Pith Number

pith:UOIA23YM

pith:2012:UOIA23YMUQ2ST6WPR3A5BQU47Q

not attested not anchored not stored refs pending

Hopf algebra structure of incidence algebras

Dieter Denneberg

arxiv:1209.1229 v2 · 2012-09-06 · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UOIA23YMUQ2ST6WPR3A5BQU47Q}

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	2026-05-18T03:45:20.794174Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3900d6f0ca43529facf8ec1d0c29cfc011438306ad0f4f5e540fdaec425d37d

Aliases

arxiv: 1209.1229 · arxiv_version: 1209.1229v2 · doi: 10.48550/arxiv.1209.1229 · pith_short_12: UOIA23YMUQ2S · pith_short_16: UOIA23YMUQ2ST6WP · pith_short_8: UOIA23YM

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/UOIA23YMUQ2ST6WPR3A5BQU47Q \
  | 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: a3900d6f0ca43529facf8ec1d0c29cfc011438306ad0f4f5e540fdaec425d37d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02d69856dde329915d310eed5cb8cb256cce13840ff68e1461733e832102dc42",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-09-06T08:59:27Z",
    "title_canon_sha256": "ad9905a92ba6e7cb2eeda52e662e5a6347756e946b7c2b911c1935f52ecbf4cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1229",
    "kind": "arxiv",
    "version": 2
  }
}