Pith Number

pith:ZG6PPN4E

pith:2006:ZG6PPN4E64ZL5YYJH4FKD7EE4Q

not attested not anchored not stored refs pending

Analytical formulas for gravitational lensing

Paolo Amore, Santiago Arceo Diaz

arxiv:gr-qc/0602106 v2 · 2006-02-25 · 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{ZG6PPN4E64ZL5YYJH4FKD7EE4Q}

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	2026-07-04T17:01:26.347308Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c9bcf7b784f732bee3093f0aa1fc84e40b360abdb11836bda634b752c081da8f

Aliases

arxiv: gr-qc/0602106 · arxiv_version: gr-qc/0602106v2 · doi: 10.48550/arxiv.gr-qc/0602106 · pith_short_12: ZG6PPN4E64ZL · pith_short_16: ZG6PPN4E64ZL5YYJ · pith_short_8: ZG6PPN4E

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/ZG6PPN4E64ZL5YYJH4FKD7EE4Q \
  | 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: c9bcf7b784f732bee3093f0aa1fc84e40b360abdb11836bda634b752c081da8f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cabdf83ddac4d5313dd85e122aae59297ad9d71a7d9656b6b330b31837406c4d",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2006-02-25T22:52:01Z",
    "title_canon_sha256": "a757f43cae6b4b4b3b71a8a880041546f00d0ad13c004a9182b05cef6b04c4cb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0602106",
    "kind": "arxiv",
    "version": 2
  }
}