Pith Number

pith:RMYAPFK2

pith:1998:RMYAPFK2B3XOB2ATZVYOHBQXEA

not attested not anchored not stored refs pending

An Exact Universal Gravitational Lensing Equation

Ezra T. Newman, Simonetta Frittelli

arxiv:gr-qc/9810017 v1 · 1998-10-05 · 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{RMYAPFK2B3XOB2ATZVYOHBQXEA}

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

Phase-plane formulation of weak gravitational deflection in static spherical spacetimes

Receipt and verification

First computed	2026-07-04T15:34:27.178290Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8b3007955a0eeee0e813cd70e3861720204b338a6a53b6a979cb239a4e52b684

Aliases

arxiv: gr-qc/9810017 · arxiv_version: gr-qc/9810017v1 · doi: 10.48550/arxiv.gr-qc/9810017 · pith_short_12: RMYAPFK2B3XO · pith_short_16: RMYAPFK2B3XOB2AT · pith_short_8: RMYAPFK2

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/RMYAPFK2B3XOB2ATZVYOHBQXEA \
  | 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: 8b3007955a0eeee0e813cd70e3861720204b338a6a53b6a979cb239a4e52b684

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ec2d5c30c26d225c4ecb69804bd1bf9d805b25b3f93e04b4d72a78ced2cad84",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "1998-10-05T18:46:01Z",
    "title_canon_sha256": "8bc989fd72528f76665ddbee0b2126e212317b55ff054ed65baa5aff66fec14d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/9810017",
    "kind": "arxiv",
    "version": 1
  }
}