Pith Number

pith:HAGLDP77

pith:2003:HAGLDP77GYURKCENLOJKBWWB3Y

not attested not anchored not stored refs pending

Path Integral Formulation for Wave Effect in Multi-lens System

Kazuhiro Yamamoto

arxiv:astro-ph/0309696 v1 · 2003-09-25 · 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{HAGLDP77GYURKCENLOJKBWWB3Y}

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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

2 papers in Pith

Wave-optics gravitational wave lensing in modified gravity

Gravitational-wave lensing beyond rays: a disordered-system approach

Receipt and verification

First computed	2026-07-04T14:12:56.081063Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

380cb1bfff362915088d5b92a0dac1de2c2ea9c572943e67c9d66e2ba1e5e3e4

Aliases

arxiv: astro-ph/0309696 · arxiv_version: astro-ph/0309696v1 · doi: 10.48550/arxiv.astro-ph/0309696 · pith_short_12: HAGLDP77GYUR · pith_short_16: HAGLDP77GYURKCEN · pith_short_8: HAGLDP77

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/HAGLDP77GYURKCENLOJKBWWB3Y \
  | 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: 380cb1bfff362915088d5b92a0dac1de2c2ea9c572943e67c9d66e2ba1e5e3e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "52802835958067e3e5e279337ab92dfefab009dd04898946ec7ec14c80890f84",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2003-09-25T10:23:35Z",
    "title_canon_sha256": "a7697f069ba2540a1ee8fa18fcfb64e86ad54dcfa9af63eddd0f1153fe300cc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0309696",
    "kind": "arxiv",
    "version": 1
  }
}