Pith Number

pith:2LMD7TO7

pith:2006:2LMD7TO7IYOJXVRHBESF4QM5TB

not attested not anchored not stored refs pending

Cluster expansion for abstract polymer models. New bounds from an old approach

Aldo Procacci, Roberto Fernandez

arxiv:math-ph/0605041 v2 · 2006-05-12 · 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{2LMD7TO7IYOJXVRHBESF4QM5TB}

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	2026-07-04T17:02:06.349550Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d2d83fcddf461c9bd62709245e419d9878f8088203d7ae0abe71d5fee3779fde

Aliases

arxiv: math-ph/0605041 · arxiv_version: math-ph/0605041v2 · doi: 10.48550/arxiv.math-ph/0605041 · pith_short_12: 2LMD7TO7IYOJ · pith_short_16: 2LMD7TO7IYOJXVRH · pith_short_8: 2LMD7TO7

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/2LMD7TO7IYOJXVRHBESF4QM5TB \
  | 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: d2d83fcddf461c9bd62709245e419d9878f8088203d7ae0abe71d5fee3779fde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c7fe67315977fa1e0afebc8b88529950ef246ffe86d77557664e6be7aea343f7",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "",
    "primary_cat": "math-ph",
    "submitted_at": "2006-05-12T14:20:38Z",
    "title_canon_sha256": "66440c7d96dcf8e6c5511178bf7918c82f0932e5df58c5f494c13747b9829864"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math-ph/0605041",
    "kind": "arxiv",
    "version": 2
  }
}