Pith Number

pith:T725PT37

pith:2012:T725PT37CYZO65ZEKI74ATGPOG

not attested not anchored not stored refs pending

Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems

David Ruelle, Eugene R. Speer, Joel L. Lebowitz

arxiv:1204.0558 v2 · 2012-04-02 · cond-mat.stat-mech · 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{T725PT37CYZO65ZEKI74ATGPOG}

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	2026-05-18T01:57:57.849641Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ff5d7cf7f1632ef7724523fc04ccf719dd2c0f948efbb64e0e8aac42ce71d33

Aliases

arxiv: 1204.0558 · arxiv_version: 1204.0558v2 · doi: 10.48550/arxiv.1204.0558 · pith_short_12: T725PT37CYZO · pith_short_16: T725PT37CYZO65ZE · pith_short_8: T725PT37

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/T725PT37CYZO65ZEKI74ATGPOG \
  | 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: 9ff5d7cf7f1632ef7724523fc04ccf719dd2c0f948efbb64e0e8aac42ce71d33

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "40a5fd5e6f0feb0c7c2e98402c5f8004d65ab57208f2d0a82f6284dd9448aa59",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2012-04-02T23:48:38Z",
    "title_canon_sha256": "db39290fc556520170d5b4e7386103511f12e4c28def002925b2f34a44dde3ac"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1204.0558",
    "kind": "arxiv",
    "version": 2
  }
}