Pith Number

pith:VPEJHP7V

pith:2001:VPEJHP7VX3CUU6Y7RF5I43K6TN

not attested not anchored not stored refs pending

Shell crossing in generalized Tolman-Bondi spacetimes

Sergio M. C. V. Goncalves (Caltech)

arxiv:gr-qc/0107087 v1 · 2001-07-26 · 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{VPEJHP7VX3CUU6Y7RF5I43K6TN}

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	2026-05-18T02:37:35.920135Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abc893bff5bec54a7b1f897a8e6d5e9b49ddde5cbf35d222f2f4519dfbc15669

Aliases

arxiv: gr-qc/0107087 · arxiv_version: gr-qc/0107087v1 · doi: 10.48550/arxiv.gr-qc/0107087 · pith_short_12: VPEJHP7VX3CU · pith_short_16: VPEJHP7VX3CUU6Y7 · pith_short_8: VPEJHP7V

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/VPEJHP7VX3CUU6Y7RF5I43K6TN \
  | 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: abc893bff5bec54a7b1f897a8e6d5e9b49ddde5cbf35d222f2f4519dfbc15669

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8da4a980c81a8c2a7417f70c47bb38c5d0acc7d56177ef8b38a9ecbffccd9dd3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2001-07-26T22:16:42Z",
    "title_canon_sha256": "097189c6b5f2bed08f07ba1bde271bee2be41d245dca17a6b387fafa190367e8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0107087",
    "kind": "arxiv",
    "version": 1
  }
}