Pith Number

pith:66VTPTQ2

pith:2012:66VTPTQ26GLKYCQ4OQGXDED7HS

not attested not anchored not stored refs pending

Infinite cycles in the random stirring model on trees

Alan Hammond

arxiv:1202.1319 v2 · 2012-02-07 · math.PR · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{66VTPTQ26GLKYCQ4OQGXDED7HS}

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	2026-05-18T03:27:32.970762Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f7ab37ce1af196ac0a1c740d71907f3c99258464cd21c2152a9c0f4ae29c7170

Aliases

arxiv: 1202.1319 · arxiv_version: 1202.1319v2 · doi: 10.48550/arxiv.1202.1319 · pith_short_12: 66VTPTQ26GLK · pith_short_16: 66VTPTQ26GLKYCQ4 · pith_short_8: 66VTPTQ2

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/66VTPTQ26GLKYCQ4OQGXDED7HS \
  | 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: f7ab37ce1af196ac0a1c740d71907f3c99258464cd21c2152a9c0f4ae29c7170

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4247140e80c0970cdfc81aed06c1fbc104e23c01e2091e36adbf0f3fce7994dc",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2012-02-07T00:18:01Z",
    "title_canon_sha256": "7e67d9944f87a61289662b0c663fd7ab19c7ad7fbb4d4a3a733ab939df444e3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1202.1319",
    "kind": "arxiv",
    "version": 2
  }
}