Pith Number

pith:F6TJG4XF

pith:2026:F6TJG4XFHUO4FZDTLVDRDR2YZ5

not attested not anchored not stored refs pending

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

Jia-Zhou Liu, Shan-Ping Wu, Shao-Wen Wei, Yu-Xiao Liu

arxiv:2605.22429 v1 · 2026-05-21 · 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{F6TJG4XFHUO4FZDTLVDRDR2YZ5}

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	2026-05-22T01:04:42.732146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2fa69372e53d1dc2e4735d4711c758cf49c42d063b96f6ad5d92cc9d13491af2

Aliases

arxiv: 2605.22429 · arxiv_version: 2605.22429v1 · doi: 10.48550/arxiv.2605.22429 · pith_short_12: F6TJG4XFHUO4 · pith_short_16: F6TJG4XFHUO4FZDT · pith_short_8: F6TJG4XF

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/F6TJG4XFHUO4FZDTLVDRDR2YZ5 \
  | 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: 2fa69372e53d1dc2e4735d4711c758cf49c42d063b96f6ad5d92cc9d13491af2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f3fa60d5edaa4576e6d4b9ecd00138dd4244817d1822ffd2a18d3ef728318854",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-05-21T12:51:49Z",
    "title_canon_sha256": "729ef946ab070c6beadfbe987de95559b0fc44f2fe76746270a11fec4d32f8c5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.22429",
    "kind": "arxiv",
    "version": 1
  }
}