Pith Number

pith:AJSHX4FN

pith:1997:AJSHX4FNSCIA6JIF2UWKGUGZGT

not attested not anchored not stored refs pending

A New Method for Determining Cumulative Gravitational Lensing Effects in Inhomogeneous Universes

Daniel E. Holz, Robert M. Wald (University of Chicago)

arxiv:astro-ph/9708036 v2 · 1997-08-04 · astro-ph · 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{AJSHX4FNSCIA6JIF2UWKGUGZGT}

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

2 papers in Pith

Cosmology Intertwined: A Review of the Particle Physics, Astrophysics, and Cosmology Associated with the Cosmological Tensions and Anomalies

Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant

Receipt and verification

First computed	2026-05-18T01:08:08.105083Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

02647bf0ad90900f2505d52ca350d934e15221a144833c2ceaab0de131fd31f1

Aliases

arxiv: astro-ph/9708036 · arxiv_version: astro-ph/9708036v2 · doi: 10.48550/arxiv.astro-ph/9708036 · pith_short_12: AJSHX4FNSCIA · pith_short_16: AJSHX4FNSCIA6JIF · pith_short_8: AJSHX4FN

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/AJSHX4FNSCIA6JIF2UWKGUGZGT \
  | 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: 02647bf0ad90900f2505d52ca350d934e15221a144833c2ceaab0de131fd31f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "02ff9fc40a63b96a794d19771c61f91bf1d10fef30058df8942d2ea9c6be2cc7",
    "cross_cats_sorted": [
      "gr-qc"
    ],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1997-08-04T22:18:39Z",
    "title_canon_sha256": "8662965b59d6ba909670bb6ed7abc749de82d18344331ad05847b60e312b9332"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9708036",
    "kind": "arxiv",
    "version": 2
  }
}