Pith Number

pith:M32BAG5R

pith:2020:M32BAG5RXHAY2D5MTUHAS72G6O

not attested not anchored not stored refs pending

Ising model and s-embeddings of planar graphs

Dmitry Chelkak

arxiv:2006.14559 v5 · 2020-06-25 · math-ph · math.CV · math.MP · 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{M32BAG5RXHAY2D5MTUHAS72G6O}

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	2026-07-05T05:13:27.736756Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

66f4101bb1b9c18d0fac9d0e097f46f3bb042d1aa357d846140ea105a5d70fd6

Aliases

arxiv: 2006.14559 · arxiv_version: 2006.14559v5 · doi: 10.48550/arxiv.2006.14559 · pith_short_12: M32BAG5RXHAY · pith_short_16: M32BAG5RXHAY2D5M · pith_short_8: M32BAG5R

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/M32BAG5RXHAY2D5MTUHAS72G6O \
  | 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: 66f4101bb1b9c18d0fac9d0e097f46f3bb042d1aa357d846140ea105a5d70fd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "afae10e88d57a171e8b1a43e7ce67ba49801d0e42a8c78bd3a10fb6cf03091bd",
    "cross_cats_sorted": [
      "math.CV",
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2020-06-25T17:02:29Z",
    "title_canon_sha256": "0c63c40928de86b40d9fe0b1c37bcc373ff65aca27ecd7fed2aefc97db0f6e68"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2006.14559",
    "kind": "arxiv",
    "version": 5
  }
}