Pith Number

pith:X6EKV75D

pith:2009:X6EKV75DDIH25FP5T724AWGV6T

not attested not anchored not stored refs pending

Cocycle deformations for Hopf algebras with a coalgebra projection

Alessandro Ardizzoni, Claudia Menini, Margaret Beattie

arxiv:0906.0239 v3 · 2009-06-01 · 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{X6EKV75DDIH25FP5T724AWGV6T}

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	2026-05-18T04:41:52.909089Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bf88aaffa31a0fae95fd9ff5c058d5f4cc585a5921ef3ba8452c3394b6bfd481

Aliases

arxiv: 0906.0239 · arxiv_version: 0906.0239v3 · doi: 10.48550/arxiv.0906.0239 · pith_short_12: X6EKV75DDIH2 · pith_short_16: X6EKV75DDIH25FP5 · pith_short_8: X6EKV75D

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/X6EKV75DDIH25FP5T724AWGV6T \
  | 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: bf88aaffa31a0fae95fd9ff5c058d5f4cc585a5921ef3ba8452c3394b6bfd481

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b149d5ab1bfa63527bb3fbbe271c12fd56d3ea6d3403ae646e72c6943068a7cd",
    "cross_cats_sorted": [
      "math.RA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.QA",
    "submitted_at": "2009-06-01T08:59:50Z",
    "title_canon_sha256": "5cea82329f385f557519bb29b2dfb5c7bed9020117d48bb7662bb461bc8eea4c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0906.0239",
    "kind": "arxiv",
    "version": 3
  }
}