Pith Number

pith:W4QXNA44

pith:2004:W4QXNA44ANUANMUZ2QYSOQFFNE

not attested not anchored not stored refs pending

Topological approach to phase transitions and inequivalence of statistical ensembles

Michael Kastner

arxiv:cond-mat/0412199 v2 · 2004-12-08 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W4QXNA44ANUANMUZ2QYSOQFFNE}

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	2026-07-04T14:48:06.777804Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b72176839c036806b299d4312740a5691a66b81e3a0a601476e2dcff803499d6

Aliases

arxiv: cond-mat/0412199 · arxiv_version: cond-mat/0412199v2 · doi: 10.48550/arxiv.cond-mat/0412199 · pith_short_12: W4QXNA44ANUA · pith_short_16: W4QXNA44ANUANMUZ · pith_short_8: W4QXNA44

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/W4QXNA44ANUANMUZ2QYSOQFFNE \
  | 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: b72176839c036806b299d4312740a5691a66b81e3a0a601476e2dcff803499d6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "54135adadb5d8deddfcb87c0277710c6c0bda9f5d152fa89a3bcdc953e42fd8d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2004-12-08T13:37:10Z",
    "title_canon_sha256": "e2d0727868ca3fc01c2c379a2ff05a4a9f6afb05401bb735cd1b667c17d9e545"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cond-mat/0412199",
    "kind": "arxiv",
    "version": 2
  }
}