Pith Number

pith:YVC746TX

pith:2010:YVC746TXVBXIF6TIDJKPQYSPNB

not attested not anchored not stored refs pending

M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra

Thomas Willwacher

arxiv:1009.1654 v4 · 2010-09-08 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YVC746TXVBXIF6TIDJKPQYSPNB}

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.

Receipt and verification

First computed	2026-05-18T02:26:45.775150Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c545fe7a77a86e82fa681a54f8624f6865f387e2394d2a8f7d6e4028722f791b

Aliases

arxiv: 1009.1654 · arxiv_version: 1009.1654v4 · doi: 10.48550/arxiv.1009.1654 · pith_short_12: YVC746TXVBXI · pith_short_16: YVC746TXVBXIF6TI · pith_short_8: YVC746TX

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/YVC746TXVBXIF6TIDJKPQYSPNB \
  | 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: c545fe7a77a86e82fa681a54f8624f6865f387e2394d2a8f7d6e4028722f791b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ac62da5b6fd71412ac418e60ae4d9039e39f05a64f92f037bc7fbc0c6c8a50be",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2010-09-08T21:17:56Z",
    "title_canon_sha256": "452a90610a90316866fc0cd192cbc95f63c52fe14870cfd47d8661f73e4572b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.1654",
    "kind": "arxiv",
    "version": 4
  }
}