Pith Number

pith:7Y4AHXTQ

pith:2016:7Y4AHXTQEMSS5HFFKA2EMEFQIE

not attested not anchored not stored refs pending

Effective gravitational couplings for cosmological perturbations in generalized Proca theories

Antonio De Felice, Lavinia Heisenberg, Ryotaro Kase, Shinji Mukohyama, Shinji Tsujikawa, Ying-li Zhang

arxiv:1605.05066 v2 · 2016-05-17 · 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{7Y4AHXTQEMSS5HFFKA2EMEFQIE}

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	2026-05-18T01:08:41.280775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe3803de7023252e9ca550344610b0411a89c5e94f5a3d7228e6ac5601b6272a

Aliases

arxiv: 1605.05066 · arxiv_version: 1605.05066v2 · doi: 10.48550/arxiv.1605.05066 · pith_short_12: 7Y4AHXTQEMSS · pith_short_16: 7Y4AHXTQEMSS5HFF · pith_short_8: 7Y4AHXTQ

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/7Y4AHXTQEMSS5HFFKA2EMEFQIE \
  | 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: fe3803de7023252e9ca550344610b0411a89c5e94f5a3d7228e6ac5601b6272a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5a45d675527d9b7c9ddb8085b7ee19f8501672477740883e50951213aa2b7568",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-05-17T09:07:52Z",
    "title_canon_sha256": "a00ecb43cc534bf58a70d6e559bfdae9e007907721d11103a449c86b484df784"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.05066",
    "kind": "arxiv",
    "version": 2
  }
}