Pith Number

pith:56MQPOQ2

pith:2012:56MQPOQ2RAXNMD76NVEGBI6CV4

not attested not anchored not stored refs pending

A manifold of pure Gibbs states of the Ising model on a Cayley tree

Daniel Gandolfo, Jean Ruiz, Senya Shlosman

arxiv:1207.0983 v1 · 2012-07-04 · 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{56MQPOQ2RAXNMD76NVEGBI6CV4}

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	2026-05-18T01:56:34.908817Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ef9907ba1a882ed60ffe6d4860a3c2af02b3a1e5cad69027b0b9ab3975d09740

Aliases

arxiv: 1207.0983 · arxiv_version: 1207.0983v1 · doi: 10.48550/arxiv.1207.0983 · pith_short_12: 56MQPOQ2RAXN · pith_short_16: 56MQPOQ2RAXNMD76 · pith_short_8: 56MQPOQ2

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/56MQPOQ2RAXNMD76NVEGBI6CV4 \
  | 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: ef9907ba1a882ed60ffe6d4860a3c2af02b3a1e5cad69027b0b9ab3975d09740

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dad578ecfdbb98164eae5310bb52c86253c4899ddcfecf5267a89d43206e009f",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2012-07-04T13:56:34Z",
    "title_canon_sha256": "68677c8e48c075792231eceaae1d2d3d9f65277af94b2409c859aba40bfffdbe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1207.0983",
    "kind": "arxiv",
    "version": 1
  }
}