Pith Number

pith:2CTBTAUO

pith:1999:2CTBTAUOP3LJOZ2ODX47KW333N

not attested not anchored not stored refs pending

A remark on the notion of robust phase transitions

Aernout C.D. van Enter

arxiv:math-ph/9911011 v1 · 1999-11-09 · math-ph · cond-mat.stat-mech · math.MP · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2CTBTAUOP3LJOZ2ODX47KW333N}

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	2026-05-18T01:38:30.451152Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d0a619828e7ed697674e1df9f55b7bdb4f1aa635cfa7990f24a58cd219775ab2

Aliases

arxiv: math-ph/9911011 · arxiv_version: math-ph/9911011v1 · doi: 10.48550/arxiv.math-ph/9911011 · pith_short_12: 2CTBTAUOP3LJ · pith_short_16: 2CTBTAUOP3LJOZ2O · pith_short_8: 2CTBTAUO

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/2CTBTAUOP3LJOZ2ODX47KW333N \
  | 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: d0a619828e7ed697674e1df9f55b7bdb4f1aa635cfa7990f24a58cd219775ab2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bb4ef8763d77b57311d01e509392a761bc0aab431a9e0b7b81b8d87f487aa80b",
    "cross_cats_sorted": [
      "cond-mat.stat-mech",
      "math.MP",
      "math.PR"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "1999-11-09T12:42:59Z",
    "title_canon_sha256": "dbc39cd140486ed6e3f881b79e228fbe23da918c61cf4392b3af2c11936a2bc6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/9911011",
    "kind": "arxiv",
    "version": 1
  }
}