Pith Number

pith:NCYU5PLH

pith:2025:NCYU5PLH4VZ7KWSVSOV3GLXHKH

not attested not anchored not stored refs pending

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

Hongbao Zhang, Yong Xiao, Yu Tian, Yu-Xiao Liu

arxiv:2512.01916 v2 · 2025-12-01 · 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{NCYU5PLH4VZ7KWSVSOV3GLXHKH}

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

2 papers in Pith

Black Hole Entropy Beyond the Wald Term in Nonminimally Coupled Gravity: A Covariant Phase Space Decomposition

Dyonic Black Holes in Lorentz-Violating Gravity with a Background Kalb--Ramond Field

Receipt and verification

First computed	2026-05-21T01:04:19.338179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

68b14ebd67e573f55a5593abb32ee751de73b3e0778685dc8b499cae63f76a1c

Aliases

arxiv: 2512.01916 · arxiv_version: 2512.01916v2 · doi: 10.48550/arxiv.2512.01916 · pith_short_12: NCYU5PLH4VZ7 · pith_short_16: NCYU5PLH4VZ7KWSV · pith_short_8: NCYU5PLH

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/NCYU5PLH4VZ7KWSVSOV3GLXHKH \
  | 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: 68b14ebd67e573f55a5593abb32ee751de73b3e0778685dc8b499cae63f76a1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1e994c7f7f98d1381475d36081a5f0f95b894739bc647e5830c62077915d3e92",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-12-01T17:33:08Z",
    "title_canon_sha256": "118f0f18d25fbdf72232f4cf00f6a459ed136a51e70d14b978ec7e1e42c88f1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2512.01916",
    "kind": "arxiv",
    "version": 2
  }
}