Pith Number

pith:VD6O72U5

pith:2001:VD6O72U5ZZBOVKY3EKYM2QROCH

not attested not anchored not stored refs pending

Combinatorial Lie bialgebras of curves on surfaces

Moira Chas

arxiv:math/0105178 v2 · 2001-05-22 · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VD6O72U5ZZBOVKY3EKYM2QROCH}

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

Quartic BV structures in supercategories and modified necklace Lie bialgebras

Receipt and verification

First computed	2026-07-04T14:49:40.756429Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a8fcefea9dce42eaab1b22b0cd422e11f3ea3858aaef4eadad36601990dc72d7

Aliases

arxiv: math/0105178 · arxiv_version: math/0105178v2 · doi: 10.48550/arxiv.math/0105178 · pith_short_12: VD6O72U5ZZBO · pith_short_16: VD6O72U5ZZBOVKY3 · pith_short_8: VD6O72U5

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/VD6O72U5ZZBOVKY3EKYM2QROCH \
  | 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: a8fcefea9dce42eaab1b22b0cd422e11f3ea3858aaef4eadad36601990dc72d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70265738dd7df0e7983465ee5b67d076ab2eee1c8e55fa33996e2e99fc577eeb",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2001-05-22T14:06:39Z",
    "title_canon_sha256": "f65dd0babb02bfaeddf5f1f153113d3bd54efac5a6f2ca3b0e08d6ad2befceba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0105178",
    "kind": "arxiv",
    "version": 2
  }
}