Pith Number

pith:NA6KHZHR

pith:2003:NA6KHZHR7WXGERECY3ARRTPR7B

not attested not anchored not stored refs pending

The Effects of Massive Substructures on Image Multiplicities in Gravitati onal Lenses

C. S. Kochanek, J. D. Cohn

arxiv:astro-ph/0306171 v2 · 2003-06-09 · 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{NA6KHZHR7WXGERECY3ARRTPR7B}

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

Probing Dark Matter Substructure with Image Number Anomaly in Strong Lensing Systems

Receipt and verification

First computed	2026-07-04T16:37:16.373752Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

683ca3e4f1fdae624482c6c118cdf1f86f496bf2f3bebbf273466eed20d8396b

Aliases

arxiv: astro-ph/0306171 · arxiv_version: astro-ph/0306171v2 · doi: 10.48550/arxiv.astro-ph/0306171 · pith_short_12: NA6KHZHR7WXG · pith_short_16: NA6KHZHR7WXGEREC · pith_short_8: NA6KHZHR

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/NA6KHZHR7WXGERECY3ARRTPR7B \
  | 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: 683ca3e4f1fdae624482c6c118cdf1f86f496bf2f3bebbf273466eed20d8396b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e9cbd8df3a5eb242c68e5060eedfb6f4d44e8e40e7e4f93349a2c173591f3415",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "astro-ph",
    "submitted_at": "2003-06-09T17:20:04Z",
    "title_canon_sha256": "07665d94a23968a50095eccc235a200a487f159aa30c8a0ccc0c65e60ba2c319"
  },
  "schema_version": "1.0",
  "source": {
    "id": "astro-ph/0306171",
    "kind": "arxiv",
    "version": 2
  }
}