Pith Number

pith:NOJX4TL4

pith:2007:NOJX4TL4UG2G5K6ROVLDCSDVMK

not attested not anchored not stored refs pending

Matter density perturbations and effective gravitational constant in modified gravity models of dark energy

Shinji Tsujikawa

arxiv:0705.1032 v4 · 2007-05-08 · astro-ph · gr-qc · hep-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{NOJX4TL4UG2G5K6ROVLDCSDVMK}

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

A Master Equation for Screening in Luminal Horndeski Gravity

Receipt and verification

First computed	2026-07-04T15:33:54.942229Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b937e4d7ca1b46eabd17556314875628072ecdcd608cda946161533daf5926d

Aliases

arxiv: 0705.1032 · arxiv_version: 0705.1032v4 · doi: 10.48550/arxiv.0705.1032 · pith_short_12: NOJX4TL4UG2G · pith_short_16: NOJX4TL4UG2G5K6R · pith_short_8: NOJX4TL4

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/NOJX4TL4UG2G5K6ROVLDCSDVMK \
  | 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: 6b937e4d7ca1b46eabd17556314875628072ecdcd608cda946161533daf5926d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df3744521ac4b6491aee53f9d8bbaf59622026f94c8c6c9e047aab460df2a831",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-ph",
      "hep-th"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2007-05-08T05:18:19Z",
    "title_canon_sha256": "f9dc79998a6e47f75f074590ff0deca0da95b2eb19cac3786b8a33460daa9e59"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0705.1032",
    "kind": "arxiv",
    "version": 4
  }
}