Pith Number

pith:4XPYTBWS

pith:2012:4XPYTBWSTGHY7YLU3NV7CUJV4P

not attested not anchored not stored refs pending

High frequency limit for gravitational perturbations of cosmological models in modified gravity theories

Akihiro Ishibashi, Keiki Saito

arxiv:1209.5159 v1 · 2012-09-24 · gr-qc · astro-ph.CO · 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{4XPYTBWSTGHY7YLU3NV7CUJV4P}

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	2026-05-18T01:12:19.137575Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e5df8986d2998f8fe174db6bf15135e3fdd2a735ef7154c2b1d4168750331990

Aliases

arxiv: 1209.5159 · arxiv_version: 1209.5159v1 · doi: 10.48550/arxiv.1209.5159 · pith_short_12: 4XPYTBWSTGHY · pith_short_16: 4XPYTBWSTGHY7YLU · pith_short_8: 4XPYTBWS

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/4XPYTBWSTGHY7YLU3NV7CUJV4P \
  | 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: e5df8986d2998f8fe174db6bf15135e3fdd2a735ef7154c2b1d4168750331990

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9cd5bfa0d6c8d95aba27737fbaeb4e33d7f0ac472ab30410ee42cb549337aef1",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2012-09-24T06:31:04Z",
    "title_canon_sha256": "499233b15e80b9f019194db0e18114fc091645a406afee816ba8d8dc42a69d67"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5159",
    "kind": "arxiv",
    "version": 1
  }
}