Pith Number

pith:VXK7TXQO

pith:2025:VXK7TXQO7OH4E7IRME3DNGMSOW

not attested not anchored not stored refs pending

Vacuum Polarization, Geodesic Equation and Sachs-Wolfe Effect

Ali Kaya

arxiv:2502.08748 v3 · 2025-02-12 · astro-ph.CO · 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{VXK7TXQO7OH4E7IRME3DNGMSOW}

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	2026-07-05T11:40:32.792351Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

add5f9de0efb8fc27d11613636999275b83465f090017f3e1154f39d8155b78e

Aliases

arxiv: 2502.08748 · arxiv_version: 2502.08748v3 · doi: 10.48550/arxiv.2502.08748 · pith_short_12: VXK7TXQO7OH4 · pith_short_16: VXK7TXQO7OH4E7IR · pith_short_8: VXK7TXQO

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/VXK7TXQO7OH4E7IRME3DNGMSOW \
  | 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: add5f9de0efb8fc27d11613636999275b83465f090017f3e1154f39d8155b78e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d627a852d41da0e9a7bafe763daf4a2e2726d41dc76a6a7ea413ab8088cdd355",
    "cross_cats_sorted": [
      "gr-qc",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2025-02-12T19:38:21Z",
    "title_canon_sha256": "5fb6b4fcb505127829f8cb5cdb5b2378124c086ea954019d373da90375d4631d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2502.08748",
    "kind": "arxiv",
    "version": 3
  }
}