Pith Number

pith:47RBAWK4

pith:2006:47RBAWK4CYZ5VJIVOFKFEY7IOF

not attested not anchored not stored refs pending

Gravitational Lensing by Wormholes

Alexander V. Zakharov, Kamal Kanti Nandi, Yuan-Zhong Zhang

arxiv:gr-qc/0602062 v4 · 2006-02-16 · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{47RBAWK4CYZ5VJIVOFKFEY7IOF}

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

2 papers in Pith

Ellis-Bronnikov Wormhole Shadows with Spherically Symmetric Accretion Flow

Dymnikova-Schwinger quantum-corrected slowly rotating wormholes: Photon and spinning particle dynamics

Receipt and verification

First computed	2026-07-04T17:01:26.118244Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e7e210595c1633daa51571545263e87163afb4f9cbd12bc5e8743b9971340563

Aliases

arxiv: gr-qc/0602062 · arxiv_version: gr-qc/0602062v4 · doi: 10.48550/arxiv.gr-qc/0602062 · pith_short_12: 47RBAWK4CYZ5 · pith_short_16: 47RBAWK4CYZ5VJIV · pith_short_8: 47RBAWK4

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/47RBAWK4CYZ5VJIVOFKFEY7IOF \
  | 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: e7e210595c1633daa51571545263e87163afb4f9cbd12bc5e8743b9971340563

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "dd994c6599a47eb31ec660a5f98d82971a5a3e20b1ae2ce5feaf56b3fce30a3e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2006-02-16T05:57:26Z",
    "title_canon_sha256": "973f166772cabde8f9c20552c25afd6c77e41d61cb28af7937137bf224dc7374"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0602062",
    "kind": "arxiv",
    "version": 4
  }
}