Pith Number

pith:PNCJJAEY

pith:2025:PNCJJAEYCWJ5RMS6GJQHSNYAGO

not attested not anchored not stored refs pending

Effects of gravitational lensing on neutrino oscillation in Hu-Sawicki f(R) gravity

Shu-Jun Rong, Ya-Ru Wang, Ze-Wen Li

arxiv:2506.23905 v4 · 2025-06-30 · hep-ph · gr-qc

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PNCJJAEYCWJ5RMS6GJQHSNYAGO}

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	2026-06-24T01:14:57.740698Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7b449480981593d8b25e3260793700339b54eb380487a90d2ec6ca878aabd566

Aliases

arxiv: 2506.23905 · arxiv_version: 2506.23905v4 · doi: 10.48550/arxiv.2506.23905 · pith_short_12: PNCJJAEYCWJ5 · pith_short_16: PNCJJAEYCWJ5RMS6 · pith_short_8: PNCJJAEY

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/PNCJJAEYCWJ5RMS6GJQHSNYAGO \
  | 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: 7b449480981593d8b25e3260793700339b54eb380487a90d2ec6ca878aabd566

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "721c054d626f390e208ef187fd2eb4539ce8a1e13748a736e3297099f3c730ce",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
    "primary_cat": "hep-ph",
    "submitted_at": "2025-06-30T14:36:24Z",
    "title_canon_sha256": "84815acc788c9adb82870eee9e90a2dea5494557a8d6ef07805635456cd6780a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2506.23905",
    "kind": "arxiv",
    "version": 4
  }
}