Pith Number

pith:JW72BQJR

pith:2018:JW72BQJRMEQGZ2UKEPDJCQQ6QN

not attested not anchored not stored refs pending

Phase transition for the interchange and quantum Heisenberg models on the Hamming graph

Micha{\l} Kotowski, Piotr Mi{\l}o\'s, Rados{\l}aw Adamczak

arxiv:1808.08902 v2 · 2018-08-27 · 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{JW72BQJRMEQGZ2UKEPDJCQQ6QN}

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.

Cited by

1 paper in Pith

Critical Parameters for Loop and Bernoulli Percolation

Receipt and verification

First computed	2026-07-05T02:25:09.452477Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4dbfa0c13161206cea8a23c691421e835faf36a65731cfb4d725acd6b11bb345

Aliases

arxiv: 1808.08902 · arxiv_version: 1808.08902v2 · doi: 10.48550/arxiv.1808.08902 · pith_short_12: JW72BQJRMEQG · pith_short_16: JW72BQJRMEQGZ2UK · pith_short_8: JW72BQJR

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/JW72BQJRMEQGZ2UKEPDJCQQ6QN \
  | 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: 4dbfa0c13161206cea8a23c691421e835faf36a65731cfb4d725acd6b11bb345

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9fbfed33271117e8f2ef8722e6070df0aaaa9173686a729a4fedf5dbf765f28e",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2018-08-27T16:10:02Z",
    "title_canon_sha256": "d00734bd131788b706a3f7b390f35a8494390a1cd2d583cb49d4d4d848b8f9d6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.08902",
    "kind": "arxiv",
    "version": 2
  }
}