Pith Number

pith:NC54KMIU

pith:1999:NC54KMIUELJ6MPSBGGIQAWJGXQ

not attested not anchored not stored refs pending

Poisson approximation for large-contours in low-temperature Ising models

Pablo A. Ferrari, Pierre Picco

arxiv:math/9912136 v1 · 1999-12-16 · 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{NC54KMIUELJ6MPSBGGIQAWJGXQ}

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	2026-05-18T04:08:35.451441Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68bbc5311422d3e63e413191005926bc39d5078bf5720060834b63a5579361d7

Aliases

arxiv: math/9912136 · arxiv_version: math/9912136v1 · doi: 10.48550/arxiv.math/9912136 · pith_short_12: NC54KMIUELJ6 · pith_short_16: NC54KMIUELJ6MPSB · pith_short_8: NC54KMIU

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/NC54KMIUELJ6MPSBGGIQAWJGXQ \
  | 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: 68bbc5311422d3e63e413191005926bc39d5078bf5720060834b63a5579361d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2c18067ee068987791c067ad5bbfac6c0f0222ff0f6aad62231e486653ca34f6",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math.PR",
    "submitted_at": "1999-12-16T23:17:11Z",
    "title_canon_sha256": "f1577a2cf6c89701aceaa4f044829e6f1db03f588e9eb020cfff5ef072c9a3e2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/9912136",
    "kind": "arxiv",
    "version": 1
  }
}