Pith Number

pith:EOXE2NOW

pith:2016:EOXE2NOWYUGMA3MHA2X2U2UTFP

not attested not anchored not stored refs pending

Discontinuity of the phase transition for the planar random-cluster and Potts models with $q>4$

Hugo Duminil-Copin, Ioan Manolescu, Matan Harel, Maxime Gagnebin, Vincent Tassion

arxiv:1611.09877 v2 · 2016-11-29 · 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{EOXE2NOWYUGMA3MHA2X2U2UTFP}

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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.

Cited by

1 paper in Pith

Topological symmetry in quantum field theory

Receipt and verification

First computed	2026-05-18T00:36:03.693035Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

23ae4d35d6c50cc06d8706afaa6a932be1706f2170bbb175a920bf5dff59c4f3

Aliases

arxiv: 1611.09877 · arxiv_version: 1611.09877v2 · doi: 10.48550/arxiv.1611.09877 · pith_short_12: EOXE2NOWYUGM · pith_short_16: EOXE2NOWYUGMA3MH · pith_short_8: EOXE2NOW

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/EOXE2NOWYUGMA3MHA2X2U2UTFP \
  | 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: 23ae4d35d6c50cc06d8706afaa6a932be1706f2170bbb175a920bf5dff59c4f3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "72e76c6941e1c3833efb26247e4cebb36c0d4c9caa07cd73ac97e4c08cb32618",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2016-11-29T21:09:21Z",
    "title_canon_sha256": "20d01b19ba8818206fd19db78b00315ba111ad40c5ce7937022198cbea3b9318"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.09877",
    "kind": "arxiv",
    "version": 2
  }
}