Pith Number

pith:CPZNEDSV

pith:2025:CPZNEDSVKYOOCZWNBSX4TUIJYD

not attested not anchored not stored refs pending

Variation in the size of the Photon Sphere and Black Hole Shadow in the Modified Gravity

Ajay Kumar Sharma, Kanav Ganguly, Murli Manohar Verma

arxiv:2506.10414 v3 · 2025-06-12 · gr-qc · astro-ph.GA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CPZNEDSVKYOOCZWNBSX4TUIJYD}

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	2026-07-05T11:58:30.924096Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

13f2d20e55561ce166cd0cafc9d109c0f5b117e1b52160ed5d9f28bdf29b5f26

Aliases

arxiv: 2506.10414 · arxiv_version: 2506.10414v3 · doi: 10.48550/arxiv.2506.10414 · pith_short_12: CPZNEDSVKYOO · pith_short_16: CPZNEDSVKYOOCZWN · pith_short_8: CPZNEDSV

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/CPZNEDSVKYOOCZWNBSX4TUIJYD \
  | 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: 13f2d20e55561ce166cd0cafc9d109c0f5b117e1b52160ed5d9f28bdf29b5f26

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "052f87c6ff6308d3f815770dac5ab563b6744ad75e2533f192506e23aff90ba0",
    "cross_cats_sorted": [
      "astro-ph.GA"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-06-12T07:09:56Z",
    "title_canon_sha256": "e473c886ed7b48d8464547feaeb8decf9fe3369eaf0cd9f78ec5f4ecb1a25d57"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.10414",
    "kind": "arxiv",
    "version": 3
  }
}