Pith Number

pith:GACY7QHI

pith:2022:GACY7QHIWRFCMK6TRQBDKWSAZQ

not attested not anchored not stored refs pending

Imprint of f(R) gravity in the cosmic magnification

Alvaro de la Cruz-Dombriz (de Salamanca, Amare Abebe (NWU, Cape Town), Didam Duniya (BIUST), NITheCS), Peter Dunsby (Cape Town)

arxiv:2210.09303 v2 · 2022-10-17 · astro-ph.CO · gr-qc · hep-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GACY7QHIWRFCMK6TRQBDKWSAZQ}

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

1 paper in Pith

Relativistic effects in k-essence

Receipt and verification

First computed	2026-07-05T07:59:01.734059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

30058fc0e8b44a262bd38c02355a40cc224584fa634870f36a39f80f3a645717

Aliases

arxiv: 2210.09303 · arxiv_version: 2210.09303v2 · doi: 10.48550/arxiv.2210.09303 · pith_short_12: GACY7QHIWRFC · pith_short_16: GACY7QHIWRFCMK6T · pith_short_8: GACY7QHI

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/GACY7QHIWRFCMK6TRQBDKWSAZQ \
  | 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: 30058fc0e8b44a262bd38c02355a40cc224584fa634870f36a39f80f3a645717

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cb7774b3e357c9f992c963f33ea46caee6eef600ebc51e7693752f80602376ec",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-ph"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2022-10-17T17:56:55Z",
    "title_canon_sha256": "9f32c9299d328e8bb26dc7a9c8d0876dd5c0cd7fe178ca8594d03509e1864d28"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2210.09303",
    "kind": "arxiv",
    "version": 2
  }
}