Pith Number

pith:GMUSRC55

pith:2024:GMUSRC55Q2QUGGQRQ7FEV2GCXB

not attested not anchored not stored refs pending

Black holes and their shadows in $F(R)$ gravity

S. D. Odintsov, Shin'ichi Nojiri

arxiv:2412.13775 v1 · 2024-12-18 · 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{GMUSRC55Q2QUGGQRQ7FEV2GCXB}

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

Photon Sphere and Shadow of a Perturbative Black Hole in $f(R,\mathcal{G})$ Gravity

Receipt and verification

First computed	2026-07-05T09:51:08.454513Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3329288bbd86a1431a1187ca4ae8c2b85c6951b7b93b0ac667e1d4ad96efe12e

Aliases

arxiv: 2412.13775 · arxiv_version: 2412.13775v1 · doi: 10.48550/arxiv.2412.13775 · pith_short_12: GMUSRC55Q2QU · pith_short_16: GMUSRC55Q2QUGGQR · pith_short_8: GMUSRC55

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/GMUSRC55Q2QUGGQRQ7FEV2GCXB \
  | 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: 3329288bbd86a1431a1187ca4ae8c2b85c6951b7b93b0ac667e1d4ad96efe12e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b9725bb7915c1e40df41f40f39a2f8b6c1457ca3ec2a5f3e2d13aa5851360a6",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2024-12-18T12:11:51Z",
    "title_canon_sha256": "67a69d4053198155ea46483cd89602f52847b3483dedb893c9e3e704df970dee"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2412.13775",
    "kind": "arxiv",
    "version": 1
  }
}