Pith Number

pith:5TGVEIVK

pith:2012:5TGVEIVKRVNIS6II7IFXDW4OWN

not attested not anchored not stored refs pending

Gravitational Lensing by Phantom Black holes

Galin N. Gyulchev, Ivan Zh. Stefanov

arxiv:1211.3458 v2 · 2012-11-14 · gr-qc · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{5TGVEIVKRVNIS6II7IFXDW4OWN}

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	2026-05-18T03:22:17.275674Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eccd5222aa8d5a897908fa0b71db8eb3511a0e63b0075d430080d71ee14c19f0

Aliases

arxiv: 1211.3458 · arxiv_version: 1211.3458v2 · doi: 10.48550/arxiv.1211.3458 · pith_short_12: 5TGVEIVKRVNI · pith_short_16: 5TGVEIVKRVNIS6II · pith_short_8: 5TGVEIVK

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/5TGVEIVKRVNIS6II7IFXDW4OWN \
  | 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: eccd5222aa8d5a897908fa0b71db8eb3511a0e63b0075d430080d71ee14c19f0

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "962c1417832a3a3af617dd194f4aae606ce0a111d09e340bc9d773aab9ec96e1",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-11-14T23:17:19Z",
    "title_canon_sha256": "8572bcda3e10017a0a32485a7721785e25f07784e0fa20b9be08f07d7546c520"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1211.3458",
    "kind": "arxiv",
    "version": 2
  }
}