Pith Number

pith:XNUOJ4ZD

pith:2016:XNUOJ4ZDQ7FXCYZXAHQFRTLJO4

not attested not anchored not stored refs pending

Strong gravitational lensing in $f\left(\chi\right)=\chi^{3/2}$ gravity

A. Diaferio, L. Fatibene, M. C. Campigotto, X.Hernandez

arxiv:1612.01535 v1 · 2016-12-05 · astro-ph.CO · 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{XNUOJ4ZDQ7FXCYZXAHQFRTLJO4}

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	2026-05-18T00:41:01.185336Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bb68e4f32387cb71633701e058cd69770418693dcd853de26a2888dc98e341ec

Aliases

arxiv: 1612.01535 · arxiv_version: 1612.01535v1 · doi: 10.48550/arxiv.1612.01535 · pith_short_12: XNUOJ4ZDQ7FX · pith_short_16: XNUOJ4ZDQ7FXCYZX · pith_short_8: XNUOJ4ZD

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/XNUOJ4ZDQ7FXCYZXAHQFRTLJO4 \
  | 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: bb68e4f32387cb71633701e058cd69770418693dcd853de26a2888dc98e341ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af6eb7f2995839ac4c5fa7b9d4afddaac148f991b8ed51bae668c4afbb89b2fa",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2016-12-05T21:00:05Z",
    "title_canon_sha256": "83726afaa2e4f9a84325a94917ec62b7b658b389a685492e465683172dc39b0a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.01535",
    "kind": "arxiv",
    "version": 1
  }
}