Pith Number

pith:L4Z5W2BE

pith:2018:L4Z5W2BECKUAFOWMV4C7632ZKC

not attested not anchored not stored refs pending

Raychaudhuri and optical equations for null geodesic congruences with torsion

Simone Speziale

arxiv:1808.00952 v3 · 2018-08-02 · 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{L4Z5W2BECKUAFOWMV4C7632ZKC}

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	2026-05-18T00:02:31.417417Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5f33db682412a802baccaf05ff6f5950852c6b084165415d3a845921cd62b341

Aliases

arxiv: 1808.00952 · arxiv_version: 1808.00952v3 · doi: 10.48550/arxiv.1808.00952 · pith_short_12: L4Z5W2BECKUA · pith_short_16: L4Z5W2BECKUAFOWM · pith_short_8: L4Z5W2BE

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/L4Z5W2BECKUAFOWMV4C7632ZKC \
  | 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: 5f33db682412a802baccaf05ff6f5950852c6b084165415d3a845921cd62b341

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "71e254820791d6036b5d358fda7a3930230491d09bf578fa4e621d18b89ed3a5",
    "cross_cats_sorted": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2018-08-02T17:56:57Z",
    "title_canon_sha256": "9b74b8b59096e8ce9b8c561d859b1fa7fbf978da887dc4c1048c93330afd20ab"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1808.00952",
    "kind": "arxiv",
    "version": 3
  }
}