Pith Number

pith:D6ITMPNY

pith:2005:D6ITMPNYMJUZT4VZIVQ24LZIK2

not attested not anchored not stored refs pending

Derivation of the Raychaudhuri Equation

Naresh Dadhich

arxiv:gr-qc/0511123 v2 · 2005-11-23 · gr-qc · astro-ph · 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{D6ITMPNYMJUZT4VZIVQ24LZIK2}

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

Exploring Cosmological Implications of the Modified Raychaudhuri Equation in Non-Gravitating Vacuum Energy Theory

Receipt and verification

First computed	2026-07-04T14:51:33.690391Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1f91363db8626999f2b94561ae2f28568cb36188f1bc6e689ddcca6c7e242591

Aliases

arxiv: gr-qc/0511123 · arxiv_version: gr-qc/0511123v2 · doi: 10.48550/arxiv.gr-qc/0511123 · pith_short_12: D6ITMPNYMJUZ · pith_short_16: D6ITMPNYMJUZT4VZ · pith_short_8: D6ITMPNY

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/D6ITMPNYMJUZT4VZIVQ24LZIK2 \
  | 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: 1f91363db8626999f2b94561ae2f28568cb36188f1bc6e689ddcca6c7e242591

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "62ee7932ca5f389a79c5b356260ae8cf78678917ad0d9417a019495745d89ced",
    "cross_cats_sorted": [
      "astro-ph",
      "hep-th"
    ],
    "license": "",
    "primary_cat": "gr-qc",
    "submitted_at": "2005-11-23T10:19:49Z",
    "title_canon_sha256": "6cf8368615afa7bc47fc63c0d27e2ac8240c7af6c76b11133f6e5d35cbd76c3a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "gr-qc/0511123",
    "kind": "arxiv",
    "version": 2
  }
}