Pith Number

pith:PHOJO7C7

pith:2019:PHOJO7C76AKH5GYXJSS6H4EWOX

not attested not anchored not stored refs pending

Gibbs and Boltzmann Entropy in Classical and Quantum Mechanics

Joel L. Lebowitz, Nino Zanghi, Roderich Tumulka, Sheldon Goldstein

arxiv:1903.11870 v2 · 2019-03-28 · cond-mat.stat-mech

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PHOJO7C76AKH5GYXJSS6H4EWOX}

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.

Cited by

3 papers in Pith

Toward a Phenomenologically Acceptable Quantum Cyclic Universe

Grand-Canonical Typicality

Combinatorial Approach to the Second Law

Receipt and verification

First computed	2026-07-05T01:14:24.103390Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

79dc977c5ff0147e9b174ca5e3f09675e12628df5f609e15b2484240399d5e39

Aliases

arxiv: 1903.11870 · arxiv_version: 1903.11870v2 · doi: 10.48550/arxiv.1903.11870 · pith_short_12: PHOJO7C76AKH · pith_short_16: PHOJO7C76AKH5GYX · pith_short_8: PHOJO7C7

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/PHOJO7C76AKH5GYXJSS6H4EWOX \
  | 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: 79dc977c5ff0147e9b174ca5e3f09675e12628df5f609e15b2484240399d5e39

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "671a50e29cc730750231641217089de6de5f52f6c2734a9308ed9b12117d24e9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2019-03-28T10:04:23Z",
    "title_canon_sha256": "96e560507f03542bef1fe0fca95f4af4ff52d4be251b1b32ace4fc57e6f6f861"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.11870",
    "kind": "arxiv",
    "version": 2
  }
}