almanacA0a — the centre of the even hybrid family quantum GL(1)

Tamás Hausel · Institute of Science and Technology Austria

Note

This almanac is part of Project Sandbox: interconnected laboratories for mathematics, where we explore and develop theories with AI agents through reasoning, computation and verification.

The pilot edition. A complete record of one small mathematical result, in three layers, with a per-claim account of what warrants each one.

Start here: open the almanac — or unzip the archive below and open edition/index.html, which needs no network at all.

Whole almanac: Download almanacA0a.zip — it unzips to exactly this folder, except this page and the folder readme-assets/, both updated on 30 October 2026: the logo shows on dark pages, and the links lead to the almanac on ISTA's server.

---

What is in here

This is a publication, not a codebase: the file list above is a table of contents, and GitHub's right-hand column shows the last commit that touched each item rather than what the item is. What they are:

edition/	the almanac itself — the paper, the proof, the formal sources, the concordance, the pages that read them, and the checksums that certify them
almanacA0a.zip	the whole thing as one download; it unzips to exactly this folder, apart from this page and readme-assets/
README.md	this page
readme-assets/	the logo and the three warrant names for this page, in copies that follow a reader's light or dark setting; added on 30 October 2026, outside the deposited archive
index.html	a signpost: opens edition/index.html, so the archive's own address works
AGENTS.md	where an AI assistant should start
CITATION.cff	how to cite the edition
LICENSE	MIT, for everything that runs
LICENSE-CC-BY-4.0	CC BY 4.0, for the text, the mathematics and the data

Inside edition/, the three files a reader is most likely to want are paper.pdf (the mathematics), index.html (the almanac, offline) and CHECKSUMS.txt (proof that every file is the one that was certified).

What an almanac is

An almanac is its own kind of publication — a citable, versioned package a reader downloads: the informal proof a mathematician would read, the computational instrument the calculations actually ran on, and the machine-checked formal development — held together by one file, edition/CONCORDANCE.json, that joins all three layers claim by claim and records what certifies each one.

The concordance — joining the three layers claim by claim — is what turns three parallel archives into a single edition.

What each warrant means

Every result carries exactly one warrant — three different kinds of check.

warrant	what it means	how many
	an argument written for a human reader and refereed	1
	verified by computation over a stated bound, which is part of the claim	2
	a proof kernel checked a proof of that statement	9

A kernel certifies the formal statement. Whether that statement is faithful to the informal one can be decided from the warrants above and the convention frame carried on every row.

Where to go

to…	read
read the mathematics	the paper, 8 pp., edition/paper.pdf
read it at length, without LaTeX	the mathematics explained — for a general reader, edition/almanac.explained.html
look around	the almanac itself — interactive, and offline in edition/index.html
see every statement and its warrant	the twelve statements — edition/statements.html
check any of it independently	how to check it yourself — including installing every piece of software from scratch, edition/FOR_A_HUMAN.md
hand it to an AI assistant	AGENTS.md at the root — it routes to edition/FOR_AN_AI_AGENT.md
rebuild the proofs yourself	edition/replay/ — cd edition/replay && ./replay.sh rebuilds every certified proof from pinned sources and prints the axioms each one used
confirm every file is intact	edition/CHECKSUMS.txt — cd edition && shasum -a 256 -c CHECKSUMS.txt

Links to pages open the published site; links to files open them here. Both work offline: the same paths exist in the archive, which is why every one of them is written out beside its link.

Cite

Tamás Hausel, almanacA0a — the centre of the even hybrid family quantum GL(1), pilot edition of the almanac series, version 0.1.0, 2026. DOI 10.5281/zenodo.22808195 — the deposited edition of record in the EU Open Research Repository; this repository publishes the same bytes.

Licence

MIT for everything that runs; CC BY 4.0 for everything written to be read. Copyright © 2026 Tamás Hausel and the Institute of Science and Technology Austria (ISTA).

what	licence	file
the renderers, the verifier, the Lean sources	MIT	LICENSE
the paper, the proofs, the guides, the concordance, the statement cards	CC BY 4.0	LICENSE-CC-BY-4.0

The split is stated file-by-file in the second file and is meant to be applied mechanically. GitHub's sidebar will say “MIT” — that is the licence a detector can read from LICENSE, and it is the one that governs the code. The mathematics is CC BY 4.0, which asks only that you credit it.

A licence is not a warrant. This says what you may do with the material, and nothing about what is proved or how well — that is the concordance's job, and every claim carries its own warrant.

Reproducing it

The toolchain is pinned to exact versions — a proof that compiles today compiles against that specific Mathlib revision:

• Lean leanprover/lean4:v4.30.0
• Mathlib c5ea00351c28e24afc9f0f84379aa41082b1188f
• Julia 1.12.6, OSCAR 1.8.0 (Manifest.toml is the pin; Project.toml states only ranges)

Everything runs entirely on a local machine, self-contained and service-free. A pinned toolchain makes a re-run possible, not identical — edition/MANIFEST.json → reproducibility_recipe says exactly what the pin does and does not promise.

Citing it

Citable identifiers arrive only with the frozen edition of record, deliberately. An identifier should mean this is citable, and this build's own front page directs citation to the edition of record. CITATION.cff and the DOI both ship with the frozen edition, which is what enters the citable sequence. Editions are versioned, and a later edition supersedes an earlier one while the earlier stays citable exactly as deposited.