dependencies and references -Self-contained here: the localization lemma, critical-point conversion, local estimate, overlap propagation and logical composition. Imported interfaces: positive unitary mode conventions; FQS representation necessity; Ising module decomposition and Sakuma overlap theorem; ALY exact classification. They are stated precisely and receive credit, not treated as verified by a small script. The endpoint does not need the disputed fifth trace, the full six-sector contraction spectrum, the readout theorem, or the extended-6/7 theorem. - -The complete primary literature proofs are not reconstructed here. No comprehensive originality, independent specialist review, or formal proof-assistant validation is claimed. This record closes the organizational obligation to state the central quantitative proof independently of the older recognition notes; it does not by itself settle its research significance or priority. +The localization lemma, critical-point conversion, local estimate, overlap propagation, and their composition are proved above. The imported inputs are positive unitary mode conventions, FQS representation necessity, Ising module decomposition, Sakuma's overlap theorem, and the Abe–Lam–Yamada classification. [DL] Dong–Lin, *Unitary vertex operator algebras*, arXiv:1308.2361v1, Definitions 2.1–2.2. https://arxiv.org/abs/1308.2361 diff --git a/results/release_preparation.json b/results/release_preparation.json index 9cb35c3..7018d8e 100644 --- a/results/release_preparation.json +++ b/results/release_preparation.json @@ -9,6 +9,12 @@ "sha256": "efe50fbbd5fe3919847298ba76bff37c36495730ce2246b181424f778a04cdf6", "previous_sha256": "77bca74a609cbf8eb162b23de7655ab97a850bf57a64aae6a60a0a6b6c1c0d8d" }, + { + "path": "AGENTS.md", + "bytes": 2322, + "sha256": "ed6b103ea8ccb9be613eade62bde425cbd182ad644175df84364a2a087c2bed2", + "previous_sha256": "e1e288d4ad55d6804c322a165ee74bfa0e28ef668fd118a4a37794bfd20cb393" + }, { "path": "PHYSICS_STATUS.md", "bytes": 5631, @@ -17,8 +23,8 @@ }, { "path": "README.md", - "bytes": 5981, - "sha256": "ddb633e59fb14d76051ee886b1b91942e873fb33a81f0fc2b6b9ed997010094e", + "bytes": 4445, + "sha256": "66b8eadc4ad851a7b10dfee6c1c38840bda4138a2db629439ca390502cef6c4e", "previous_sha256": "07c05d6314d03e76b786acf32d85d8533a5a5f5b350a06268e865df3ec8d2f5f" }, { @@ -27,10 +33,16 @@ "sha256": "9d8f96cca1cb89368cb4f43cace66f8aedc71fad447dfaa29c6c0b368f448200", "previous_sha256": "cf7a7fa4cbed6e4234e480f07992081ff46ccb535a3a9544de92aa4feef932f2" }, + { + "path": "WORKSPACES.md", + "bytes": 483, + "sha256": "a978d1ff9ee8c1c10d290d3f3181ac2948b570f345004f5d79622cd7d9d6b382", + "previous_sha256": "e10b268c0668b9dec24dec715f6462fda7cf2d6df04fbc3694def4dcb886fd66" + }, { "path": "audits/README.md", - 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source snapshot. Membership and unchanged records are retained; reader cleanup updates README and the audit index deliberately. Full inventory and before/after hashes: results/release_preparation.json. Historical scientific reports remain frozen."} diff --git a/work_orders/CURRENT.md b/work_orders/CURRENT.md index beafefc..ad8a1db 100644 --- a/work_orders/CURRENT.md +++ b/work_orders/CURRENT.md @@ -1,13 +1,15 @@ -# Current work order: maintain the reviewed quantitative core +# Maintenance scope -The active reader entry is README.md and docs/RESEARCH_STATUS.md. Read AGENTS.md and WORKSPACES.md before changes. +Maintain the [correlation criterion](../research/uniform_extraction_core.md), +[sharpness and calibration](../research/sharpness_and_calibration.md), tutorial, +and reproducible certificates. Use [results and assumptions](../docs/RESEARCH_STATUS.md) +as the scientific scope and [AGENTS.md](../AGENTS.md) for repository rules. -The selected bounded scientific result is the quantitative correlation criterion in research/uniform_extraction_core.md, with research/sharpness_and_calibration.md and the evidence in docs/background_claims.md. Its final adversarial review is audits/final_quantitative_review.md. Do not resume the historical five-label exploration simply because an older ledger still calls it current. +Changes should resolve a concrete proof, source, implementation, or documentation +issue. Record intentional source changes and their before/after fingerprints in +the current integrity manifest. Preserve the original license, scientific +records, provenance archives, recorded outputs, and replay tolerances. -No blocking gap was found in the selected proof at the recorded source-interface depth. The next authorized maintenance is to resolve a concrete objection, source overlap, reproducibility failure or reader defect. Do not invent a new required theorem solely because unrestricted moonshine uniqueness or approximate-VOA stability remains unproved. Those questions are outside the stated conditional contribution. - -Keep exact classification and generic variational methods credited to prior work. Do not convert a scoped priority assessment into an exhaustive firstness claim. The review does not certify the entire historical PR backlog. Additional research branches may contain relevant results but are not automatically merged or treated as dependencies. - -Preserve the original LICENSE, provenance archives, historical research and scientific outputs, and the two reviewed core proofs/checkers. Correct mistakes by explicit errata or a described source change. Do not widen replay tolerances or replace recorded reports to conceal a failure. Reader/work-order and manifest updates must be declared with before/after hashes. - -Run the three selected checkers in normal/-O/-OO, the root verification and the separate unchanged portability comparison. Inspect actual logs and distinguish each outcome. The target journal and private submission planning are not public repository material. Drafting will arrange completed science only after a separate owner decision; it is not authorized by this work order. +Run `python verify_current.py --all` and inspect current checks, strict historical +replay, and bounded portability separately. Imported mathematical results retain +their source attribution. diff --git a/work_orders/INDEPENDENT_AUDIT.md b/work_orders/INDEPENDENT_AUDIT.md index 080a9cf..cf7b5f0 100644 --- a/work_orders/INDEPENDENT_AUDIT.md +++ b/work_orders/INDEPENDENT_AUDIT.md @@ -1,35 +1,15 @@ -# First additional workspace: falsification-oriented proof audit +# Proof-review protocol -You are the proof-audit workspace for Ruge Lin's Monster Correlation Rigidity project. -Canonical repository: https://github.com/GoGoKo699/Monster-Correlation-Rigidity -Read the current main branch before reasoning from any previous conversation. Begin with AGENTS.md, WORKSPACES.md, README.md, STATUS.md, and work_orders/CURRENT.md. Record the base commit. Work on `audit/voa-extrema` (or an unused derivative if that branch is already occupied); submit a pull request and do not merge or force-push. +Record the reviewed commit and the exact statement under review. Reconstruct +the argument from its hypotheses and cited primary sources, checking +normalizations, dependencies, circularity, and counterexamples. -## Purpose and evidence boundary +For each finding, record PASS, ERROR, or UNRESOLVED with the supporting proof, +source passage, or counterexample and the affected claim. Identify the source +version and inspection depth. Finite arithmetic checks support the review; +analytic and imported classification arguments require their own evidence. -The five research notes contain candidate written derivations, not established new theorems. Their scalar and small-example verifiers do not establish the high-dimensional algebra, imported classifications, or novelty. Reconstruct the vulnerable arguments from definitions and primary literature. Look actively for a counterexample, missing hypothesis, circular step, or normalization error. A correction is a successful outcome. - -## First bounded assignment: the VOA-to-extremum dependency - -Start with research/03_uniform_axis_rounding.md and its dependency on research/01_local_rigidity.md and research/02_pair_correlations.md, then trace its use in research/04_average_transport.md and research/05_normalizer_rounding.md. - -Audit the claim that every real critical point of the cubic on the traceless unit sphere gives a genuine positive-energy unitary Virasoro representation via a full Griess idempotent. Check, separately: - -1. The identity direction, projected product, idempotent reconstruction, branch choice, and conversion `c = 8 ||e||^2`. Derive the normalization rather than importing it from the displayed constants. -2. Closure of the relevant vertex subalgebra, adjoint relations, positive definiteness, grading/lower-energy hypothesis, and legitimacy of applying the unitary Virasoro classification. A positive algebra norm alone is not an adequate substitute for these hypotheses. -3. The exclusion of zero central charge, the identity branch, and spurious critical points. Check precisely what the classification implies; do not infer existence at the next allowed central charge. -4. Whether every maximal direction is one of the stated Ising axes, with the claimed sign convention; distinguish the literature input from a project deduction. -5. The critical-value gap and the finite-radius inequalities used for global localization. Check the compact-domain boundary argument and the radius-one-half extension, not only the Hessian. - -Deliver the first report even if a blocking gap is found. Do not silently assume the disputed step to proceed to a stronger theorem. - -## Deliverable - -Create `audits/voa_extrema_audit.md` with the audited base commit, an explicit dependency map to claim IDs C07, C08, C12 and C13 (and any others actually affected), and a table of PASS / ERROR / UNRESOLVED findings. For each entry give an equation or section reference, an independently reconstructed argument or precise missing justification, and primary source attribution. Distinguish logical soundness, numerical consistency, and priority. Add a small standalone verification or counterexample script only where it materially tests an identity. - -If an error is found, propose the narrowest repair and state which downstream claims survive, must become conditional, or must be withdrawn. Leave original notes unchanged. Do not mark a result independently expert-reviewed or novelty-cleared. - -Run `python verify.py` before and after the audit changes. Preserve all original bytes guarded by provenance/repository_import.json. New code must not rely on assertions that disappear under optimization and must not require a large simulation. - -## Only after the first assignment - -Continue to the eight-item complete-proof audit in work_orders/CURRENT.md if the first assignment is resolved and reportable. Keep the priority audit and probe-access feasibility as distinct outputs; do not replace mathematical scrutiny with another list of speculative applications. The integration workspace handles front-door claim changes and merging. +Use a separate branch and focused pull request. Follow [AGENTS.md](../AGENTS.md) +and [the maintainer workflow](../WORKSPACES.md), preserve existing evidence, and +run the checks in [the reproduction guide](../docs/REPRODUCIBILITY.md). Describe +assistant review accurately as assistant review.