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.
This repository contains research proofs, source comparisons, scope controls and reproducible certificates, not a drafted paper. The current scientific status records the reviewed scope and remaining boundaries.
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.
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.
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 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 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. |
| Final bounded review | Adversarial proof/source/implementation checks and their limits. |
| Contribution comparison | Closest inspected prior results, attribution and a scoped priority judgment. |
| Background evidence | Scientific support for eventual framing, without manuscript prose. |
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.
The current exact checks and documentation checks use Python's standard library:
python verify_current.pyThe command runs the selected checks in normal, -O, and -OO modes and
compares current fingerprints. The reproduction guide
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 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.
Use the archive and research index 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. Protected source notes,
provenance archives, and saved evidence remain available unchanged; legacy
mathematics may not render correctly in every GitHub viewer.
Release scope, the changelog, and citation metadata describe the current research package without claiming a manuscript, publication, DOI, or tagged release. For LLM-assisted research, the source map points questions to the theorem, its exact assumptions, teaching anchors, verification, and historical boundaries.
Original code and documentation retain the owner's MIT license. Imported mathematical results remain attributed to their authors.