Pith Number

pith:MXG5V6DH

pith:2015:MXG5V6DHAVUF52GC5OM6NEPF6J

not attested not anchored not stored refs pending

Props of ribbon graphs, involutive Lie bialgebras and moduli spaces of curves

Sergei Merkulov, Thomas Willwacher

arxiv:1511.07808 v1 · 2015-11-24 · 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{MXG5V6DHAVUF52GC5OM6NEPF6J}

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

2 papers in Pith

A low-valence ribbon graph complex computing the cohomology of $M_{g,m}$

Receipt and verification

First computed	2026-05-18T01:26:03.523160Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65cddaf86705685ee8c2eb99e691e5f2606514cb53728210c3c63d86f2677ac2

Aliases

arxiv: 1511.07808 · arxiv_version: 1511.07808v1 · doi: 10.48550/arxiv.1511.07808 · pith_short_12: MXG5V6DHAVUF · pith_short_16: MXG5V6DHAVUF52GC · pith_short_8: MXG5V6DH

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/MXG5V6DHAVUF52GC5OM6NEPF6J \
  | 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: 65cddaf86705685ee8c2eb99e691e5f2606514cb53728210c3c63d86f2677ac2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c5b62f84287e9b17e8797f2ddad3bd5ce616b295912b34422e8153aff937cabf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2015-11-24T17:09:40Z",
    "title_canon_sha256": "d9198f1f5cfea043fa772001842d93ea10fc81b4df4934ba419f2f6ebeda369a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1511.07808",
    "kind": "arxiv",
    "version": 1
  }
}