Pith Number

pith:UNELCV7K

pith:2025:UNELCV7KDQJEYOKM2MTLNHAUIN

not attested not anchored not stored refs pending

Gravitational Lensing by a Dark Compact Object in Modified Gravity and Observational Constraints from Einstein Rings

Mubasher Jamil, Mustapha Azreg-A\"inou, Nagina Rehman, Zoe C. S. Chan

arxiv:2502.06313 v1 · 2025-02-10 · 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{UNELCV7KDQJEYOKM2MTLNHAUIN}

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	2026-07-05T10:25:17.085782Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a348b157ea1c124c394cd326b69c1443594be28df9d6811717fe9082122e17e6

Aliases

arxiv: 2502.06313 · arxiv_version: 2502.06313v1 · doi: 10.48550/arxiv.2502.06313 · pith_short_12: UNELCV7KDQJE · pith_short_16: UNELCV7KDQJEYOKM · pith_short_8: UNELCV7K

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/UNELCV7KDQJEYOKM2MTLNHAUIN \
  | 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: a348b157ea1c124c394cd326b69c1443594be28df9d6811717fe9082122e17e6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ee2f48bde3026b856a6df8e6b8b38c4b09e4dcb5c0bbfc992b8ade09f3bc7850",
    "cross_cats_sorted": [
      "astro-ph.GA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-02-10T10:05:56Z",
    "title_canon_sha256": "312c011810bf61ec29325538ce0fa12ccadf8be7e4136cda4046c712dd272072"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.06313",
    "kind": "arxiv",
    "version": 1
  }
}