Dated research snapshot: 5 October 2026. Prepared for a separate public repository; this copy does not itself establish publication. AI-assisted manuscripts and reproducible symbolic checks, not a completed physical string theory or peer-reviewed work.
moving-pole/: manuscript PDF and editable LaTeX source for scalar dominance in the known three-pole planar family with massive poles {1, 2, r}. The proposed all-spin criterion is 3 < D <= d(r) for 3 <= r < 4; d(r) is a unique scalar zero. The manuscript proves monotonicity and the stated boundary asymptotic rather than inferring them from a spin cutoff. Novelty is provisionalsharp-gap/: PDF, LaTeX, exact coefficient certificate and finite tests for the sharper central-factorial positivity endpoint (125-sqrt(1081))/9. This refines the earlier 51/5 bound. It is not evidence of an integer spacetime dimension above tenphysical-completion-gate/: precise preliminary physical-completion diagnostics and symbolic checks. Read the later restricted-contact note for the repaired-forward-data qualificationrestricted-contact-completion/: full argument and checks for a finite-pole-deletion obstruction under a specified meromorphic cocycle or polynomial high-energy restriction. It does not exclude all possible completions outside those hypotheses
The prior finite-product paper is already available in the existing research archive. Its all-level positivity proof and finite-base dependencies are not replaced by this folder. This repository is a continuation of that archive, not a new claim to its construction or the established Veneziano positivity literature.
Python 3.11+; tested with SymPy 1.14.0 and mpmath 1.3.0. Install the packages in requirements.txt in your own isolated environment. From the repository root:
python moving-pole/exact_checks.py
python sharp-gap/sharp_gap.py
python sharp-gap/cutoff_check.py
python sharp-gap/audit_rerun.py
python sharp-gap/independent_audit.py
python sharp-gap/independent_cutoff_audit.py
python physical-completion-gate/exact_checks.py
python restricted-contact-completion/exact_checks.pyOptional numerical cross-checks: python moving-pole/audit_numerics.py and python moving-pole/audit_quadrature.py. They do not replace the analytic proof or exact certificates. Checkers may regenerate adjacent outputs. Run normal Python, not python -O, because these research checkers use assertions.
To build a manuscript, change into its directory and run pdflatex -interaction=nonstopmode -halt-on-error <name>.tex twice. PDFs supplied here are the previously generated research manuscripts; this packaging pass did not retypeset them. The sharp-gap manuscript's “private candidate” label describes its preparation status, not a confidentiality restriction on this authorized public snapshot.
- Shao and Vichi, finite-product family: https://arxiv.org/abs/2607.27300
- Arkani-Hamed et al., positivity of string amplitudes: https://arxiv.org/abs/2201.11575
- Chen and Yin, bosonic positivity: https://arxiv.org/abs/2608.25183
- Mansfield, direct Veneziano positivity: https://arxiv.org/abs/2502.20372
- Wan and Zhou, analytic bootstrap: https://arxiv.org/abs/2605.11084
- Sung, six-point consistency: https://arxiv.org/abs/2609.29919
Full hypotheses and attribution are in the manuscripts and notes. No copied third-party paper is distributed. See AI_DISCLOSURE.md and LICENSE_STATUS.md.