Pith Number

pith:UPWKKTPX

pith:2002:UPWKKTPXISX4JR2PIEHJVBDVJV

not attested not anchored not stored refs pending

Linear second-order differential equations for barotropic FRW cosmologies

D. Jimenez, H.C. Rosu, M. Reyes, O. Cornejo

arxiv:gr-qc/0206044 v2 · 2002-06-15 · 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{UPWKKTPXISX4JR2PIEHJVBDVJV}

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	2026-05-18T01:06:47.662907Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a3eca54df744afc4c74f410e9a84754d66b5100d9424d863031b20f748c8ad0b

Aliases

arxiv: gr-qc/0206044 · arxiv_version: gr-qc/0206044v2 · doi: 10.48550/arxiv.gr-qc/0206044 · pith_short_12: UPWKKTPXISX4 · pith_short_16: UPWKKTPXISX4JR2P · pith_short_8: UPWKKTPX

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/UPWKKTPXISX4JR2PIEHJVBDVJV \
  | 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: a3eca54df744afc4c74f410e9a84754d66b5100d9424d863031b20f748c8ad0b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f79ec758e31c98093aa8d82f40e85484d3c001ce3b771bec4e2cbfee575d4c00",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2002-06-15T23:56:53Z",
    "title_canon_sha256": "657e19bf608290302f77e1dc16e5a2d5a5c35da96878e83fb81f7f5d4458f209"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0206044",
    "kind": "arxiv",
    "version": 2
  }
}