render-html.mjs

import { execFileSync } from "node:child_process";
import { readFileSync, writeFileSync } from "node:fs";
import { resolve } from "node:path";

const project = resolve(import.meta.dirname, "../../..");
const source = resolve(import.meta.dirname, "main.tex");
const temporary = resolve(project, "tmp/supertannakian-publication.html");
const output = resolve(project, "app/data/supertannakian-publication.json");

execFileSync("pandoc", [
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  `--output=${temporary}`,
]);

const citationLinks = {
  CS: '<a class="citation" href="https://arxiv.org/abs/2608.13137">[Coulembier--Sherman]</a>',
  Kac: '<a class="citation" href="https://doi.org/10.1016/0001-8708(77)90017-2">[Kac]</a>',
  "Ma Sh": '<span class="citation">[<a href="https://arxiv.org/abs/1111.2387">Masuoka</a>; <a href="https://arxiv.org/abs/2012.11317">Sherman</a>]</span>',
  Wall: '<a class="citation" href="https://doi.org/10.1515/crll.1964.213.187">[Wall]</a>',
};

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const header = `<header id="title-block-header">
<h1 class="title">Absolutely flat finite algebras in<br />characteristic-zero supertannakian categories</h1>
<p class="author">FPRD Lab</p>
<p class="date">Internally audited preprint, 6 September 2026</p>
<div class="abstract">
<div class="abstract-title">Abstract</div>
<p>Coulembier and Sherman ask whether six classical semisimplicity conditions are equivalent for a finite algebra object in a characteristic-zero supertannakian category. We give an affirmative answer. A minimal connected-invariant ideal is differentiably simple, so Kac's theorem identifies it with a simple associative superalgebra tensored with a Grassmann algebra. The Grassmann factor is its canonical supercenter. Coulembier--Sherman's commutative theorem makes that center absolutely flat, and separability of the simple factor transfers flatness to the full algebra. A separate internal <span class="math inline">\\(\\operatorname{Ext}^1\\)</span> argument closes the remaining implication.</p>
</div>
</header>
<aside class="status-boundary"><p><strong>Status: internally audited preprint.</strong> The proof answers Coulembier--Sherman Question 5.16 under its stated algebraically closed, characteristic-zero, finite-algebra hypotheses. It has no external specialist review. A bounded search found no earlier resolution but does not establish priority.</p></aside>`;

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writeFileSync(output, `${JSON.stringify({ html: body }, null, 2)}\n`);