Pith Number

pith:SF7GT2DN

pith:2009:SF7GT2DNQAO2R34I6JIURMJQGQ

not attested not anchored not stored refs pending

Mixing time of critical Ising model on trees is polynomial in the height

Eyal Lubetzky, Jian Ding, Yuval Peres

arxiv:0901.4152 v1 · 2009-01-27 · 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{SF7GT2DNQAO2R34I6JIURMJQGQ}

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	2026-05-18T02:14:55.736248Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

917e69e86d801da8ef88f25148b130340c5353ebb2bfb28147bb3080bac447fd

Aliases

arxiv: 0901.4152 · arxiv_version: 0901.4152v1 · doi: 10.48550/arxiv.0901.4152 · pith_short_12: SF7GT2DNQAO2 · pith_short_16: SF7GT2DNQAO2R34I · pith_short_8: SF7GT2DN

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/SF7GT2DNQAO2R34I6JIURMJQGQ \
  | 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: 917e69e86d801da8ef88f25148b130340c5353ebb2bfb28147bb3080bac447fd

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5552e2a926874c227bfad01cd84d02998cdda3b909f3324e008f9a07b404165",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-01-27T01:21:20Z",
    "title_canon_sha256": "536f0056f689bd22e853d56f02d4250065b7018c4d4475e3e97adb0ab8065f89"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0901.4152",
    "kind": "arxiv",
    "version": 1
  }
}