Pith Number

pith:AAUAPXA3

pith:2012:AAUAPXA36QSKEUGBBDKTHCKRX7

not attested not anchored not stored refs pending

Equivalent crossed products and cross product bialgebras

Florin Panaite

arxiv:1203.0037 v2 · 2012-02-29 · math.QA · 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{AAUAPXA36QSKEUGBBDKTHCKRX7}

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	2026-05-18T03:48:23.226578Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

002807dc1bf424a250c108d5338951bfe25ca3447616cfb04f8569c88372ff99

Aliases

arxiv: 1203.0037 · arxiv_version: 1203.0037v2 · doi: 10.48550/arxiv.1203.0037 · pith_short_12: AAUAPXA36QSK · pith_short_16: AAUAPXA36QSKEUGB · pith_short_8: AAUAPXA3

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/AAUAPXA36QSKEUGBBDKTHCKRX7 \
  | 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: 002807dc1bf424a250c108d5338951bfe25ca3447616cfb04f8569c88372ff99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a206ffc3b725aefea41baa6efcf983618caa3e451443ce8817b6e745c54f942f",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2012-02-29T22:38:52Z",
    "title_canon_sha256": "d6ce34f889e6e4b0d1e04cc33c05682b46722ca88f23a89e937000afa9dd5795"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1203.0037",
    "kind": "arxiv",
    "version": 2
  }
}