Pith Number

pith:PF745J7A

pith:2011:PF745J7ANBQF3PFEQAEEO57T76

not attested not anchored not stored refs pending

Random rigidity in the free group

Alden Walker, Danny Calegari

arxiv:1104.1768 v2 · 2011-04-10 · math.GR · math.DS · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PF745J7ANBQF3PFEQAEEO57T76}

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	2026-05-18T03:19:11.914493Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

797fcea7e068605dbca480084777f3ffa3ada1f7d0e6d421c12165854c3254be

Aliases

arxiv: 1104.1768 · arxiv_version: 1104.1768v2 · doi: 10.48550/arxiv.1104.1768 · pith_short_12: PF745J7ANBQF · pith_short_16: PF745J7ANBQF3PFE · pith_short_8: PF745J7A

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/PF745J7ANBQF3PFEQAEEO57T76 \
  | 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: 797fcea7e068605dbca480084777f3ffa3ada1f7d0e6d421c12165854c3254be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "884b204b9e3601ef3be2b5be6d80107af642d8bf31635cc09cdc1603d3bf9e87",
    "cross_cats_sorted": [
      "math.DS",
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-04-10T14:00:33Z",
    "title_canon_sha256": "07beaef726d4de4d8d8fb5aa298bca8fee9e322b837c6c854c1ee31dfda080b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.1768",
    "kind": "arxiv",
    "version": 2
  }
}