Pith Number

pith:LX3RYIQ2

pith:2011:LX3RYIQ2K3D45JQ25QGC6P6SXP

not attested not anchored not stored refs pending

Revisiting the concept of chemical potential in classical and quantum gases: A perspective from Equilibrium Statistical Mechanics

(2) Universidad Aut\'onoma de la Ciudad de M\'exico, corresponding Author), Francisco J. Sevilla (1), Luis Olivares-Quiroz (2) ((1) Instituto de F\'isica, Universidad Nacional Aut\'onoma de M\'exico

arxiv:1104.2611 v1 · 2011-04-13 · cond-mat.stat-mech · cond-mat.quant-gas

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LX3RYIQ2K3D45JQ25QGC6P6SXP}

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	2026-05-18T04:24:27.229098Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5df71c221a56c7cea61aec0c2f3fd2bbdba9b8862735f496795f7d427f6fa0af

Aliases

arxiv: 1104.2611 · arxiv_version: 1104.2611v1 · doi: 10.48550/arxiv.1104.2611 · pith_short_12: LX3RYIQ2K3D4 · pith_short_16: LX3RYIQ2K3D45JQ2 · pith_short_8: LX3RYIQ2

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/LX3RYIQ2K3D45JQ25QGC6P6SXP \
  | 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: 5df71c221a56c7cea61aec0c2f3fd2bbdba9b8862735f496795f7d427f6fa0af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "28a4f99504607526c7d5db4ed111fefeaa146fbcab88041219d8bb4ee158d085",
    "cross_cats_sorted": [
      "cond-mat.quant-gas"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2011-04-13T20:25:41Z",
    "title_canon_sha256": "8c583a3e80d1943bedd25fcd09b767cd7e6da31f3a798381e763ac891ca08b47"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.2611",
    "kind": "arxiv",
    "version": 1
  }
}