Pith Number

pith:M7K4EI6W

pith:2000:M7K4EI6WDKSCDYBCIDHHKAKNG5

not attested not anchored not stored refs pending

The statistics of wide-separation lensed quasars

2), (2) Cambridge University), Daniel J. Mortlock (1, Rachel L. Webster (1) ((1) University of Melbourne

arxiv:astro-ph/0008081 v1 · 2000-08-04 · astro-ph

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M7K4EI6WDKSCDYBCIDHHKAKNG5}

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

From Matter Density to Deflection Angle and Gravitational Lensing Using a Perturbative Method

Receipt and verification

First computed	2026-07-04T16:17:00.002991Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

67d5c223d61aa421e02240ce75014d37525e607901cd3afcfeeb5f5da036c7e9

Aliases

arxiv: astro-ph/0008081 · arxiv_version: astro-ph/0008081v1 · doi: 10.48550/arxiv.astro-ph/0008081 · pith_short_12: M7K4EI6WDKSC · pith_short_16: M7K4EI6WDKSCDYBC · pith_short_8: M7K4EI6W

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/M7K4EI6WDKSCDYBCIDHHKAKNG5 \
  | 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: 67d5c223d61aa421e02240ce75014d37525e607901cd3afcfeeb5f5da036c7e9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fca080431c1d063d1479d040fac5c2bcd914a9a4b3ca5241359f303ac4642ee4",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2000-08-04T13:42:06Z",
    "title_canon_sha256": "63cb07e58abcf2b21f1df78bfa7a7fc5d229f4f4b750a759e5721e17081eafe7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0008081",
    "kind": "arxiv",
    "version": 1
  }
}