Pith Number

pith:JB7UGIWU

pith:2024:JB7UGIWUOUV4DKCATGALZRC5GQ

not attested not anchored not stored refs pending

Toward Gravitational Lensing in Modified Theories of Gravity

Ali Tizfahm, Antonino Del Popolo, Javad T. Firouzjaee, Saeed Fakhry

arxiv:2411.06945 v2 · 2024-11-11 · gr-qc · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JB7UGIWUOUV4DKCATGALZRC5GQ}

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	2026-07-05T09:56:02.203788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

487f4322d4752bc1a8409980bcc45d34343bceac6ee58ee9145a9de64f23aa54

Aliases

arxiv: 2411.06945 · arxiv_version: 2411.06945v2 · doi: 10.48550/arxiv.2411.06945 · pith_short_12: JB7UGIWUOUV4 · pith_short_16: JB7UGIWUOUV4DKCA · pith_short_8: JB7UGIWU

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/JB7UGIWUOUV4DKCATGALZRC5GQ \
  | 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: 487f4322d4752bc1a8409980bcc45d34343bceac6ee58ee9145a9de64f23aa54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0564db2bc7cb9b823e4df70fbe2dec88a9b75c06ca5fbce77714ff7fd2930b25",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2024-11-11T12:54:02Z",
    "title_canon_sha256": "23b7afafbfacedf71467a78b94076345af2b054bbd78a8b4c6d0e202b532dc3c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2411.06945",
    "kind": "arxiv",
    "version": 2
  }
}