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…certificate The uncontracted condition from Note18 is redundant: the real symmetric cubic trace identities through order five and the positive metric imply G(9Q_x+24336 ad_x-2704 ad_Gx)G=0 for every exterior input x. Calculate the complete Gram of three six-index tensors; its exact kernel is (1,1,-1). Three scalar contractions are fixed by a nonsingular three-row fifth-trace system. Only the non-alternating fifth trace is used, so the disputed five-form coefficient is eliminated before the proof begins. Add Note24, a complete reproducible graph-reduction certificate and 95 exact scoped checks. Preserve every existing main file and pending branch. This is a positive-metric implication, not complex ideal membership, formal verification, independent expert review, novelty clearance, or a classification of the original interaction tensor. No manuscript or outreach.
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Verification checkpoint for head71f09cedc8e0d846409ca4ea3614e46bbf9f833a / treef4bd1a4afbca9a028be9bb4213acce73e15b3d7b: dedicated workflow36216612795/job108333708732 completed successfully and its actual decoded logs were inspected. At04:02:24.3678898Z the baseline reports STRICT_REPLAY FAIL_RECOGNIZED_FLOAT_REPORT; at04:02:30.9519874Z the candidate reports the same. Both are the recognized prior average-toy byte mismatch. The separate unchanged bounded-portability comparisons PASS, with ALL_REPORTS_BYTE_IDENTICAL=False and98 differing float leaves each. This is NOT strict historical byte replay. No report or tolerance was changed. The new95-check report agrees under normal/-O/-OO with exact SHA2563c508a61056b9a0c7f4a0f9a660932a2ecdc84d6f386238d69402507211cd753. All frozen baseline files and new payload hashes pass preservation. The actual PR-merge checkout9aa427800c6400fb43ab3ec4f98034682a94c793 has exactly the proposed candidate tree. The ordinary workflow36216612780/job108333708763 also completed successfully; the detailed strict/portability claims above refer to the dedicated logs. A fresh standalone ZIP extraction verifies all14 payload hashes and reproduces the complete1.35MB exact certificate in all three modes. The independent direct-matrix/Einstein controls do not satisfy the physical antecedents; they validate tensor bookkeeping, not a Monster simulation. Largest explicit matrix6x6, numerical tensor729 entries, symbolic graph16 cubic vertices. The central result is a positive-metric implication from explicit traces1–5, not a numerical fit or an additional selection axiom. The disputed alternating fifth coefficient is eliminated before use. The full operator equation of Note18 is therefore redundant on the stated real-positive solution set; ordinary complex ideal membership and classification of the cubic are not claimed. Source theorems retain their separate audit obligations. No independent specialist/formal verification or comprehensive priority clearance is claimed. PR21 remains open, and every other pending branch remains unchanged. |
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Disposition — 28 September 2026
Closed without merge: archived separate research.
Separate positive-norm redundancy certificate for an earlier operator equation; the current proof does not need fifth-order trace inputs.
This archival disposition preserves separate research outside the selected quantitative criterion. It is neither a rejection of its mathematics nor a new proof or reproducibility certification.
The research-backlog index records the comparison against main
7b9b14dc5d2a693b8607332089407f11a08f84a9. The inspected research record, branchresearch/operator-factorization-closure, and commit71f09cedc8e0d846409ca4ea3614e46bbf9f833aare retained. No scientific files from this PR were merged by this housekeeping action.Original proposal (preserved)
The outstanding implication is resolved
Base
09e3f98ad79034eefab43f4fb9ea432368fc19e7; head71f09cedc8e0d846409ca4ea3614e46bbf9f833a; treef4bd1a4afbca9a028be9bb4213acce73e15b3d7b. Six additions only; all existing main files and pending branches remain unchanged.Note24 proves that the operator condition left unresolved in Note18 is NOT an independent selection condition on real positive-metric cubics satisfying the stated traces through order five:
G(9 Q_x + 24336 ad_x - 2704 ad_(Gx))G = 0 for all exterior x.
Instead of reducing every six-index matrix element, calculate the positive squared mismatch. Three scaled tensors have the exact Gram matrix
K * [[17069,221,17290],[221,349,570],[17290,570,17860]],
with K=107700439863024387072>0. The kernel vector (1,1,-1) proves the complete tensor identity. The positive 2x2 minor5908240 also proves this is the only linear relation within that specified three-tensor span. It is not a classification of all cubic identities.
Source and normalization safeguard
Only the NON-ALTERNATING fifth trace is used. Subtracting the normalized alternating trace removes the five-form term for any convention, so neither26 nor52 is an input. Full-to-primary block subtraction gives explicit coefficients89/3,4,-22,185/9,10/3. The source assumptions and all four lower projected trace coefficients are stated. This does not restore PR12's rejected condition.
Short-cycle reductions leave three closed scalar graphs. Three fifth-trace substitutions fix them with coefficient determinant11/18. The checker emits every raw Gram contraction, all136 local replacement steps, all three final relations and their rational solutions. No unresolved scalar is fitted to the desired answer or supplied by a Monster example. Largest symbolic graph16 cubic vertices. The conclusion uses positivity of the REAL metric; it is not ordinary ideal membership over complex bilinear fields.
Evidence and boundaries
95 labelled integer/fraction checks reproduce locally under normal/-O/-OO, with report SHA256
3c508a61056b9a0c7f4a0f9a660932a2ecdc84d6f386238d69402507211cd753. Independent direct matrix actions and dense Einstein contractions agree on all six component Gram entries for arbitrary cubics in dimensions2 and3. The dimension3 control correctly has nonzero mismatch because it does not satisfy the exceptional antecedents. Generic full block matrices separately test all fifth-trace conversions and all120 alternating permutations. Largest explicit square matrix6x6; largest numeric tensor729 entries. NumPy object arrays contain integers/Fractions, not floating estimates.This is a source-based symbolic implication proof plus finite independent controls, not proof-assistant formalization, independent expert review, comprehensive priority clearance or a simulation of the full Monster tensor. It does not prove unique physical selection. The original real-positive cubic system remains to be classified; no competing full CFT is constructed.
The preceding supplied pure-state checkpoint remains unchanged: all13 payload hashes and all119 checks reproduce in its three modes. It is not a premise of this proof. Relevant Matsuo Corollary4.1/Remark4.3 were inspected; printed page16 was visually checked. Hoehn's design-to-trace interface remains the recorded inherited source. No original Norton1996 full chapter was obtained.
Integration
A dedicated read-only workflow checks every frozen-baseline file, the supplemental manifest, unchanged historical verify.py and separate bounded portability on baseline/candidate, and the new exact checker under normal/-O/-OO. Actual results must be inspected separately; no strict-pass claim is inferred from an overall green status. Runtime Git DNS failed, so local new checks are not a local current-main replay. No old evidence or tolerance changed.
The repository stores the report fingerprint; its complete1.35MB exact certificate is emitted by the checker and included in the standalone checkpoint. No other pending PR is merged or modified. No manuscript, release, outreach or physical implementation is claimed.