Pith Number

pith:2XSZ75AT

pith:2009:2XSZ75AT3JSO73NUQ5WEDYMQU6

not attested not anchored not stored refs pending

Hopf algebras: motivations and examples

A. Horzela (IFJ-PAN - Polish Academy of Sciences), A. I. Solomon (LPTMC), G. H. E. Duchamp (LIPN), K. A. Penson (LPTMC), P. Blasiak (IFJ-PAN - Polish Academy of Sciences)

arxiv:0912.3866 v1 · 2009-12-19 · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2XSZ75AT3JSO73NUQ5WEDYMQU6}

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	2026-05-18T02:10:15.406088Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d5e59ff413da64efedb4876c41e190a7863af63bd80bfebeeadb00c0ea6b1e54

Aliases

arxiv: 0912.3866 · arxiv_version: 0912.3866v1 · doi: 10.48550/arxiv.0912.3866 · pith_short_12: 2XSZ75AT3JSO · pith_short_16: 2XSZ75AT3JSO73NU · pith_short_8: 2XSZ75AT

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/2XSZ75AT3JSO73NUQ5WEDYMQU6 \
  | 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: d5e59ff413da64efedb4876c41e190a7863af63bd80bfebeeadb00c0ea6b1e54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "39712ce78434576667eedd259acb009551223d7bb552a1c155456a3777e05d5a",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-12-19T06:59:53Z",
    "title_canon_sha256": "fc8be7e70121adef66edbb1f90f713b0a3d8596257df673f47ccca9fa647b7c3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.3866",
    "kind": "arxiv",
    "version": 1
  }
}