Pith Number

pith:6NG7NA66

pith:2012:6NG7NA66GARCR46PDAWSXHEC2P

not attested not anchored not stored refs pending

The microscopic meaning of grand potential: cluster properties of the one-dimensional lattice gas

Agata Fronczak

arxiv:1209.4231 v1 · 2012-09-18 · physics.gen-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{6NG7NA66GARCR46PDAWSXHEC2P}

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	2026-05-18T02:54:47.244986Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f34df683de302228f3cf182d2b9c82d3cc4e35ba0a6ee1d2a99de6c7937c3e40

Aliases

arxiv: 1209.4231 · arxiv_version: 1209.4231v1 · doi: 10.48550/arxiv.1209.4231 · pith_short_12: 6NG7NA66GARC · pith_short_16: 6NG7NA66GARCR46P · pith_short_8: 6NG7NA66

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/6NG7NA66GARCR46PDAWSXHEC2P \
  | 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: f34df683de302228f3cf182d2b9c82d3cc4e35ba0a6ee1d2a99de6c7937c3e40

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2a7cc45082f7b939757b694f34df13ccb1a6609c955fed2801a7d017f606c1d8",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "physics.gen-ph",
    "submitted_at": "2012-09-18T07:13:51Z",
    "title_canon_sha256": "dca06cb047bdd8d77f95ce456f28b203363029f1fe9f306da7926425e0856735"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.4231",
    "kind": "arxiv",
    "version": 1
  }
}