Pith Number

pith:TMMOEJC7

pith:1998:TMMOEJC7POZ5ABLPOESELLKL4V

not attested not anchored not stored refs pending

The Ray Bundle method for calculating weak magnification by gravitational lenses

C. J. Fluke, Daniel J. Mortlock (University of Melbourne), R. L. Webster

arxiv:astro-ph/9812300 v1 · 1998-12-16 · astro-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TMMOEJC7POZ5ABLPOESELLKL4V}

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	2026-07-04T16:07:22.638168Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9b18e2245f7bb3d0056f712445ad4be551498ff1e071832dd191e87531104c0e

Aliases

arxiv: astro-ph/9812300 · arxiv_version: astro-ph/9812300v1 · doi: 10.48550/arxiv.astro-ph/9812300 · pith_short_12: TMMOEJC7POZ5 · pith_short_16: TMMOEJC7POZ5ABLP · pith_short_8: TMMOEJC7

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/TMMOEJC7POZ5ABLPOESELLKL4V \
  | 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: 9b18e2245f7bb3d0056f712445ad4be551498ff1e071832dd191e87531104c0e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d3eccf92566bae0d27f351ad9283d486b77210b03ddfa80ed381b473c353d8ed",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1998-12-16T04:27:43Z",
    "title_canon_sha256": "639f1fc49a306dca095a5231d2a16a1af5cf578f8a12ae6ace6b954d2cf04b45"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9812300",
    "kind": "arxiv",
    "version": 1
  }
}