Pith Number

pith:BB345CUY

pith:2015:BB345CUY5TOESQRHWQUCF34ZO6

not attested not anchored not stored refs pending

Gravitational lensing and ghost images in the regular Bardeen no-horizon spacetimes

Jan Schee, Zdenek Stuchlik

arxiv:1501.00835 v3 · 2015-01-05 · astro-ph.HE · 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{BB345CUY5TOESQRHWQUCF34ZO6}

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	2026-05-18T01:36:38.532496Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0877ce8a98ecdc494227b42822ef9977971be1fad8c7ccd6820571f67e6910dc

Aliases

arxiv: 1501.00835 · arxiv_version: 1501.00835v3 · doi: 10.48550/arxiv.1501.00835 · pith_short_12: BB345CUY5TOE · pith_short_16: BB345CUY5TOESQRH · pith_short_8: BB345CUY

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/BB345CUY5TOESQRHWQUCF34ZO6 \
  | 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: 0877ce8a98ecdc494227b42822ef9977971be1fad8c7ccd6820571f67e6910dc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4492ac4ce9a733281d12d869ed0b8b8fa37c0bffa04b0efcd45ddcf0fe9d4cf0",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.HE",
    "submitted_at": "2015-01-05T12:20:57Z",
    "title_canon_sha256": "db1f78a6517bf6e42fc6630b79c869692134375314d79b89781fca46821936ca"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1501.00835",
    "kind": "arxiv",
    "version": 3
  }
}