Pith Number

pith:HLVPGYP6

pith:2015:HLVPGYP6AMHWINCCQHM5674WI2

not attested not anchored not stored refs pending

f(R) gravity on non-linear scales: The post-Friedmann expansion and the vector potential

Baojiu Li, Daniel B Thomas, Gong-Bo Zhao, Kazuya Koyama, Marco Bruni

arxiv:1503.07204 v2 · 2015-03-24 · gr-qc · 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{HLVPGYP6AMHWINCCQHM5674WI2}

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	2026-05-18T01:27:46.207767Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3aeaf361fe030f64344281d9df7f9646b7d22a4407fb96e8bb2e629116f74719

Aliases

arxiv: 1503.07204 · arxiv_version: 1503.07204v2 · doi: 10.48550/arxiv.1503.07204 · pith_short_12: HLVPGYP6AMHW · pith_short_16: HLVPGYP6AMHWINCC · pith_short_8: HLVPGYP6

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/HLVPGYP6AMHWINCCQHM5674WI2 \
  | 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: 3aeaf361fe030f64344281d9df7f9646b7d22a4407fb96e8bb2e629116f74719

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "171bfd535ad713bea277ac1338b0ad187f71ffdd4e020106da6a6c1601a85b03",
    "cross_cats_sorted": [
      "astro-ph.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2015-03-24T21:02:27Z",
    "title_canon_sha256": "49ae830d4a882919a75796b4d1d7d68835c74685d9c82a5078b01d2d0e873511"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1503.07204",
    "kind": "arxiv",
    "version": 2
  }
}