Pith Number

pith:O7Z4PUKW

pith:2018:O7Z4PUKW3UZH3EPOD4RNPSCEAU

not attested not anchored not stored refs pending

Critical point for infinite cycles in a random loop model on trees

Alan Hammond, Milind Hegde

arxiv:1805.11772 v1 · 2018-05-30 · 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{O7Z4PUKW3UZH3EPOD4RNPSCEAU}

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	2026-05-18T00:14:36.568431Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

77f3c7d156dd327d91ee1f22d7c8440528ef5b03b8a8081840f1fbbeed767457

Aliases

arxiv: 1805.11772 · arxiv_version: 1805.11772v1 · doi: 10.48550/arxiv.1805.11772 · pith_short_12: O7Z4PUKW3UZH · pith_short_16: O7Z4PUKW3UZH3EPO · pith_short_8: O7Z4PUKW

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/O7Z4PUKW3UZH3EPOD4RNPSCEAU \
  | 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: 77f3c7d156dd327d91ee1f22d7c8440528ef5b03b8a8081840f1fbbeed767457

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c1952ba8596d4c6141fa063f80436a887e6664c904954e1479e768d77011aef9",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-05-30T01:55:58Z",
    "title_canon_sha256": "74de3af925daba3f8e66b51f22dfc1a32edae313fb097be2494091f83d8afa49"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1805.11772",
    "kind": "arxiv",
    "version": 1
  }
}