Pith Number

pith:F3SZYITS

pith:2009:F3SZYITSM2EX5TYMIOWNP7UQU2

not attested not anchored not stored refs pending

Absence of phase transitions in a class of integer spin systems

Aldo Procacci, Thiago Morais

arxiv:0907.5432 v1 · 2009-07-30 · 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{F3SZYITSM2EX5TYMIOWNP7UQU2}

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	2026-05-18T02:12:45.960995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2ee59c227266897ecf0c43acd7fe90a6979ad6340a47d4e54991f706340298fb

Aliases

arxiv: 0907.5432 · arxiv_version: 0907.5432v1 · doi: 10.48550/arxiv.0907.5432 · pith_short_12: F3SZYITSM2EX · pith_short_16: F3SZYITSM2EX5TYM · pith_short_8: F3SZYITS

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/F3SZYITSM2EX5TYMIOWNP7UQU2 \
  | 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: 2ee59c227266897ecf0c43acd7fe90a6979ad6340a47d4e54991f706340298fb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fba24ccbb1ffa930754317511dd6451675a90a54184eae23e427641e2c5b67b",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2009-07-30T21:26:05Z",
    "title_canon_sha256": "77ba6ad0745a960a00a90c4d170137f29ffb3635064b8f69278ad6894a7ea809"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0907.5432",
    "kind": "arxiv",
    "version": 1
  }
}