Pith Number

pith:XLZRHRCU

pith:2024:XLZRHRCU6QSOPFITCW2PUKWDWR

not attested not anchored not stored refs pending

On the Euler characteristic of the commutative graph complex and the top weight cohomology of $\mathcal M_g$

Don Zagier, Michael Borinsky

arxiv:2405.04190 v2 · 2024-05-07 · math.AT · math-ph · math.AG · math.CO · math.MP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XLZRHRCU6QSOPFITCW2PUKWDWR}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Cited by

1 paper in Pith

The 11-loop graph cohomology

Receipt and verification

First computed	2026-07-05T08:56:19.637353Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

baf313c454f424e7951315b4fa2ac3b446219e2cc907e0029a484fcea55febdf

Aliases

arxiv: 2405.04190 · arxiv_version: 2405.04190v2 · doi: 10.48550/arxiv.2405.04190 · pith_short_12: XLZRHRCU6QSO · pith_short_16: XLZRHRCU6QSOPFIT · pith_short_8: XLZRHRCU

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/XLZRHRCU6QSOPFITCW2PUKWDWR \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: baf313c454f424e7951315b4fa2ac3b446219e2cc907e0029a484fcea55febdf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8b4a4340ce7990f5c9028b8d104fbf7c4be955852b50b57edf34593545d2021a",
    "cross_cats_sorted": [
      "math-ph",
      "math.AG",
      "math.CO",
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2024-05-07T10:52:25Z",
    "title_canon_sha256": "129539e06075297bf5376afa8880717a4bc9c59d086f15dd2b5a8862ebfdb484"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2405.04190",
    "kind": "arxiv",
    "version": 2
  }
}