Pith Number

pith:GNEOD3PF

pith:2025:GNEOD3PFA75DQ4XEHFS6BRUYZO

not attested not anchored not stored refs pending

Learning Null Geodesics for Gravitational Lensing Rendering in General Relativity

Jiaxu Wang, Kunyi Zhang, Mingyuan Sun, Qiang Zhang, Renjing Xu, Zheng Fang

arxiv:2507.15775 v1 · 2025-07-21 · gr-qc · astro-ph.IM · cs.AI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GNEOD3PFA75DQ4XEHFS6BRUYZO}

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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

1 paper in Pith

Revisiting The Gravitational Mirroring In Presence of Compact Objects

Receipt and verification

First computed	2026-07-05T11:40:44.189289Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3348e1ede507fa3872e43965e0c698cb80334706650bf4aedaf9fa88249aae1e

Aliases

arxiv: 2507.15775 · arxiv_version: 2507.15775v1 · doi: 10.48550/arxiv.2507.15775 · pith_short_12: GNEOD3PFA75D · pith_short_16: GNEOD3PFA75DQ4XE · pith_short_8: GNEOD3PF

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/GNEOD3PFA75DQ4XEHFS6BRUYZO \
  | 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: 3348e1ede507fa3872e43965e0c698cb80334706650bf4aedaf9fa88249aae1e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "add96a6683505ed08ed796e32b58b73c66c96cdb740977f49bc9c2187d907d6c",
    "cross_cats_sorted": [
      "astro-ph.IM",
      "cs.AI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-07-21T16:30:36Z",
    "title_canon_sha256": "05d75535dbc58a34ebae19ea40159fb3621805137b708db848e51edeed539405"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2507.15775",
    "kind": "arxiv",
    "version": 1
  }
}