Pith Number

pith:PCVLMIG3

pith:2014:PCVLMIG334PNIZRGZ5GJYWJEJY

not attested not anchored not stored refs pending

The Potts and random-cluster models

Geoffrey R. Grimmett

arxiv:1412.2522 v1 · 2014-12-08 · math.CO · math.PR

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PCVLMIG334PNIZRGZ5GJYWJEJY}

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	2026-05-18T02:31:57.669602Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78aab620dbdf1ed46626cf4c9c59244e1a85cef3eb59575a3ffb2471447921c6

Aliases

arxiv: 1412.2522 · arxiv_version: 1412.2522v1 · doi: 10.48550/arxiv.1412.2522 · pith_short_12: PCVLMIG334PN · pith_short_16: PCVLMIG334PNIZRG · pith_short_8: PCVLMIG3

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/PCVLMIG334PNIZRGZ5GJYWJEJY \
  | 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: 78aab620dbdf1ed46626cf4c9c59244e1a85cef3eb59575a3ffb2471447921c6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0b367ad69743bcb83e55406f523dc6db82306c2da22bbfe2eb12c4072058dac5",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2014-12-08T11:36:13Z",
    "title_canon_sha256": "c71467442ea124afa5181eaa2d10e4b6a9a814a4af81f6f2ba764cd3114e7789"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1412.2522",
    "kind": "arxiv",
    "version": 1
  }
}