Pith Number

pith:OAPKQXTL

pith:1993:OAPKQXTLW2HE6MDZBLZ2CUM5U5

not attested not anchored not stored refs pending

Dirac equation in some homogeneous$sqace-times, separation of variables and exact solutions

V\'ictor M. Villalba

arxiv:gr-qc/9306019 v1 · 1993-06-16 · 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{OAPKQXTLW2HE6MDZBLZ2CUM5U5}

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	2026-05-18T01:09:19.394266Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

701ea85e6bb68e4f30790af3a1519da753f5a72fe283ff41ebef56366f8df710

Aliases

arxiv: gr-qc/9306019 · arxiv_version: gr-qc/9306019v1 · doi: 10.48550/arxiv.gr-qc/9306019 · pith_short_12: OAPKQXTLW2HE · pith_short_16: OAPKQXTLW2HE6MDZ · pith_short_8: OAPKQXTL

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/OAPKQXTLW2HE6MDZBLZ2CUM5U5 \
  | 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: 701ea85e6bb68e4f30790af3a1519da753f5a72fe283ff41ebef56366f8df710

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ea7886204c74b7a5c5913657d1280d6f1ae2ef9941af8ccef01560a066837b24",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "1993-06-16T04:54:33Z",
    "title_canon_sha256": "095bf7d61ad0bd28235feb5797e30e9ca060b46c62c3adae16176098cbcf1f7e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/9306019",
    "kind": "arxiv",
    "version": 1
  }
}