Pith Number

pith:JU6F7QLW

pith:2009:JU6F7QLWZMNSYCMTYB4ICAWCVF

not attested not anchored not stored refs pending

Characterizing the linear growth rate of cosmological density perturbations in an f(R) model

Kazuhiro Yamamoto, Tatsuya Narikawa

arxiv:0912.1445 v4 · 2009-12-08 · astro-ph.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{JU6F7QLWZMNSYCMTYB4ICAWCVF}

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	2026-05-18T02:33:57.238427Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

4d3c5fc176cb1b2c0993c0788102c2a94638d3a1930d7500aa4e4e7d9cfea4d3

Aliases

arxiv: 0912.1445 · arxiv_version: 0912.1445v4 · doi: 10.48550/arxiv.0912.1445 · pith_short_12: JU6F7QLWZMNS · pith_short_16: JU6F7QLWZMNSYCMT · pith_short_8: JU6F7QLW

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/JU6F7QLWZMNSYCMTYB4ICAWCVF \
  | 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: 4d3c5fc176cb1b2c0993c0788102c2a94638d3a1930d7500aa4e4e7d9cfea4d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4b46c8f7726db98559706305e58ef399dfcad7b9616b48460345c50c547dbbf5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2009-12-08T09:31:53Z",
    "title_canon_sha256": "b6a154137c3b2832e6480e0106b92030eeb0fb91026aad9f27edbd585ad0a499"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1445",
    "kind": "arxiv",
    "version": 4
  }
}