Pith Number

pith:NVPJX3T7

pith:2005:NVPJX3T762T5TH3NTXH4WJ2K2Z

not attested not anchored not stored refs pending

An ergodic action of the outer automorphism group of a free group

William M. Goldman

arxiv:math/0506401 v3 · 2005-06-20 · math.DG · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NVPJX3T762T5TH3NTXH4WJ2K2Z}

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	2026-05-18T04:18:33.416380Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d5e9bee7ff6a7d99f6d9dcfcb274ad66d7de33db858744cb7ed65f3ceb05e25

Aliases

arxiv: math/0506401 · arxiv_version: math/0506401v3 · doi: 10.48550/arxiv.math/0506401 · pith_short_12: NVPJX3T762T5 · pith_short_16: NVPJX3T762T5TH3N · pith_short_8: NVPJX3T7

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/NVPJX3T762T5TH3NTXH4WJ2K2Z \
  | 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: 6d5e9bee7ff6a7d99f6d9dcfcb274ad66d7de33db858744cb7ed65f3ceb05e25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5cfcd823bbd84275ce2922cdf80b0825b8a38e429fc39c932d4c1a35c8afe056",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "",
    "primary_cat": "math.DG",
    "submitted_at": "2005-06-20T14:54:17Z",
    "title_canon_sha256": "c149da0aab710901e043a327b65a002b0f93a90ff621ff2372c5b4ff8e15e211"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0506401",
    "kind": "arxiv",
    "version": 3
  }
}