Pith Number

pith:P26K3JVI

pith:2026:P26K3JVIRG3YUNOBB476BC4V6T

not attested not anchored not stored refs pending

Approximate FKG inequalities for phase-bound spin systems, with applications to central limit theorems for exponential random graphs

Satyaki Mukherjee, Vilas Winstein

arxiv:2601.07169 v2 · 2026-01-12 · math.PR · cond-mat.stat-mech · cs.DM · math.CO · 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{P26K3JVIRG3YUNOBB476BC4V6T}

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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	2026-05-21T01:05:14.606823Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7ebcada6a889b78a35c10f3fe08b95f4ffd2f760d5807680bff6a00de2b84896

Aliases

arxiv: 2601.07169 · arxiv_version: 2601.07169v2 · doi: 10.48550/arxiv.2601.07169 · pith_short_12: P26K3JVIRG3Y · pith_short_16: P26K3JVIRG3YUNOB · pith_short_8: P26K3JVI

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/P26K3JVIRG3YUNOBB476BC4V6T \
  | 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: 7ebcada6a889b78a35c10f3fe08b95f4ffd2f760d5807680bff6a00de2b84896

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f4f80980a4b760137d93c0899284322a0ae0e40f95b4c6e1f917ef971a7a7f79",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "cs.DM",
      "math.CO",
      "math.ST",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2026-01-12T03:28:39Z",
    "title_canon_sha256": "7851bd955e938d9a4e0782c88494a74d6e634369eac2e1db2b4b95148632a9b2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.07169",
    "kind": "arxiv",
    "version": 2
  }
}