Pith Number

pith:TLJPPOYG

pith:2015:TLJPPOYGFFDPYU32WVXVEL44LH

not attested not anchored not stored refs pending

The truncated correlations of the Ising model in any dimension decay exponentially fast at all but the critical temperature

Hugo Duminil-Copin, Michael Aizenman

arxiv:1506.00625 v2 · 2015-06-01 · 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{TLJPPOYGFFDPYU32WVXVEL44LH}

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	2026-05-18T00:09:20.641920Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9ad2f7bb062946fc537ab56f522f9c59f547170fa13117d9c62b02c1ca59fd6b

Aliases

arxiv: 1506.00625 · arxiv_version: 1506.00625v2 · doi: 10.48550/arxiv.1506.00625 · pith_short_12: TLJPPOYGFFDP · pith_short_16: TLJPPOYGFFDPYU32 · pith_short_8: TLJPPOYG

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/TLJPPOYGFFDPYU32WVXVEL44LH \
  | 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: 9ad2f7bb062946fc537ab56f522f9c59f547170fa13117d9c62b02c1ca59fd6b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7fb5c51ae898969f15f5750af1f66badd052bb51cebbd225d3ee00b29c1f1809",
    "cross_cats_sorted": [
      "math.MP",
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2015-06-01T19:51:28Z",
    "title_canon_sha256": "42a0940db9e88675353b92af66d146f048896a560113437268d06bf3802face2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1506.00625",
    "kind": "arxiv",
    "version": 2
  }
}