Pith Number

pith:PXK45CCV

pith:2012:PXK45CCVF3AY5K26XNJV3NH5JA

not attested not anchored not stored refs pending

The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons

Andreas G. A. Pithis

arxiv:1209.2016 v3 · 2012-09-06 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PXK45CCVF3AY5K26XNJV3NH5JA}

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	2026-05-18T00:56:52.497957Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7dd5ce88552ec18eab5ebb535db4fd48384ab956b983d0e24258e5313dc22024

Aliases

arxiv: 1209.2016 · arxiv_version: 1209.2016v3 · doi: 10.48550/arxiv.1209.2016 · pith_short_12: PXK45CCVF3AY · pith_short_16: PXK45CCVF3AY5K26 · pith_short_8: PXK45CCV

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/PXK45CCVF3AY5K26XNJV3NH5JA \
  | 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: 7dd5ce88552ec18eab5ebb535db4fd48384ab956b983d0e24258e5313dc22024

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b03ec9c75dd8edba1669d0d31b2bba0ace5803fad29707e40de372f8ed9f414d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-09-06T17:47:16Z",
    "title_canon_sha256": "886639793c41d5af37771f2d2f622d46712b58263b86879876e1a1c2b48482d3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.2016",
    "kind": "arxiv",
    "version": 3
  }
}