Pith Number

pith:3XCWKFYJ

pith:2010:3XCWKFYJANVXK7VN6F2FXKGPL6

not attested not anchored not stored refs pending

Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume

C.N. Pope, D. Kubiznak, G.W. Gibbons, M. Cvetic

arxiv:1012.2888 v2 · 2010-12-13 · hep-th · 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{3XCWKFYJANVXK7VN6F2FXKGPL6}

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

18 papers in Pith

The Smarr Formula is Gauss's Law: A Kerr-Schild Single-Copy Perspective

Quasi-topological Electromagnetism: Dark Energy, Dyonic Black Holes, Stable Photon Spheres and Hidden Electromagnetic Duality

A new rotating axionic AdS$_4$ black hole dressed with a scalar field

Holographic pressure and volume for black holes

Explicit and covariant formula for thermodynamic volume in extended black hole thermodynamics

Receipt and verification

First computed	2026-05-18T04:16:02.114930Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ddc5651709036b757eadf1745ba8cf5f82c3650bcb821a189a2c74d0eff7bc62

Aliases

arxiv: 1012.2888 · arxiv_version: 1012.2888v2 · doi: 10.48550/arxiv.1012.2888 · pith_short_12: 3XCWKFYJANVX · pith_short_16: 3XCWKFYJANVXK7VN · pith_short_8: 3XCWKFYJ

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/3XCWKFYJANVXK7VN6F2FXKGPL6 \
  | 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: ddc5651709036b757eadf1745ba8cf5f82c3650bcb821a189a2c74d0eff7bc62

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "067057d2bdb2d02bf62c5b09a86672eba7bf49988881b19e47dbaca1a05e3c42",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2010-12-13T21:40:12Z",
    "title_canon_sha256": "c3bec45eae1dd5fc9f5e71ac767da206d085c9fd71d0205e8877d1a87ee74b82"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1012.2888",
    "kind": "arxiv",
    "version": 2
  }
}