Pith Number

pith:RKIWER3X

pith:2026:RKIWER3XX6K36PISXILKJULRVX

not attested not anchored not stored refs pending

Primordial Black Hole Formation in $f(R)=R+\alpha R^2$ Gravity: Perturbative and Non-Perturbative Analysis

A. Eid, G.G.L. Nashed

arxiv:2601.02416 v2 · 2026-01-03 · 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{RKIWER3XX6K36PISXILKJULRVX}

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	2026-06-05T01:14:32.949078Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

8a91624777bf95bf3d12ba16a4d171add509fbc3841fbb00bf36b2394db31a19

Aliases

arxiv: 2601.02416 · arxiv_version: 2601.02416v2 · doi: 10.48550/arxiv.2601.02416 · pith_short_12: RKIWER3XX6K3 · pith_short_16: RKIWER3XX6K36PIS · pith_short_8: RKIWER3X

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/RKIWER3XX6K36PISXILKJULRVX \
  | 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: 8a91624777bf95bf3d12ba16a4d171add509fbc3841fbb00bf36b2394db31a19

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "35eeeb2535367936bef2a63af127154a68e9e1d967cf191a4ecbea777731bfe2",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "hep-th"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2026-01-03T09:47:38Z",
    "title_canon_sha256": "e6e888a7791678163055addd4520625c52600536caaed052f035e6518d3e1060"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2601.02416",
    "kind": "arxiv",
    "version": 2
  }
}