Pith Number

pith:FYJW6AXO

pith:2024:FYJW6AXO5B7QDAZ6G2GGCIZ2T3

not attested not anchored not stored refs pending

Correspondence between two gravitational lens equations in a static and spherically symmetric spacetime

Hideki Asada, Ryuya Kudo

arxiv:2407.02046 v3 · 2024-07-02 · 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{FYJW6AXO5B7QDAZ6G2GGCIZ2T3}

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

Equatorial periodic orbits and gravitational wave signatures in Euler-Heisenberg black holes surrounded by perfect fluid dark matter

Receipt and verification

First computed	2026-07-05T10:25:07.834949Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

2e136f02eee87f01833e368c61233a9edb06fac8e7e6ace641e9e3d42ade99d4

Aliases

arxiv: 2407.02046 · arxiv_version: 2407.02046v3 · doi: 10.48550/arxiv.2407.02046 · pith_short_12: FYJW6AXO5B7Q · pith_short_16: FYJW6AXO5B7QDAZ6 · pith_short_8: FYJW6AXO

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/FYJW6AXO5B7QDAZ6G2GGCIZ2T3 \
  | 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: 2e136f02eee87f01833e368c61233a9edb06fac8e7e6ace641e9e3d42ade99d4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "38f386c65eb51f90d08cb1fae116d8fdf6473b9a8273fe42f3ac114018ab6ca1",
    "cross_cats_sorted": [
      "astro-ph.HE"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2024-07-02T08:19:17Z",
    "title_canon_sha256": "e12544beccf2d2949bfaddbaff517beed7151ca05fce037d21d090da45c4a353"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.02046",
    "kind": "arxiv",
    "version": 3
  }
}