Exact algebraic confluence for torus one-point Virasoro-block recursions

This repository contains the manuscript and exact-arithmetic audit code for Leslie P. Polzer's paper Exact algebraic confluence for torus one-point Virasoro-block recursions.

Read the current manuscript

Main result

At every fixed nonzero algebraic Coulomb-gas parameter, the paper gives a finite coefficientwise construction of the eta-reduced torus one-point Virasoro block at the corresponding central charge. Generic Kac-recursion terms with a common limiting internal weight are combined along the exact formal germ b = b_star + t. Their fixed-central-charge partial-fraction coefficients are obtained as collision moments: constant terms of finite sums of Laurent germs.

Separated pole sets establish classwise cancellation, while a valuation majorant and backward precision rule give a finite Laurent-jet budget at each level. Partial-fraction uniqueness identifies the result with the inverse-Shapovalov definition of the meromorphic Verma-module block. The Ising specialization includes exact level-seven and level-ten examples, including the first double pole.

The result is coefficientwise in the nome and concerns the meromorphic Verma-module block. It is not an intrinsic recursion in the specialized representation category or a construction of irreducible minimal-model traces at degenerate internal weights.

Repository contents

• paper.tex — manuscript source.
• paper.pdf — current compiled manuscript.
• tools/ — eight audit scripts and two shared exact-arithmetic libraries.
• AUDIT_MANIFEST.md — audit scope, commands, success conditions, and source hashes.
• ARXIV_ANCILLARY_README.md — instructions packaged with the arXiv ancillary files.
• requirements-audit.txt — pinned symbolic dependency.

Reproduce the calculations

The audit environment uses CPython 3.12 and SymPy 1.12. Install the pinned dependency with:

python3 -u -m pip install -r requirements-audit.txt

Run the standard exact suite:

make audit

Add the complete direct level-ten inverse-Shapovalov reconstruction:

make audit-deep

Set VIRASORO_AUDIT_JOBS to control the worker count used by the direct level-ten reconstruction. Every successful identity is reported with a PASS marker; a failed identity exits nonzero. See AUDIT_MANIFEST.md for the responsibility and independence of each check.

Build the manuscript

A PDFLaTeX installation with the standard packages used by paper.tex is required.

make pdf

To generate the clean source archive prepared for arXiv:

make arxiv-bundle

The resulting archive is written to dist/virasoro-arxiv-v1.tar.gz. It contains paper.tex and the audit package under anc/, without generated TeX files or repository metadata.

Contact

Leslie P. Polzer
Independent Researcher
polzer@fastmail.com