Pith Number

pith:TZA4QXVG

pith:2008:TZA4QXVG55PIMGNLNYKSKXGKTZ

not attested not anchored not stored refs pending

Third-Order Density Perturbation and One-Loop Power Spectrum in Dark-Energy-Dominated Universe

Ryuichi Takahashi

arxiv:0806.1437 v3 · 2008-06-09 · astro-ph · 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{TZA4QXVG55PIMGNLNYKSKXGKTZ}

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	2026-07-04T15:34:08.692015Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

9e41c85ea6ef5e8619ab6e15255cca9e7502a1a9d290070304f1f72bd2cb6bbe

Aliases

arxiv: 0806.1437 · arxiv_version: 0806.1437v3 · doi: 10.48550/arxiv.0806.1437 · pith_short_12: TZA4QXVG55PI · pith_short_16: TZA4QXVG55PIMGNL · pith_short_8: TZA4QXVG

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/TZA4QXVG55PIMGNLNYKSKXGKTZ \
  | 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: 9e41c85ea6ef5e8619ab6e15255cca9e7502a1a9d290070304f1f72bd2cb6bbe

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "687d7f9817115345584bbbcbaf9abd828016a862cee79d666537579f8d6a8334",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph",
    "submitted_at": "2008-06-09T12:06:27Z",
    "title_canon_sha256": "2f9bbb8d2be3f0a4897da309cf8285a618edc2726d0e14806c7939e34a9f5995"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0806.1437",
    "kind": "arxiv",
    "version": 3
  }
}