Pith Number

pith:U43QGGEZ

pith:1999:U43QGGEZFT3TI2YO4PUJD6C72R

not attested not anchored not stored refs pending

The random geometry of equilibrium phases

C. Maes, H.-O. Georgii, O. H\"aggstr\"om

arxiv:math/9905031 v1 · 1999-05-05 · math.PR · 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{U43QGGEZFT3TI2YO4PUJD6C72R}

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	2026-05-18T01:05:33.079417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7370318992cf7346b0ee3e891f85fd465016c3c255b36fee73a8d9221934cfd

Aliases

arxiv: math/9905031 · arxiv_version: math/9905031v1 · doi: 10.48550/arxiv.math/9905031 · pith_short_12: U43QGGEZFT3T · pith_short_16: U43QGGEZFT3TI2YO · pith_short_8: U43QGGEZ

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/U43QGGEZFT3TI2YO4PUJD6C72R \
  | 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: a7370318992cf7346b0ee3e891f85fd465016c3c255b36fee73a8d9221934cfd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a55e1c935a37264cfc9f4937597da3b8e3586889922c7c48b9ccfe7b4f510c29",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1999-05-05T16:41:13Z",
    "title_canon_sha256": "1a8d8e68a33714171694e0e952ea11e93ce286df4862fb284a4dfb2013083b1a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9905031",
    "kind": "arxiv",
    "version": 1
  }
}