Pith Number

pith:JI45ISQY

pith:2011:JI45ISQY52Y7ODTTS44FLOKFGA

not attested not anchored not stored refs pending

The Lie bialgebra structure of the vector space of cyclic words

Ana Gonz\'alez

arxiv:1111.4709 v1 · 2011-11-21 · math.AT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JI45ISQY52Y7ODTTS44FLOKFGA}

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	2026-05-18T04:08:02.797351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4a39d44a18eeb1f70e73973855b945300d4f93aafbf7b98b55de316cfcb49dc5

Aliases

arxiv: 1111.4709 · arxiv_version: 1111.4709v1 · doi: 10.48550/arxiv.1111.4709 · pith_short_12: JI45ISQY52Y7 · pith_short_16: JI45ISQY52Y7ODTT · pith_short_8: JI45ISQY

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/JI45ISQY52Y7ODTTS44FLOKFGA \
  | 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: 4a39d44a18eeb1f70e73973855b945300d4f93aafbf7b98b55de316cfcb49dc5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b65f8d7da4a9896341278b7905053e83c59f45bd26dd2e7c169599b6e16c75a6",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2011-11-21T00:57:08Z",
    "title_canon_sha256": "d6f77d802ee2f047a3698aa52469a91e824093050afa0461601ecc7eec45364d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1111.4709",
    "kind": "arxiv",
    "version": 1
  }
}