Pith Number

pith:FJ5XCX5G

pith:2006:FJ5XCX5G37AWGC5HPQJ2E4DQBF

not attested not anchored not stored refs pending

First-Order Phase Transition in Potts Models with finite-range interactions

Immacolata Merola, Thierry Gobron (LPTM)

arxiv:math-ph/0609051 v1 · 2006-09-18 · 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{FJ5XCX5G37AWGC5HPQJ2E4DQBF}

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	2026-05-18T02:41:59.902443Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2a7b715fa6dfc1630ba77c13a27070096a1b4a786ea5b16d14e80a4c58eebe30

Aliases

arxiv: math-ph/0609051 · arxiv_version: math-ph/0609051v1 · doi: 10.48550/arxiv.math-ph/0609051 · pith_short_12: FJ5XCX5G37AW · pith_short_16: FJ5XCX5G37AWGC5H · pith_short_8: FJ5XCX5G

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/FJ5XCX5G37AWGC5HPQJ2E4DQBF \
  | 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: 2a7b715fa6dfc1630ba77c13a27070096a1b4a786ea5b16d14e80a4c58eebe30

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "092d7caddd7228dc4e3797fff536b81d4d24ddc2b47c0fa3fc021edd50bb121e",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2006-09-18T13:21:17Z",
    "title_canon_sha256": "86da04cef189485a9febe89216a01a7c56ef3317232656fe733d1fef63ed4a21"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0609051",
    "kind": "arxiv",
    "version": 1
  }
}