Pith Number

pith:XIWLK5NV

pith:2024:XIWLK5NVC3HJK2CF7MNN66ADGM

not attested not anchored not stored refs pending

Phase Transitions on 1d Long-Range Ising Models with Decaying Fields: A Direct Proof via Contours

Henrique Corsini, Kelvyn Welsch, Lucas Affonso, Rodrigo Bissacot

arxiv:2412.07098 v2 · 2024-12-10 · math-ph · cond-mat.stat-mech · math.MP · math.PR

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Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XIWLK5NVC3HJK2CF7MNN66ADGM}

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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.

Cited by

1 paper in Pith

Phase transitions in low-dimensional long-range random field Ising models

Receipt and verification

First computed	2026-07-05T09:54:49.019210Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ba2cb575b516ce956845fb1adf7803332d75aa76c324a0df87f8fe97b5bde9d2

Aliases

arxiv: 2412.07098 · arxiv_version: 2412.07098v2 · doi: 10.48550/arxiv.2412.07098 · pith_short_12: XIWLK5NVC3HJ · pith_short_16: XIWLK5NVC3HJK2CF · pith_short_8: XIWLK5NV

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/XIWLK5NVC3HJK2CF7MNN66ADGM \
  | 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: ba2cb575b516ce956845fb1adf7803332d75aa76c324a0df87f8fe97b5bde9d2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cc26d63ae06088ebafca5119066d94cc8dc5d7ba98f748b104d2d3aad4456840",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2024-12-10T01:34:13Z",
    "title_canon_sha256": "ceb8aa599ed92bc8895e2efcb23c06a398959e3839bf3094ac2833baa3a2de2c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.07098",
    "kind": "arxiv",
    "version": 2
  }
}