Pith Number

pith:OEB7D4KX

pith:2019:OEB7D4KXTYTPCLUEPYCFRSSZ7D

not attested not anchored not stored refs pending

The Lie bracket of undirected curves on a surface

Arpan Kabiraj, Moira Chas

arxiv:1910.08991 v2 · 2019-10-20 · math.GR · 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{OEB7D4KXTYTPCLUEPYCFRSSZ7D}

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

A family of algebraic operations extending the Turaev cobracket

Receipt and verification

First computed	2026-07-05T01:59:09.777067Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7103f1f1579e26f12e847e0458ca59f8da31a0c368417a8ab5d03a1ce0b43147

Aliases

arxiv: 1910.08991 · arxiv_version: 1910.08991v2 · doi: 10.48550/arxiv.1910.08991 · pith_short_12: OEB7D4KXTYTP · pith_short_16: OEB7D4KXTYTPCLUE · pith_short_8: OEB7D4KX

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/OEB7D4KXTYTPCLUEPYCFRSSZ7D \
  | 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: 7103f1f1579e26f12e847e0458ca59f8da31a0c368417a8ab5d03a1ce0b43147

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9da16a26f105688b57a9abf887024f40cca17b278b4d16ed4779cf89e2a6f319",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2019-10-20T14:33:37Z",
    "title_canon_sha256": "ee264827b79d8a8a295013a37ed9d4241b67669876073962755b0bae32577582"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1910.08991",
    "kind": "arxiv",
    "version": 2
  }
}