Pith Number

pith:YP7HTSFM

pith:2019:YP7HTSFMKXMK4MHOAHTPR37E7Q

not attested not anchored not stored refs pending

Second-order Gauge-invariant Cosmological Perturbation Theory: Current Status updated in 2019

Kouji Nakamura

arxiv:1912.12805 v2 · 2019-12-30 · gr-qc · astro-ph.CO · hep-th · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YP7HTSFMKXMK4MHOAHTPR37E7Q}

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

Gravitational Memory in Generalized Proca Gravity

Receipt and verification

First computed	2026-07-05T00:38:10.530995Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c3fe79c8ac55d8ae30ee01e6f8efe4fc3ca9b542989f5b451211e7fd164ac0d3

Aliases

arxiv: 1912.12805 · arxiv_version: 1912.12805v2 · doi: 10.48550/arxiv.1912.12805 · pith_short_12: YP7HTSFMKXMK · pith_short_16: YP7HTSFMKXMK4MHO · pith_short_8: YP7HTSFM

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/YP7HTSFMKXMK4MHOAHTPR37E7Q \
  | 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: c3fe79c8ac55d8ae30ee01e6f8efe4fc3ca9b542989f5b451211e7fd164ac0d3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3317c7b3bab11ec932c5c884f7c8f50e10f35d671861e0d81b7fa4281a6ba041",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "hep-th",
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2019-12-30T04:09:20Z",
    "title_canon_sha256": "4ff1ade2d4f248039aaa029d44fc92236f09b8da755040ab183c7b7820dd0e11"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1912.12805",
    "kind": "arxiv",
    "version": 2
  }
}