Pith Number

pith:M4YDMJZM

pith:2009:M4YDMJZMACSH3R6JTNPYWY3OZP

not attested not anchored not stored refs pending

On the mixing time of the 2D stochastic Ising model with "plus" boundary conditions at low temperature

ENS Lyon), F. Martinelli (Matematica, F. Toninelli (CNRS, Roma 3)

arxiv:0905.3040 v2 · 2009-05-19 · 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{M4YDMJZMACSH3R6JTNPYWY3OZP}

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	2026-05-18T04:06:21.251762Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

673036272c00a47dc7c99b5f8b636ecbe4bb5d379beff48740ad6f1e86731957

Aliases

arxiv: 0905.3040 · arxiv_version: 0905.3040v2 · doi: 10.48550/arxiv.0905.3040 · pith_short_12: M4YDMJZMACSH · pith_short_16: M4YDMJZMACSH3R6J · pith_short_8: M4YDMJZM

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/M4YDMJZMACSH3R6JTNPYWY3OZP \
  | 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: 673036272c00a47dc7c99b5f8b636ecbe4bb5d379beff48740ad6f1e86731957

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ca87c612a0b5a8fa52a976d49232709067082000b0ab26afff93d5b6d3bed59d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2009-05-19T08:08:50Z",
    "title_canon_sha256": "b1116e6367a2cd58155505eb62287890a788008b28305e281dfd98b50a58df88"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.3040",
    "kind": "arxiv",
    "version": 2
  }
}