Pith Number

pith:WQWA6MKE

pith:1993:WQWA6MKEWK7DTFGSGPZNSNCPYB

not attested not anchored not stored refs pending

A further discussion on quasar-galaxy associations from gravitational lensing

Xiang-Ping Wu

arxiv:astro-ph/9312058 v1 · 1993-12-24 · 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{WQWA6MKEWK7DTFGSGPZNSNCPYB}

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	2026-05-18T04:21:41.273358Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b42c0f3144b2be3994d233f2d9344fc059135cafddee698e927b44e0b60d5512

Aliases

arxiv: astro-ph/9312058 · arxiv_version: astro-ph/9312058v1 · doi: 10.48550/arxiv.astro-ph/9312058 · pith_short_12: WQWA6MKEWK7D · pith_short_16: WQWA6MKEWK7DTFGS · pith_short_8: WQWA6MKE

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/WQWA6MKEWK7DTFGSGPZNSNCPYB \
  | 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: b42c0f3144b2be3994d233f2d9344fc059135cafddee698e927b44e0b60d5512

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "69c892de004bde0448b57b032c46f1ef325c7221fd1141da55e13ac8faecd4a3",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "1993-12-24T17:51:51Z",
    "title_canon_sha256": "c0434f0287d001897cc31476b0e8d503476741ae29141a8ef17af535e13f6cf7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/9312058",
    "kind": "arxiv",
    "version": 1
  }
}