Pith Number

pith:4X3SESA3

pith:2013:4X3SESA3CZ4X7DHT2ZVM7U5HB4

not attested not anchored not stored refs pending

Regular phantom black hole gravitational lensing

Carlos M. Sendra, Ernesto F. Eiroa

arxiv:1308.5959 v2 · 2013-08-27 · 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{4X3SESA3CZ4X7DHT2ZVM7U5HB4}

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	2026-05-18T03:06:12.931254Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5f722481b16797f8cf3d66acfd3a70f13c05839a1e0524f248f5789d13424f5

Aliases

arxiv: 1308.5959 · arxiv_version: 1308.5959v2 · doi: 10.48550/arxiv.1308.5959 · pith_short_12: 4X3SESA3CZ4X · pith_short_16: 4X3SESA3CZ4X7DHT · pith_short_8: 4X3SESA3

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/4X3SESA3CZ4X7DHT2ZVM7U5HB4 \
  | 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: e5f722481b16797f8cf3d66acfd3a70f13c05839a1e0524f248f5789d13424f5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "942ff35a023ef85de24266da41722097928e16352a0e66b656ab9b393f6d2daf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2013-08-27T19:42:14Z",
    "title_canon_sha256": "b471dac66ce6882a2aaf78e50041d0218695a4a1576d1714fe09c7dfbcf4614e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1308.5959",
    "kind": "arxiv",
    "version": 2
  }
}