Pith Number

pith:57YGLPWY

pith:2016:57YGLPWYAWHJQN4UHZGFV5AMSV

not attested not anchored not stored refs pending

Gravitational lens optical scalars in terms of energy-momentum distributions in the cosmological framework

Ezequiel F. Boero, Osvaldo M. Moreschi

arxiv:1610.06032 v5 · 2016-10-19 · 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{57YGLPWYAWHJQN4UHZGFV5AMSV}

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	2026-05-18T00:15:31.019369Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eff065bed8058e9837943e4c5af40c9573a1f2697e9710a0c9c3ad69ad3a4db7

Aliases

arxiv: 1610.06032 · arxiv_version: 1610.06032v5 · doi: 10.48550/arxiv.1610.06032 · pith_short_12: 57YGLPWYAWHJ · pith_short_16: 57YGLPWYAWHJQN4U · pith_short_8: 57YGLPWY

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/57YGLPWYAWHJQN4UHZGFV5AMSV \
  | 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: eff065bed8058e9837943e4c5af40c9573a1f2697e9710a0c9c3ad69ad3a4db7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "eb22d079447b76e6331ee23281f8679b3656cdc908e886ef540a46b7af0ddeb0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "gr-qc",
    "submitted_at": "2016-10-19T14:32:14Z",
    "title_canon_sha256": "0c3f058d3c34671b327d25deda2fe0480160cd5d6b471980b89c3380116c319c"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1610.06032",
    "kind": "arxiv",
    "version": 5
  }
}