Pith Number

pith:5PHTPG2E

pith:2023:5PHTPG2ESPWFK3GTXQGTIVLZOP

not attested not anchored not stored refs pending

Cluster expansion methods in rigorous statistical mechanics

Aldo Procacci

arxiv:2308.06380 v1 · 2023-08-11 · 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{5PHTPG2ESPWFK3GTXQGTIVLZOP}

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	2026-07-05T06:40:39.174048Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ebcf379b4493ec556cd3bc0d34557973c9b7c12f6f2545fc10e230e9308f33f9

Aliases

arxiv: 2308.06380 · arxiv_version: 2308.06380v1 · doi: 10.48550/arxiv.2308.06380 · pith_short_12: 5PHTPG2ESPWF · pith_short_16: 5PHTPG2ESPWFK3GT · pith_short_8: 5PHTPG2E

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/5PHTPG2ESPWFK3GTXQGTIVLZOP \
  | 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: ebcf379b4493ec556cd3bc0d34557973c9b7c12f6f2545fc10e230e9308f33f9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2b9a1420e04c41354a0f89332ac732151b983adabadf0555f1b6d55c4b805cba",
    "cross_cats_sorted": [
      "math.MP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2023-08-11T20:36:16Z",
    "title_canon_sha256": "f27b01abba8349b643c2de16d3a63f9197404b4452ec6f2bb1fb894101f5ba75"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2308.06380",
    "kind": "arxiv",
    "version": 1
  }
}