Pith Number

pith:A4MLBR4H

pith:2008:A4MLBR4HFPVXODG3YMEDPQFO5B

not attested not anchored not stored refs pending

Gibbsianness and non-Gibbsianness in divide and color models

Andr\'as B\'alint

arxiv:0812.2399 v4 · 2008-12-12 · 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{A4MLBR4HFPVXODG3YMEDPQFO5B}

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	2026-05-18T04:39:08.278811Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0718b0c7872beb770cdbc30837c0aee85cbecfc41bb5cfdfd1a8be5b1ccb59a3

Aliases

arxiv: 0812.2399 · arxiv_version: 0812.2399v4 · doi: 10.48550/arxiv.0812.2399 · pith_short_12: A4MLBR4HFPVX · pith_short_16: A4MLBR4HFPVXODG3 · pith_short_8: A4MLBR4H

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/A4MLBR4HFPVXODG3YMEDPQFO5B \
  | 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: 0718b0c7872beb770cdbc30837c0aee85cbecfc41bb5cfdfd1a8be5b1ccb59a3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0c75506d75bbc48cce30edf2ad21546e3cc1653aca32e1a0abe5be41540b41d",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2008-12-12T15:34:11Z",
    "title_canon_sha256": "eb6c79b3cdca3b05ee7e97826c2c568f50d258eb589f2f712e4dff3f9d2f5b2b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0812.2399",
    "kind": "arxiv",
    "version": 4
  }
}