Pith Number

pith:XD45EBN5

pith:1997:XD45EBN5F7334YNPOIXMN7ZRVY

not attested not anchored not stored refs pending

Weak Lensing, Shear and the Cosmic Virial Theorem in a Model with a Scale-Dependent Gravitational Coupling

Orfeu Bertolami

arxiv:astro-ph/9702140 v2 · 1997-02-17 · astro-ph

Open paper page JSON Open Graph Bundle Merged state What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XD45EBN5F7334YNPOIXMN7ZRVY}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more

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	2026-05-18T01:40:18.107845Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b8f9d205bd2ff7be61af722ec6ff31ae3275d7d58f2e3494439ee9c6f413c13e

Aliases

arxiv: astro-ph/9702140 · arxiv_version: astro-ph/9702140v2 · doi: 10.48550/arxiv.astro-ph/9702140 · pith_short_12: XD45EBN5F733 · pith_short_16: XD45EBN5F7334YNP · pith_short_8: XD45EBN5

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/XD45EBN5F7334YNPOIXMN7ZRVY \
  | 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: b8f9d205bd2ff7be61af722ec6ff31ae3275d7d58f2e3494439ee9c6f413c13e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "819b21c77252bca3f6f19615e6809e0bfcf45851545b76550ca81d14380b09e6",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1997-02-17T13:06:27Z",
    "title_canon_sha256": "b379db1f8b49ae5169144c4e757d240c24450c1b56fe5797ca92ed0fe5c59aae"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9702140",
    "kind": "arxiv",
    "version": 2
  }
}