Pith Number

pith:HJPGJ73Q

pith:2016:HJPGJ73QZ4WRSVB4JIBA26GJES

not attested not anchored not stored refs pending

The phase transitions of the random-cluster and Potts models on slabs with $q \geq 1$ are sharp

Aran Raoufi, Ioan Manolescu

arxiv:1604.01299 v1 · 2016-04-05 · 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{HJPGJ73QZ4WRSVB4JIBA26GJES}

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	2026-07-05T03:41:21.501387Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3a5e64ff70cf2d19543c4a020d78c924aacc167158600b3d96278ba3bd6bcc3a

Aliases

arxiv: 1604.01299 · arxiv_version: 1604.01299v1 · doi: 10.48550/arxiv.1604.01299 · pith_short_12: HJPGJ73QZ4WR · pith_short_16: HJPGJ73QZ4WRSVB4 · pith_short_8: HJPGJ73Q

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/HJPGJ73QZ4WRSVB4JIBA26GJES \
  | 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: 3a5e64ff70cf2d19543c4a020d78c924aacc167158600b3d96278ba3bd6bcc3a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3980e146ba8ff1a4115f3a7afa7154c9f0704ed876b89036e6a9cb8a6cb9322",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-04-05T15:28:57Z",
    "title_canon_sha256": "518813b9bb0bc14c1274caff320a288ea63b79b0253b696083e41c2df30cece2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.01299",
    "kind": "arxiv",
    "version": 1
  }
}