Pith Number

pith:LPLSF6WA

pith:2018:LPLSF6WA6AYPI7TURCAPW6VPQG

not attested not anchored not stored refs pending

Gravitational lensing beyond geometric optics: I. Formalism and observables

Abraham I. Harte

arxiv:1808.06203 v2 · 2018-08-19 · gr-qc · astro-ph.HE

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{LPLSF6WA6AYPI7TURCAPW6VPQG}

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	2026-05-17T23:56:53.025459Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5bd722fac0f030f47e748880fb7aaf818a4e96b89c6a9aebfad779d02a7267cb

Aliases

arxiv: 1808.06203 · arxiv_version: 1808.06203v2 · doi: 10.48550/arxiv.1808.06203 · pith_short_12: LPLSF6WA6AYP · pith_short_16: LPLSF6WA6AYPI7TU · pith_short_8: LPLSF6WA

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/LPLSF6WA6AYPI7TURCAPW6VPQG \
  | 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: 5bd722fac0f030f47e748880fb7aaf818a4e96b89c6a9aebfad779d02a7267cb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "92a320cd4c8bb6be624b5295291547309fec7c9642e1ac904b22b7129669cad5",
    "cross_cats_sorted": [
      "astro-ph.HE"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2018-08-19T12:42:44Z",
    "title_canon_sha256": "6e98ec8dab9dc7e1d7c760e82884180b995b5a42e1522a661465e95bd1330206"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.06203",
    "kind": "arxiv",
    "version": 2
  }
}