Pith Number

pith:BMRFPDR2

pith:2013:BMRFPDR2XTLCZIVAYSDPLVJGIV

not attested not anchored not stored refs pending

Comparison Theorems for Gibbs Measures

Patrick Rebeschini, Ramon van Handel

arxiv:1308.4117 v1 · 2013-08-19 · math.PR · math-ph · math.MP · math.ST · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BMRFPDR2XTLCZIVAYSDPLVJGIV}

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	2026-05-18T02:28:05.539503Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0b22578e3abcd62ca2a0c486f5d526454b191ba0d40ab7dfd79f528a554d2dc7

Aliases

arxiv: 1308.4117 · arxiv_version: 1308.4117v1 · doi: 10.48550/arxiv.1308.4117 · pith_short_12: BMRFPDR2XTLC · pith_short_16: BMRFPDR2XTLCZIVA · pith_short_8: BMRFPDR2

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/BMRFPDR2XTLCZIVAYSDPLVJGIV \
  | 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: 0b22578e3abcd62ca2a0c486f5d526454b191ba0d40ab7dfd79f528a554d2dc7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fbcbac595a9776151578101ac997f66a0f9371e18140c02c36c39443447075db",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2013-08-19T19:56:56Z",
    "title_canon_sha256": "5e4a4a17ac80882e9359c32abe0d9161c4f29371425c5076da14ed4319010ebd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.4117",
    "kind": "arxiv",
    "version": 1
  }
}