Pith Number

pith:PAAG4KPY

pith:2010:PAAG4KPYXHM7PA2JHZKS5ZGPS7

not attested not anchored not stored refs pending

Partition functions of the Ising model on some self-similar Schreier graphs

Alfredo Donno, Daniele D'Angeli, Tatiana Nagnibeda

arxiv:1003.0611 v1 · 2010-03-02 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PAAG4KPYXHM7PA2JHZKS5ZGPS7}

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	2026-05-18T04:21:22.865105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78006e29f8b9d9f783493e552ee4cf97e6d8bc64c507e693eb7f55b45755240c

Aliases

arxiv: 1003.0611 · arxiv_version: 1003.0611v1 · doi: 10.48550/arxiv.1003.0611 · pith_short_12: PAAG4KPYXHM7 · pith_short_16: PAAG4KPYXHM7PA2J · pith_short_8: PAAG4KPY

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/PAAG4KPYXHM7PA2JHZKS5ZGPS7 \
  | 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: 78006e29f8b9d9f783493e552ee4cf97e6d8bc64c507e693eb7f55b45755240c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1d080a410aadc481896f54d6eceb2e9b53024caad6fbd72a669ac9cf6eecc40",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2010-03-02T15:05:46Z",
    "title_canon_sha256": "4f42824209e09377f86745639b1704ed814204fcd20dde52b6fb206b48af1248"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1003.0611",
    "kind": "arxiv",
    "version": 1
  }
}