Pith Number

pith:NXD7ZKS2

pith:2012:NXD7ZKS2PGMIECNKTGGZU64SE2

not attested not anchored not stored refs pending

The paramagnetic and glass transitions in sudoku

Alex Williams, Graeme .J. Ackland

arxiv:1212.1649 v1 · 2012-12-07 · 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{NXD7ZKS2PGMIECNKTGGZU64SE2}

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	2026-05-18T03:38:56.721337Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6dc7fcaa5a79988209aa998d9a7b922683ad1e66c86bfed47b0c687b6d561409

Aliases

arxiv: 1212.1649 · arxiv_version: 1212.1649v1 · doi: 10.48550/arxiv.1212.1649 · pith_short_12: NXD7ZKS2PGMI · pith_short_16: NXD7ZKS2PGMIECNK · pith_short_8: NXD7ZKS2

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/NXD7ZKS2PGMIECNKTGGZU64SE2 \
  | 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: 6dc7fcaa5a79988209aa998d9a7b922683ad1e66c86bfed47b0c687b6d561409

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d9b7cc0f2c4b56e32db593163bd9cb2882c584f7e5bc71c8df3bee903089f74a",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-12-07T16:36:33Z",
    "title_canon_sha256": "30f0b507bfe2ba2e07c36ce7d18de4fe1b235e90c9692983d50ebce9686368cf"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.1649",
    "kind": "arxiv",
    "version": 1
  }
}