Pith Number

pith:6HVF7X2E

pith:2010:6HVF7X2EGYLRQQRRQKB2DXCAQX

not attested not anchored not stored refs pending

Free and cofree Hopf algebras

Lo\"ic Foissy (LM-Reims)

arxiv:1010.5402 v3 · 2010-10-26 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6HVF7X2EGYLRQQRRQKB2DXCAQX}

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	2026-05-18T04:19:33.416942Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f1ea5fdf4436171842318283a1dc4085def6ef3e0a8c980a1eeefcb4aaf49805

Aliases

arxiv: 1010.5402 · arxiv_version: 1010.5402v3 · doi: 10.48550/arxiv.1010.5402 · pith_short_12: 6HVF7X2EGYLR · pith_short_16: 6HVF7X2EGYLRQQRR · pith_short_8: 6HVF7X2E

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/6HVF7X2EGYLRQQRRQKB2DXCAQX \
  | 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: f1ea5fdf4436171842318283a1dc4085def6ef3e0a8c980a1eeefcb4aaf49805

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a18e7355ef5b9664ecfad3c5806784b2e9039b717809e9e0a9e132cd8de0e86f",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2010-10-26T14:13:09Z",
    "title_canon_sha256": "a1bebdfeae1d6974dfe41fe7c6df43d3e966a819233ea644cf5e671133de1d2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.5402",
    "kind": "arxiv",
    "version": 3
  }
}