Pith Number

pith:QKBU4WGA

pith:1994:QKBU4WGAFDNZHR7DPYBGLG4SQT

not attested not anchored not stored refs pending

Cosmological solutions of the Vlasov-Einstein system with spherical, plane, and hyperbolic symmetry

Gerhard Rein

arxiv:gr-qc/9409041 v1 · 1994-09-20 · 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{QKBU4WGAFDNZHR7DPYBGLG4SQT}

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	2026-05-18T01:39:19.722504Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

82834e58c028db93c7e37e02659b9284edfdfad49cf6733f26313810f77d75a9

Aliases

arxiv: gr-qc/9409041 · arxiv_version: gr-qc/9409041v1 · doi: 10.48550/arxiv.gr-qc/9409041 · pith_short_12: QKBU4WGAFDNZ · pith_short_16: QKBU4WGAFDNZHR7D · pith_short_8: QKBU4WGA

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/QKBU4WGAFDNZHR7DPYBGLG4SQT \
  | 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: 82834e58c028db93c7e37e02659b9284edfdfad49cf6733f26313810f77d75a9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b9638df68cc2d20f5decc78a66ce988850f7811d833d77083537decbc691019e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "1994-09-20T08:14:19Z",
    "title_canon_sha256": "fe5c30572b89d3a98aae45cf1b81f34b52f31601e7a8b1e281dc2fc539105fa4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/9409041",
    "kind": "arxiv",
    "version": 1
  }
}