Pith Number

pith:MWRBAQMO

pith:2010:MWRBAQMO5J7GTH3SLCOP62AJAS

not attested not anchored not stored refs pending

Critical Ising on the square lattice mixes in polynomial time

Allan Sly, Eyal Lubetzky

arxiv:1001.1613 v4 · 2010-01-11 · 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{MWRBAQMO5J7GTH3SLCOP62AJAS}

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	2026-05-18T04:42:34.454019Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65a210418eea7e699f72589cff6809048390f661031192b24e6a769d129cf985

Aliases

arxiv: 1001.1613 · arxiv_version: 1001.1613v4 · doi: 10.48550/arxiv.1001.1613 · pith_short_12: MWRBAQMO5J7G · pith_short_16: MWRBAQMO5J7GTH3S · pith_short_8: MWRBAQMO

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/MWRBAQMO5J7GTH3SLCOP62AJAS \
  | 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: 65a210418eea7e699f72589cff6809048390f661031192b24e6a769d129cf985

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "14cd39267f4ad3a836ec0ca2326f9f8a3a0359d1a397e572710718e5221499f1",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2010-01-11T20:58:58Z",
    "title_canon_sha256": "6b2d26327798406b6ccccdfe4a890a6c69cfea29ebc8810d3fa1fb9fcdfa14ba"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1001.1613",
    "kind": "arxiv",
    "version": 4
  }
}