Pith Number

pith:QWPZMYR5

pith:2017:QWPZMYR5XW3AMXZLPQGECJDSR2

not attested not anchored not stored refs pending

Sharp phase transition for the random-cluster and Potts models via decision trees

Aran Raoufi, Hugo Duminil-Copin, Vincent Tassion

arxiv:1705.03104 v2 · 2017-05-08 · 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{QWPZMYR5XW3AMXZLPQGECJDSR2}

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	2026-05-17T23:57:32.899437Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

859f96623dbdb6065f2b7c0c4124728eb5d5309294b9e8abd95b6ecdd75f6518

Aliases

arxiv: 1705.03104 · arxiv_version: 1705.03104v2 · doi: 10.48550/arxiv.1705.03104 · pith_short_12: QWPZMYR5XW3A · pith_short_16: QWPZMYR5XW3AMXZL · pith_short_8: QWPZMYR5

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/QWPZMYR5XW3AMXZLPQGECJDSR2 \
  | 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: 859f96623dbdb6065f2b7c0c4124728eb5d5309294b9e8abd95b6ecdd75f6518

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3764ee1ebf3ccf412a22989975494d8d9f78e266cbc01459c01a6489552bdc1",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2017-05-08T22:05:54Z",
    "title_canon_sha256": "897f35043ee6c3b582d74a7d5ff79b9223a673bdd16b42a799da7d5bea830151"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1705.03104",
    "kind": "arxiv",
    "version": 2
  }
}