Pith Number

pith:ZPRC2IIF

pith:2004:ZPRC2IIFG6ZGS6BZYFCLHS4XD3

not attested not anchored not stored refs pending

The Primordial Perturbation Spectrum from Various Expanding and Contracting Phases

Yuan-Zhong Zhang, Yun-Song Piao

arxiv:astro-ph/0403671 v1 · 2004-03-30 · 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{ZPRC2IIFG6ZGS6BZYFCLHS4XD3}

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.

Cited by

1 paper in Pith

Analytic Gravitational Wave Spectrum in Next-to-Minimal Bouncing Cosmology

Receipt and verification

First computed	2026-07-04T16:43:29.397594Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

cbe22d210537b2697839c144b3cb971ef995c8b08c9242dbc61639bf1a28a5bb

Aliases

arxiv: astro-ph/0403671 · arxiv_version: astro-ph/0403671v1 · doi: 10.48550/arxiv.astro-ph/0403671 · pith_short_12: ZPRC2IIFG6ZG · pith_short_16: ZPRC2IIFG6ZGS6BZ · pith_short_8: ZPRC2IIF

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/ZPRC2IIFG6ZGS6BZYFCLHS4XD3 \
  | 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: cbe22d210537b2697839c144b3cb971ef995c8b08c9242dbc61639bf1a28a5bb

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "738abc3117b68ef884d581c968fa6bf3b8a25a2caec18f794ee8c9bc2619217e",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2004-03-30T11:50:09Z",
    "title_canon_sha256": "e1410db3158dbf35c9b9a206b71a28b1adcc087cff4f42642f87f22def952d27"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0403671",
    "kind": "arxiv",
    "version": 1
  }
}