Pith Number

pith:TEPQZ4HS

pith:2023:TEPQZ4HSHAH25DNWMYRPLCSMPV

not attested not anchored not stored refs pending

Kramers-Kronig relation in gravitational lensing

So Tanaka, Teruaki Suyama

arxiv:2303.05650 v2 · 2023-03-10 · gr-qc · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TEPQZ4HSHAH25DNWMYRPLCSMPV}

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

Wave-optics gravitational wave lensing in modified gravity

Receipt and verification

First computed	2026-07-05T06:50:54.155889Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

991f0cf0f2380fae8db66622f58a4c7d48f8c831e5252b3177e8b1a9b1d2d5b0

Aliases

arxiv: 2303.05650 · arxiv_version: 2303.05650v2 · doi: 10.48550/arxiv.2303.05650 · pith_short_12: TEPQZ4HSHAH2 · pith_short_16: TEPQZ4HSHAH25DNW · pith_short_8: TEPQZ4HS

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/TEPQZ4HSHAH25DNWMYRPLCSMPV \
  | 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: 991f0cf0f2380fae8db66622f58a4c7d48f8c831e5252b3177e8b1a9b1d2d5b0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9ec72a55dc9fd091c358dc6f1e6250b30888f67a3b13767d45a8b2186bebdeb2",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2023-03-10T01:56:16Z",
    "title_canon_sha256": "b450cf253f52407f3a2910abd56ea9bcccc4103bb1a841064670b18a3daf64d2"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2303.05650",
    "kind": "arxiv",
    "version": 2
  }
}