Pith Number

pith:MFRXJ6IE

pith:2026:MFRXJ6IED7KQN2RDQSMS4PFMQT

not attested not anchored not stored refs pending

A Cluster Expansion and the Decay of Correlations of the 1D Long-Range Ising Model at Low Temperatures

Henrique Corsini, Rodrigo Bissacot

arxiv:2602.12447 v2 · 2026-02-12 · math-ph · cond-mat.stat-mech · math.MP · physics.class-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MFRXJ6IED7KQN2RDQSMS4PFMQT}

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	2026-06-01T01:02:34.205583Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

616374f9041fd506ea2384992e3cac84f5b6d8e6b596ace0a2c0dfa071062149

Aliases

arxiv: 2602.12447 · arxiv_version: 2602.12447v2 · doi: 10.48550/arxiv.2602.12447 · pith_short_12: MFRXJ6IED7KQ · pith_short_16: MFRXJ6IED7KQN2RD · pith_short_8: MFRXJ6IE

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/MFRXJ6IED7KQN2RDQSMS4PFMQT \
  | 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: 616374f9041fd506ea2384992e3cac84f5b6d8e6b596ace0a2c0dfa071062149

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "57fab2d5d42a934b392598858a42e0eead54e6cd56822056fd5df32a24223924",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.MP",
      "physics.class-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-02-12T22:11:52Z",
    "title_canon_sha256": "30028c9f65baea4159ed1256886cd4643acdac34d345a69e1cf86a6d85477fd4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.12447",
    "kind": "arxiv",
    "version": 2
  }
}