Pith Number

pith:LTZ2OYUJ

pith:2001:LTZ2OYUJSNG5NXDIKCGT3IWJFL

not attested not anchored not stored refs pending

Gravitational lensing in spherically symmetric static spacetimes with centrifugal force reversal

Volker Perlick, Wolfgang Hasse

arxiv:gr-qc/0108002 v1 · 2001-08-01 · 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{LTZ2OYUJSNG5NXDIKCGT3IWJFL}

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	2026-05-18T04:35:35.157606Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5cf3a76289934dd6dc68508d3da2c92ac43fd3253461eefdcaf0bf6d7fccf8e4

Aliases

arxiv: gr-qc/0108002 · arxiv_version: gr-qc/0108002v1 · doi: 10.48550/arxiv.gr-qc/0108002 · pith_short_12: LTZ2OYUJSNG5 · pith_short_16: LTZ2OYUJSNG5NXDI · pith_short_8: LTZ2OYUJ

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/LTZ2OYUJSNG5NXDIKCGT3IWJFL \
  | 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: 5cf3a76289934dd6dc68508d3da2c92ac43fd3253461eefdcaf0bf6d7fccf8e4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7308559049855e5d4229921b801ab96760252e1aef9caa02640c9cd16184b110",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2001-08-01T15:02:14Z",
    "title_canon_sha256": "f7121af6b999a8207875fd03793577553f6f17c9c03fbc1212688939d14db8e9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0108002",
    "kind": "arxiv",
    "version": 1
  }
}