Pith Number

pith:CLD33PJR

pith:2025:CLD33PJRK4NIXC4RROVQ6PEHVC

not attested not anchored not stored refs pending

Hopf formulae for cocommutative Hopf algebras

Andrea Sciandra, Marino Gran

arxiv:2509.09992 v1 · 2025-09-12 · math.CT · math.QA · math.RA · math.RT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CLD33PJRK4NIXC4RROVQ6PEHVC}

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	2026-07-05T12:09:53.351803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

12c7bdbd31571a8b8b918bab0f3c87a89792641c51739917ae0cc246d7322e27

Aliases

arxiv: 2509.09992 · arxiv_version: 2509.09992v1 · doi: 10.48550/arxiv.2509.09992 · pith_short_12: CLD33PJRK4NI · pith_short_16: CLD33PJRK4NIXC4R · pith_short_8: CLD33PJR

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/CLD33PJRK4NIXC4RROVQ6PEHVC \
  | 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: 12c7bdbd31571a8b8b918bab0f3c87a89792641c51739917ae0cc246d7322e27

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f37614ffbfd3135935fc7b0955f3b7e66ab8c11534d96c4210897f2df67e1119",
    "cross_cats_sorted": [
      "math.QA",
      "math.RA",
      "math.RT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CT",
    "submitted_at": "2025-09-12T06:30:02Z",
    "title_canon_sha256": "1ed5d040237acc775c650d2e0eef13eeaceb0b9dcbc025e3df6ad42f9d0f7e74"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.09992",
    "kind": "arxiv",
    "version": 1
  }
}