Status on 6 October 2026: the large-N BFSS/quantum-gravity goal is UNSOLVED. This repository is an open research archive, not a solution of quantum gravity, a certified theorem, or a claim of scientific priority.
Finite-N status: CANDIDATE analytical proof. The exterior Hardy and singlet-decay manuscript has not received independent human specialist review or proof-assistant verification. Its local and global analytical dependencies remain substantive. AI-assisted analytic reviews, symbolic simplifications and finite numerical regressions are not equivalent to either kind of validation.
中文：大 N 目标仍未解决。有限 N 外域定理是待核查的候选证明；计算检查和 AI 审读不等于人工同行评审或形式化证明。
Author attribution: Yicheng Pan (潘奕成). Substantial OpenAI AI assistance is disclosed in AI_DISCLOSURE.md. No affiliation, endorsement or journal acceptance is claimed.
- Research catalog and dependencies: all main components and eleven subsequent branches
- 116-page v2.1 manuscript, editable TeX, manuscript guide
- 9-page leading-coefficient audit together with the 4-page clarification; scope and reproduction
- What was checked and what was not, publication changes, reproduction guide
The three PDFs preserve their original review-draft bytes. Historical wording such as “local review copy” or “not publicly published” records their preparation status; they are now publicly archived here without upgrading their mathematical status.
At each fixed finite rank, the manuscript assembles a proposed exterior form estimate with coefficient c < 49/4 for physical vectors and c < 121/4 for physical Spin(9) singlets. If the complete analytical argument and stated realization/domain hypotheses are valid, the existing Hasler–Hoppe invariance theorem gives ordinary radial moments 0 ≤ m < 9 for actual compatible physical L² zero modes.
The separate coefficient audit and clarification develop conditional leading-coefficient calculations under the manuscript's exact reduced kinetic/frozen-pair definitions. They do not certify the full complementary reserve, higher-order mixed estimates, global localization, form domains, or global theorem. The latest branches document useful reductions and obstructions, not closure of the target bound.
- Full specialist validation of the finite-N local estimates, complete source inventory, reserve bookkeeping, singular-stratum localization and form-domain arguments
- A justified rank-uniform connected spin-2 / mixed-moment or low-energy spectral upper estimate
- Uniform control of regulator removal, selection of the relevant BMN branch, and weighted convergence strong enough to transfer the needed observables
- The large-N/decompactification limit and the exchange of that limit with soft or zero-energy limits
- Zero-mode existence and uniqueness, the m = 9 endpoint, full-Hamiltonian sharpness, full BFSS soft theorems, scattering completeness and eleven-dimensional Lorentz invariance
Scalar radius lower bounds, formal Ward identities, assumed planar factorization, positive Gram matrices, and protected BMN/localization observables do not by themselves supply the missing unprotected rank-uniform upper bound. Fixed-rank decay does not establish a large-N theorem.
The original top-level quadrupole/rank gate, descendant/cluster gate, four scripts and recorded outputs are preserved. They remain useful background, but the catalog and current status above govern interpretation. The free-channel diagnostics are neither an actual BFSS computation nor a BFSS counterexample.
The manuscript and branch notes contain section-specific primary references. Essential precedents include Sethi–Stern and Hasler–Hoppe invariance and asymptotic work, Agmon's weighted methods, Konechny's asymptotic Hamiltonian, Fröhlich–Graf–Hasler–Hoppe–Yau and Lin–Yin wavefunction analysis, and Polchinski's existing below-nine Born–Oppenheimer expectation. Matrix-current identities, BFSS bootstrap methods, BMN deformation/localization and Nicolai-map literature are credited in their relevant notes.
The below-nine expectation, rotation identities, spectral tools and published results are not claimed as new. This archive makes no priority or breakthrough claim and does not redistribute third-party papers.
Original code: MIT. Original documentation, manuscript sources and original result files: CC BY 4.0, as specified in LICENSE.md. Preserve author attribution, title/version, license notices and changes. Third-party works retain their own terms.