Pith Number

pith:Q5PI2WZ6

pith:2000:Q5PI2WZ6UKHU6F3Y7EOX2TG34W

not attested not anchored not stored refs pending

Acoustics of early universe. I. Flat versus open universe models

Andrzej Woszczyna, Zdzislaw A. Golda

arxiv:gr-qc/0002050 v2 · 2000-02-15 · gr-qc · astro-ph

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q5PI2WZ6UKHU6F3Y7EOX2TG34W}

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	2026-05-18T01:06:48.140335Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

875e8d5b3ea28f4f1778f91d7d4cdbe5a4f1b89817a6c455f8820ba3e0ae6496

Aliases

arxiv: gr-qc/0002050 · arxiv_version: gr-qc/0002050v2 · doi: 10.48550/arxiv.gr-qc/0002050 · pith_short_12: Q5PI2WZ6UKHU · pith_short_16: Q5PI2WZ6UKHU6F3Y · pith_short_8: Q5PI2WZ6

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/Q5PI2WZ6UKHU6F3Y7EOX2TG34W \
  | 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: 875e8d5b3ea28f4f1778f91d7d4cdbe5a4f1b89817a6c455f8820ba3e0ae6496

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4fedf028236d5eb62c5c7702d2a75eb7f53f89f2701cc19c52f7133e9a582d7b",
    "cross_cats_sorted": [
      "astro-ph"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2000-02-15T11:44:59Z",
    "title_canon_sha256": "a9258869fbf13f6f7335a0e7c55631741eb7c0939fc4f23adb27ed6bd2d64f43"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0002050",
    "kind": "arxiv",
    "version": 2
  }
}