Pith Number

pith:MZA4BF2Z

pith:2004:MZA4BF2ZXSGALVWMB2V4QGM5TH

not attested not anchored not stored refs pending

Phase ordering after a deep quench: the stochastic Ising and hard core gas models on a tree

Fabio Martinelli, Pietro Caputo

arxiv:math/0412450 v1 · 2004-12-22 · 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{MZA4BF2ZXSGALVWMB2V4QGM5TH}

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	2026-05-18T04:39:51.523255Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6641c09759bc8c05d6cc0eabc8199d99f3090927e60266b4ec07e8ee17678731

Aliases

arxiv: math/0412450 · arxiv_version: math/0412450v1 · doi: 10.48550/arxiv.math/0412450 · pith_short_12: MZA4BF2ZXSGA · pith_short_16: MZA4BF2ZXSGALVWM · pith_short_8: MZA4BF2Z

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/MZA4BF2ZXSGALVWMB2V4QGM5TH \
  | 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: 6641c09759bc8c05d6cc0eabc8199d99f3090927e60266b4ec07e8ee17678731

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "06d88111abef7d0d836f3ca1f230315584e0f2f23557d38649b5ba542b53d4cd",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "2004-12-22T12:12:32Z",
    "title_canon_sha256": "7c7fbf4d4e9276502853e7de0a060dbc6dbdee51b3b033c8cd8858eb77a35fe0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0412450",
    "kind": "arxiv",
    "version": 1
  }
}