Pith Number

pith:6TX4NWCI

pith:2019:6TX4NWCIPRSPTNST642HSVK5DR

not attested not anchored not stored refs pending

A short proof of the discontinuity of phase transition in the planar random-cluster model with $q>4$

Gourab Ray, Yinon Spinka

arxiv:1904.10557 v1 · 2019-04-23 · 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{6TX4NWCIPRSPTNST642HSVK5DR}

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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

Finitary codings for gradient models and a new graphical representation for the six-vertex model

Receipt and verification

First computed	2026-07-05T01:46:40.908775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4efc6d8487c64f9b653f73479555d1c5721815d8be633546dab2cebbe60c3c9

Aliases

arxiv: 1904.10557 · arxiv_version: 1904.10557v1 · doi: 10.48550/arxiv.1904.10557 · pith_short_12: 6TX4NWCIPRSP · pith_short_16: 6TX4NWCIPRSPTNST · pith_short_8: 6TX4NWCI

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/6TX4NWCIPRSPTNST642HSVK5DR \
  | 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: f4efc6d8487c64f9b653f73479555d1c5721815d8be633546dab2cebbe60c3c9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a0244c3d56b809a23aca9697a351a8dc3679760c6d1be90753a5d1ff45885a81",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-04-23T22:27:49Z",
    "title_canon_sha256": "2463b08a35b3e67d4557da6d981cc0a4a213f9c3ca3a0f07363a9523e16514f3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1904.10557",
    "kind": "arxiv",
    "version": 1
  }
}