Pith Number

pith:NIJW5N4P

pith:2015:NIJW5N4P245ASYMV74XPHERDI2

not attested not anchored not stored refs pending

Continuity of the phase transition for planar random-cluster and Potts models with $1\le q\le4$

Hugo Duminil-Copin, Vincent Tassion, Vladas Sidoravicius

arxiv:1505.04159 v1 · 2015-05-15 · 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{NIJW5N4P245ASYMV74XPHERDI2}

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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	2026-05-18T01:00:40.642099Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6a136eb78fd73a096195ff2ef39223468ea8b525d3c0b147a70839c23bdeb9bf

Aliases

arxiv: 1505.04159 · arxiv_version: 1505.04159v1 · doi: 10.48550/arxiv.1505.04159 · pith_short_12: NIJW5N4P245A · pith_short_16: NIJW5N4P245ASYMV · pith_short_8: NIJW5N4P

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/NIJW5N4P245ASYMV74XPHERDI2 \
  | 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: 6a136eb78fd73a096195ff2ef39223468ea8b525d3c0b147a70839c23bdeb9bf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "47e29040f4d7477625fe7d553aca6e17d38ddeb3ae0d5b6adfbd36d8dab0bc76",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2015-05-15T18:57:16Z",
    "title_canon_sha256": "8be4ff029133e7d19455a53600f8c28e5ec3c335af841f7049b3c61c3ca4289d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1505.04159",
    "kind": "arxiv",
    "version": 1
  }
}