Pith Number

pith:AFP4SBRU

pith:2010:AFP4SBRUC4I6BSSNO57SXFQXU4

not attested not anchored not stored refs pending

Poincar\'e inequality for Markov random fields via disagreement percolation

F. Redig, F. V\"ollering, J.-R. Chazottes

arxiv:1012.2489 v3 · 2010-12-11 · 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{AFP4SBRUC4I6BSSNO57SXFQXU4}

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	2026-05-18T04:12:44.686439Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

015fc906341711e0ca4d777f2b9617a73824ed5051a69f491aa7f82312b14f6b

Aliases

arxiv: 1012.2489 · arxiv_version: 1012.2489v3 · doi: 10.48550/arxiv.1012.2489 · pith_short_12: AFP4SBRUC4I6 · pith_short_16: AFP4SBRUC4I6BSSN · pith_short_8: AFP4SBRU

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/AFP4SBRUC4I6BSSNO57SXFQXU4 \
  | 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: 015fc906341711e0ca4d777f2b9617a73824ed5051a69f491aa7f82312b14f6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "240934212fd1620bcb67cdf8963390fe86084dc87865771f7b9ab76b1a542776",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-11T21:29:52Z",
    "title_canon_sha256": "3f6e72bd184d9474b993daa4644db4b9567673dfd415aedb07bc1d82abc2ec36"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2489",
    "kind": "arxiv",
    "version": 3
  }
}