Pith Number

pith:2R5UIJQL

pith:2021:2R5UIJQLCWGDOX5UK5TEL7Y4OA

not attested not anchored not stored refs pending

First law of black hole thermodynamics and Smarr formula with a cosmological constant

Bayram Tekin, Hikmet \"Oz\c{s}ahin, Kamal Hajian

arxiv:2103.10983 v2 · 2021-03-19 · 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{2R5UIJQLCWGDOX5UK5TEL7Y4OA}

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

5 papers in Pith

An Exact Single-Rotating Near-Horizon Geometry in Einstein-Gauss-Bonnet Gravity

Dynamical Completion of Coupling-Charge Thermodynamics

The Role of the Volume in Black Hole Thermodynamics

Gravitational constant as a conserved charge in black hole thermodynamics

Extended symmetry of the Maxwell theory with a gauge coupling constant as a conserved charge

Receipt and verification

First computed	2026-07-05T04:08:14.745540Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d47b44260b158c375fb4576645ff1c70079dbcfcdff210479d7b50d280062079

Aliases

arxiv: 2103.10983 · arxiv_version: 2103.10983v2 · doi: 10.48550/arxiv.2103.10983 · pith_short_12: 2R5UIJQLCWGD · pith_short_16: 2R5UIJQLCWGDOX5U · pith_short_8: 2R5UIJQL

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/2R5UIJQLCWGDOX5UK5TEL7Y4OA \
  | 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: d47b44260b158c375fb4576645ff1c70079dbcfcdff210479d7b50d280062079

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "07eba0d39b3191d066e8c091b5312941e0af82d7af0e6e95055cb9c637961617",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-03-19T18:40:25Z",
    "title_canon_sha256": "0b4198faa07550b15acbd3522dcac3c25c7384c9b21589f7087ad037ae174099"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2103.10983",
    "kind": "arxiv",
    "version": 2
  }
}