Pith Number

pith:NWJM5ZEI

pith:2025:NWJM5ZEIFNAGDMSV4UWYWWR4MI

not attested not anchored not stored refs pending

Gravitational lensing and shadows in the toron solution of Einstein's equations using ray tracing methods

D. Korotkin, Eddy B. de Leon. C. Klein

arxiv:2501.04509 v2 · 2025-01-08 · gr-qc · nlin.SI

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NWJM5ZEIFNAGDMSV4UWYWWR4MI}

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	2026-07-05T10:29:32.268629Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6d92cee4882b4061b255e52d8b5a3c6234ef8776e782e7b914fbfca782c4ffde

Aliases

arxiv: 2501.04509 · arxiv_version: 2501.04509v2 · doi: 10.48550/arxiv.2501.04509 · pith_short_12: NWJM5ZEIFNAG · pith_short_16: NWJM5ZEIFNAGDMSV · pith_short_8: NWJM5ZEI

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/NWJM5ZEIFNAGDMSV4UWYWWR4MI \
  | 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: 6d92cee4882b4061b255e52d8b5a3c6234ef8776e782e7b914fbfca782c4ffde

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f530d3b8d1e8fe1de179e200ae6f39a1145e700ccaa9c02e1191b4cae4efcb14",
    "cross_cats_sorted": [
      "nlin.SI"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2025-01-08T13:55:55Z",
    "title_canon_sha256": "b1bdd92341f321171182fed0930562c1df63b91367648d0ef28796ed37a96ac7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2501.04509",
    "kind": "arxiv",
    "version": 2
  }
}