Pith Number

pith:ZLLGMOW7

pith:2006:ZLLGMOW7XY7C7UAV35F3HSLM6U

not attested not anchored not stored refs pending

Analytical formulas for gravitational lensing: higher order calculation

Francisco Fernandez, Paolo Amore, Santiago Arceo

arxiv:gr-qc/0608089 v1 · 2006-08-18 · 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{ZLLGMOW7XY7C7UAV35F3HSLM6U}

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	2026-07-04T17:01:35.200146Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cad6663adfbe3e2fd015df4bb3c96cf5390a11f4aa1772b5c6a08dea837193cf

Aliases

arxiv: gr-qc/0608089 · arxiv_version: gr-qc/0608089v1 · doi: 10.48550/arxiv.gr-qc/0608089 · pith_short_12: ZLLGMOW7XY7C · pith_short_16: ZLLGMOW7XY7C7UAV · pith_short_8: ZLLGMOW7

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/ZLLGMOW7XY7C7UAV35F3HSLM6U \
  | 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: cad6663adfbe3e2fd015df4bb3c96cf5390a11f4aa1772b5c6a08dea837193cf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "cf07e691044601b9a2d86db4164e29539ad651b6e6dcdb1ba97d9e080bc2c41c",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2006-08-18T15:06:20Z",
    "title_canon_sha256": "aacb9ad2bcb11eea1c5f936cdbbe9c7fb9aa277a4fc126cca9ce8f078a5c9b1f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0608089",
    "kind": "arxiv",
    "version": 1
  }
}