Pith Number

pith:O2BV7DBJ

pith:2020:O2BV7DBJI5AHNXUTF42ZI3Z742

not attested not anchored not stored refs pending

Null geodesic congruences, gravitational lensing and CMB intensity profile

Ali Kaya

arxiv:2010.10551 v2 · 2020-10-20 · 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{O2BV7DBJI5AHNXUTF42ZI3Z742}

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

Vacuum Polarization, Geodesic Equation and Sachs-Wolfe Effect

Receipt and verification

First computed	2026-07-05T02:12:09.297805Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

76835f8c29474076de932f35946f3fe6834959cac3dcff38d001bc7cafe5a634

Aliases

arxiv: 2010.10551 · arxiv_version: 2010.10551v2 · doi: 10.48550/arxiv.2010.10551 · pith_short_12: O2BV7DBJI5AH · pith_short_16: O2BV7DBJI5AHNXUT · pith_short_8: O2BV7DBJ

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/O2BV7DBJI5AHNXUTF42ZI3Z742 \
  | 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: 76835f8c29474076de932f35946f3fe6834959cac3dcff38d001bc7cafe5a634

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "42c355880f3b3592b5700be386c373c29e60b1a7d1cc483060e5c5e3bd5d0b85",
    "cross_cats_sorted": [
      "astro-ph.CO",
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2020-10-20T18:07:39Z",
    "title_canon_sha256": "70d5132cec52e42846e7a9f39c957c89606ec6d2d5c7dc9eecd397071fd46a1e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2010.10551",
    "kind": "arxiv",
    "version": 2
  }
}