Pith Number

pith:7FBGWDR3

pith:2001:7FBGWDR3MLGD3H22XSDAVZYI7Q

not attested not anchored not stored refs pending

Cosmological perturbations: a new gauge-invariant approach

Bahram Mashhoon (University of Missouri-Columbia), Juan Ramirez (Universidad Complutense de Madrid), Mikhail V. Sazhin (Sternberg Astronomical Institute), Sergei M. Kopeikin (University of Missouri-Columbia)

arxiv:gr-qc/0106064 v5 · 2001-06-21 · gr-qc · astro-ph · hep-th

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7FBGWDR3MLGD3H22XSDAVZYI7Q}

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	2026-05-18T04:17:53.137969Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9426b0e3b62cc3d9f5abc860ae708fc1fe4022d465b13957a3b6278c6a80513

Aliases

arxiv: gr-qc/0106064 · arxiv_version: gr-qc/0106064v5 · doi: 10.48550/arxiv.gr-qc/0106064 · pith_short_12: 7FBGWDR3MLGD · pith_short_16: 7FBGWDR3MLGD3H22 · pith_short_8: 7FBGWDR3

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/7FBGWDR3MLGD3H22XSDAVZYI7Q \
  | 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: f9426b0e3b62cc3d9f5abc860ae708fc1fe4022d465b13957a3b6278c6a80513

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a5ef7e58e914428b83f66113b4e6cf8249d1b03906361f2412d45365510bfb60",
    "cross_cats_sorted": [
      "astro-ph",
      "hep-th"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2001-06-21T00:00:40Z",
    "title_canon_sha256": "82547c8d7f9d6992073f8e40af358c4b7519ece86fcb2644074669cf41b4aacc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0106064",
    "kind": "arxiv",
    "version": 5
  }
}