Pith Number

pith:NPKIO3G3

pith:2012:NPKIO3G37W4IN5KY5UTLMBIR34

not attested not anchored not stored refs pending

Ising Model Observables and Non-Backtracking Walks

Tyler Helmuth

arxiv:1209.3996 v3 · 2012-09-18 · 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{NPKIO3G37W4IN5KY5UTLMBIR34}

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	2026-05-18T02:40:18.917593Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6bd4876cdbfdb886f558ed26b60511df3da8485d5aa4eadee51ad58ede264cba

Aliases

arxiv: 1209.3996 · arxiv_version: 1209.3996v3 · doi: 10.48550/arxiv.1209.3996 · pith_short_12: NPKIO3G37W4I · pith_short_16: NPKIO3G37W4IN5KY · pith_short_8: NPKIO3G3

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/NPKIO3G37W4IN5KY5UTLMBIR34 \
  | 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: 6bd4876cdbfdb886f558ed26b60511df3da8485d5aa4eadee51ad58ede264cba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1d42af5b491f94594bd17c77b126a66f94a7f6a96604e66ee30385fef150aa4f",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-09-18T15:45:21Z",
    "title_canon_sha256": "8f66fe6c66e13d0f17f1b81255aa08dd9ddde0718e29ef78d1ca6cc46098da3f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.3996",
    "kind": "arxiv",
    "version": 3
  }
}