GLUING DEFECTS FOR PROJECTED COARSE GRAINING IN FINITE SPIN-FOAM MODELS
Author: Zhenyu Sun
Revised source package, 22 October 2026

CONTENTS

main.tex                     Complete LaTeX manuscript
refs.bib                     Bibliographic records cited in the manuscript
anc/code/reproduce.py            Reproduction program
requirements.txt             Python dependency versions used for the calculations
figures/error_constants.pdf  Vector figure included in the manuscript
anc/data/                    Seven CSV tables and verification.json

BUILD THE MANUSCRIPT

From the extracted package directory, run:

  latexmk -pdf -interaction=nonstopmode -halt-on-error main.tex

Alternatively, run:

  pdflatex -interaction=nonstopmode -halt-on-error main.tex
  bibtex main
  pdflatex -interaction=nonstopmode -halt-on-error main.tex
  pdflatex -interaction=nonstopmode -halt-on-error main.tex

The manuscript uses the standard article class and common TeX Live packages.
Hexagon generates the bibliography and manuscript PDF from these source files.
The uploaded package therefore omits main.bbl and main.pdf.
All source, bibliography, figure, and data references are project-relative.

REPRODUCE THE CALCULATIONS

The supplied results were generated with Python 3.13.12, NumPy 2.3.5, and
Matplotlib 3.10.8. Figure 1 uses LaTeX to match the manuscript's Latin Modern
fonts. Regenerating it requires latex on PATH and the lmodern, type1cm, and
type1ec packages, available in TeX Live. Install the Python dependencies and run:

  python3 -m pip install -r requirements.txt
  python3 anc/code/reproduce.py

The script locates the project from its own file location. It can also be
called from another working directory. It rewrites the data tables,
verification.json, and the vector figure inside the extracted package.
Matplotlib uses an operating-system temporary directory for its cache.

Finite-group sums, projection identities, residual comparisons, and the
sharpness examples use exact rational arithmetic. NumPy is used for numerical
eigenvalue checks and tensor-matrix norms; Matplotlib produces the figure.

DATA TABLES

bf_normalization.csv
  BF disk and sphere values for Z2, Z3, Z2xZ2, and S3. The program checks
  400 equalities, including fixed-boundary disk subdivisions and gluing.

blocking_residuals.csv
  Exact residuals and bounds for 1 <= m,n <= 6 in each of the two models
  with nonzero two-step residual (72 pairs in total).

blocking_schedules.csv
  Largest exact residual at each length from one through ten, obtained by
  checking every ordered partition (1,023 partitions per model; 2,046 total).

matched_models.csv
  Exact one-step and two-step coefficients and residuals for the matched
  positive-semidefinite models A=(3/8,1/8) and B=(1/4,1/4).

interface_constants.csv
  Operator and Hilbert-Schmidt residual norms for 1 through 64 independent
  channels. Squared Hilbert-Schmidt norms are exact rational values. Direct
  tensor matrices independently check the first seven channel counts.

test_graph_constants.csv
  Path and complete-graph spectral gaps and linear correction constants
  for 2 through 64 vertices. Both sets of Laplacian spectra are checked
  numerically. The residual norm sums squared errors over the tested edges.

sharpness_witness.csv
  Fifteen exact matrix calculations for the optimal schedule-bound constant.

verification.json
  Calculation results, check counts, and Python and dependency versions.

AI ASSISTANCE

ChatGPT was used for proofreading and language polishing.