Pith Number

pith:TNK25XK7

pith:2010:TNK25XK7TSOUUIHXUX4BCYUMHO

not attested not anchored not stored refs pending

Exact Sampling for the Ising Model at all Temperatures

Mario Ullrich

arxiv:1012.3944 v2 · 2010-12-17 · math.PR · 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{TNK25XK7TSOUUIHXUX4BCYUMHO}

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	2026-05-18T02:53:42.020716Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b55aedd5f9c9d4a20f7a5f811628c3b91ae831d75c71394dc7da3f621304dd7

Aliases

arxiv: 1012.3944 · arxiv_version: 1012.3944v2 · doi: 10.48550/arxiv.1012.3944 · pith_short_12: TNK25XK7TSOU · pith_short_16: TNK25XK7TSOUUIHX · pith_short_8: TNK25XK7

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/TNK25XK7TSOUUIHXUX4BCYUMHO \
  | 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: 9b55aedd5f9c9d4a20f7a5f811628c3b91ae831d75c71394dc7da3f621304dd7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d0804c8dc946d8292870125c30ea97bf3e43fe2350a734a514a31422921b9985",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-12-17T18:01:58Z",
    "title_canon_sha256": "ef9c2bf15489f08ea18548c523663aef250caa255afd07cdb8c9b504be5e7a7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.3944",
    "kind": "arxiv",
    "version": 2
  }
}