Pith Number

pith:VP44H552

pith:2010:VP44H552UC3PQ3G7EXCWNUBFNN

not attested not anchored not stored refs pending

The fundamental group of random 2-complexes

Christopher Hoffman, Eric Babson, Matthew Kahle

arxiv:1010.6043 v2 · 2010-10-28 · math.GR · math.GT · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VP44H552UC3PQ3G7EXCWNUBFNN}

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	2026-05-18T04:22:31.877915Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abf9c3f7baa0b6f86cdf25c566d0256b555b5f5aab735052bba97062e0f95837

Aliases

arxiv: 1010.6043 · arxiv_version: 1010.6043v2 · doi: 10.48550/arxiv.1010.6043 · pith_short_12: VP44H552UC3P · pith_short_16: VP44H552UC3PQ3G7 · pith_short_8: VP44H552

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/VP44H552UC3PQ3G7EXCWNUBFNN \
  | 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: abf9c3f7baa0b6f86cdf25c566d0256b555b5f5aab735052bba97062e0f95837

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "391d48880ec26597699e7a1a9a9b0bf4739e2e535b73302d8c56ee77ebba9182",
    "cross_cats_sorted": [
      "math.GT",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-10-28T18:41:34Z",
    "title_canon_sha256": "a17e0f1e4c5fb27cbeeb31d8c88f8b8ebddf7402bc2c53081c3a204092c9ee55"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.6043",
    "kind": "arxiv",
    "version": 2
  }
}