Quantitative identification of the moonshine vertex operator algebra from near-extremal low-energy correlation coefficients under exact structural assumptions. Research by Ruge Lin.
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.
Can nearly extremal interaction coefficients identify an exact chiral theory within a specified class? Begin with the five-lesson learning path: 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 interleaves short source selections with local explanations, calculations, and self-checks; it does not require two complete courses. Assumptions and source roles separates the physical language, exact premises, imported theorems, and project estimates.
Work in an exact simple unitary, rational,
If
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 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.
| Document | Purpose |
|---|---|
| Self-contained core proof | Exact hypotheses, uniform localization, pair rounding and attributed classification endpoint. |
| Sharpness and calibration | Optimal extraction exponent and certified scalar preprocessing. |
| Contribution comparison | Closest inspected prior results, attribution and a scoped priority judgment. |
| Scientific context and sources | Physical interpretation and primary-source roles. |
| Results and assumptions | Result map and input requirements. |
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.
The exact certificates and documentation checks use Python's standard library:
python verify_current.pyThe command runs the exact certificates, implementation checks, and documentation
checks in normal, -O, and -OO modes. The reproduction guide
contains the full suite, pinned environment, and interpretation of the results.
See calibration precision for the input contract
and precision limit.
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Original code and documentation retain the owner's MIT license. Imported mathematical results remain attributed to their authors.