Pith Number

pith:ENI57L7W

pith:2009:ENI57L7WGCBISPVJUDERSGODRJ

not attested not anchored not stored refs pending

The dunce hat in a minimal non-extendably collapsible 3-ball

Bruno Benedetti, Frank H. Lutz

arxiv:0912.3723 v2 · 2009-12-18 · math.AT · math.CO · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{ENI57L7WGCBISPVJUDERSGODRJ}

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	2026-05-18T03:34:48.678391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2351dfaff63082893ea9a0c91919c38a4452a6a75984974555c9c405ffb1a544

Aliases

arxiv: 0912.3723 · arxiv_version: 0912.3723v2 · doi: 10.48550/arxiv.0912.3723 · pith_short_12: ENI57L7WGCBI · pith_short_16: ENI57L7WGCBISPVJ · pith_short_8: ENI57L7W

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/ENI57L7WGCBISPVJUDERSGODRJ \
  | 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: 2351dfaff63082893ea9a0c91919c38a4452a6a75984974555c9c405ffb1a544

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f58eb5bcbda2f8190840442ba6fea59a4b2c7b3880391de56d591a33f947b403",
    "cross_cats_sorted": [
      "math.CO",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AT",
    "submitted_at": "2009-12-18T16:18:04Z",
    "title_canon_sha256": "5dc7b59cbc34a8c91dab2775dfdbe0cdcdfc1191b65d5f315ff330b5adc36949"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.3723",
    "kind": "arxiv",
    "version": 2
  }
}