Pith Number

pith:XNXKDPJK

pith:2012:XNXKDPJKQX6IYU5QHCVVL3MVSK

not attested not anchored not stored refs pending

Where is the PdV term in the first law of black hole thermodynamics?

Brian P. Dolan

arxiv:1209.1272 v3 · 2012-09-06 · gr-qc · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XNXKDPJKQX6IYU5QHCVVL3MVSK}

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

4 papers in Pith

Joule-Thomson Effect and Geodesic Structure of Charged AdS Black Holes in f(R,T) Coupled with Nonlinear Electrodynamics

The Role of the Volume in Black Hole Thermodynamics

Quantum-statistical constraints on Kerr-anti-de Sitter thermodynamics

Black hole chemistry: thermodynamics with Lambda

Receipt and verification

First computed	2026-07-05T02:05:34.966421Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb6ea1bd2a85fc8c53b038ab55ed9592b88415cba9e83fd62214099044ef08e6

Aliases

arxiv: 1209.1272 · arxiv_version: 1209.1272v3 · doi: 10.48550/arxiv.1209.1272 · pith_short_12: XNXKDPJKQX6I · pith_short_16: XNXKDPJKQX6IYU5Q · pith_short_8: XNXKDPJK

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/XNXKDPJKQX6IYU5QHCVVL3MVSK \
  | 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: bb6ea1bd2a85fc8c53b038ab55ed9592b88415cba9e83fd62214099044ef08e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3e31df0a27aab3e491c8ebf45304d4043c1ee3989b5c8a8f01bbafe3695a5cbd",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-09-06T12:52:21Z",
    "title_canon_sha256": "ce195a6cf57c9f3f54f5973ce78a05ec01685fbfe9530b6c3110ddf3b9931986"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1272",
    "kind": "arxiv",
    "version": 3
  }
}