Pith Number

pith:KT3QHRWR

pith:2013:KT3QHRWRKULMGDHFOJXANSFFFS

not attested not anchored not stored refs pending

Phase transition free regions in the Ising model via the Kac-Ward operator

Marcin Lis

arxiv:1306.2253 v2 · 2013-06-10 · math-ph · 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{KT3QHRWRKULMGDHFOJXANSFFFS}

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	2026-05-18T02:07:32.203544Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

54f703c6d15516c30ce5726e06c8a52ca2d5a43844a119ad85c7f75624e267c8

Aliases

arxiv: 1306.2253 · arxiv_version: 1306.2253v2 · doi: 10.48550/arxiv.1306.2253 · pith_short_12: KT3QHRWRKULM · pith_short_16: KT3QHRWRKULMGDHF · pith_short_8: KT3QHRWR

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/KT3QHRWRKULMGDHFOJXANSFFFS \
  | 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: 54f703c6d15516c30ce5726e06c8a52ca2d5a43844a119ad85c7f75624e267c8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "36ea4b41177f1138f15fd72fa3f2aae894cae729ca507a4c2c6c685a483578c6",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2013-06-10T17:30:19Z",
    "title_canon_sha256": "e8156bb9e23f527cf27f6e916bbbbc7abeff22cf1716ab22c355eac63dc8c4cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1306.2253",
    "kind": "arxiv",
    "version": 2
  }
}