Pith Number

pith:2MXC7QCB

pith:2021:2MXC7QCB26NAA5LZARQRCVWRXA

not attested not anchored not stored refs pending

Pre-Inflationary Bounce Effects on Primordial Gravitational Waves of $f(R)$ Gravity

S.D. Odintsov, V.K. Oikonomou

arxiv:2112.02584 v1 · 2021-12-05 · gr-qc · 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{2MXC7QCB26NAA5LZARQRCVWRXA}

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

Freeze-out and spectral running of primordial gravitational waves in viscous cosmology

Receipt and verification

First computed	2026-07-05T03:45:55.766796Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d32e2fc041d79a00757904611156d1b8153e997a172ae86f6442c148be068154

Aliases

arxiv: 2112.02584 · arxiv_version: 2112.02584v1 · doi: 10.48550/arxiv.2112.02584 · pith_short_12: 2MXC7QCB26NA · pith_short_16: 2MXC7QCB26NAA5LZ · pith_short_8: 2MXC7QCB

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/2MXC7QCB26NAA5LZARQRCVWRXA \
  | 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: d32e2fc041d79a00757904611156d1b8153e997a172ae86f6442c148be068154

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fa11fde3022612708a10c2f6320597bd8b48d21820942eb4f16e137067f3bbc9",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2021-12-05T14:35:16Z",
    "title_canon_sha256": "17ef43c5a7d2e954c753cf1d06f8ca2f28f661a813685212b964810bb55d0308"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2112.02584",
    "kind": "arxiv",
    "version": 1
  }
}