Pith Number

pith:COJBC24P

pith:2009:COJBC24PZEA7J63ALJDKMWGWRI

not attested not anchored not stored refs pending

Collapses, products and LC manifolds

Bruno Benedetti

arxiv:0911.4656 v2 · 2009-11-24 · math.GT · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{COJBC24PZEA7J63ALJDKMWGWRI}

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	2026-05-18T04:18:34.844782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1392116b8fc901f4fb605a46a658d68a1015bc0020dfa2f4bba02013e4cb9fb7

Aliases

arxiv: 0911.4656 · arxiv_version: 0911.4656v2 · doi: 10.48550/arxiv.0911.4656 · pith_short_12: COJBC24PZEA7 · pith_short_16: COJBC24PZEA7J63A · pith_short_8: COJBC24P

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/COJBC24PZEA7J63ALJDKMWGWRI \
  | 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: 1392116b8fc901f4fb605a46a658d68a1015bc0020dfa2f4bba02013e4cb9fb7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ad1eedd583b5aafbdae930607b8d66f681b279547d8734716377183848ba58b",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-11-24T16:16:57Z",
    "title_canon_sha256": "0adceb0617581e403300f5f620d23e7f5bf3a51cd11992a14bde02690e5df049"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0911.4656",
    "kind": "arxiv",
    "version": 2
  }
}