Pith Number

pith:MNP2TVND

pith:2025:MNP2TVNDES5XZBRW62NDEGUVBT

not attested not anchored not stored refs pending

Gravitational Lensing and Topological Photon Sphere of Holonomy Corrected Schwarzschild Black Hole with a Cloud of Strings

Faizuddin Ahmed, Shubham Kala

arxiv:2509.07686 v1 · 2025-09-09 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MNP2TVNDES5XZBRW62NDEGUVBT}

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

Revisiting The Gravitational Mirroring In Presence of Compact Objects

Receipt and verification

First computed	2026-07-05T12:07:26.372007Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

635fa9d5a324bb7c8636f69a321a950cd6ec62e959f5f1df10f0838dd7c3e430

Aliases

arxiv: 2509.07686 · arxiv_version: 2509.07686v1 · doi: 10.48550/arxiv.2509.07686 · pith_short_12: MNP2TVNDES5X · pith_short_16: MNP2TVNDES5XZBRW · pith_short_8: MNP2TVND

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/MNP2TVNDES5XZBRW62NDEGUVBT \
  | 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: 635fa9d5a324bb7c8636f69a321a950cd6ec62e959f5f1df10f0838dd7c3e430

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4245f4332b09f2656aa7d0304be009b659681af96d7a7dba5ea34783b22efa11",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-09-09T12:53:16Z",
    "title_canon_sha256": "0edf20d004662f513069df33f9f69c69ab2cb12516b4dca74b3b02c748fb33ad"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2509.07686",
    "kind": "arxiv",
    "version": 1
  }
}