Pith Number

pith:P2YN4YWG

pith:2024:P2YN4YWG7W72BQIWTO7JSIX6R3

not attested not anchored not stored refs pending

Phase Transitions via Complex Extensions of Markov Chains

Chunyang Wang, Jingcheng Liu, Yitong Yin, Yixiao Yu

arxiv:2411.06857 v2 · 2024-11-11 · cs.DS · cs.DM · 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{P2YN4YWG7W72BQIWTO7JSIX6R3}

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	2026-07-05T09:56:02.170682Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7eb0de62c6fdbfa0c1169bbe9922fe8ee886c7ac2560d210fa73afd96d6bba09

Aliases

arxiv: 2411.06857 · arxiv_version: 2411.06857v2 · doi: 10.48550/arxiv.2411.06857 · pith_short_12: P2YN4YWG7W72 · pith_short_16: P2YN4YWG7W72BQIW · pith_short_8: P2YN4YWG

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/P2YN4YWG7W72BQIWTO7JSIX6R3 \
  | 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: 7eb0de62c6fdbfa0c1169bbe9922fe8ee886c7ac2560d210fa73afd96d6bba09

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "37b893a5204ab20493ed5528daca6ccf82f0fb401bed14b365f59dbc7ff53626",
    "cross_cats_sorted": [
      "cs.DM",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2024-11-11T10:40:43Z",
    "title_canon_sha256": "f05ceeafb55abae0e722f802f1966389855956f022f6048ae4a3defe6ba7762a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.06857",
    "kind": "arxiv",
    "version": 2
  }
}