Pith Number

pith:XXZ7UK6E

pith:1999:XXZ7UK6E2TGSDHZAMAY7XHDPWU

not attested not anchored not stored refs pending

A Lower Bound on the Average-Case Complexity of Shellsort

Ming Li (U. Waterloo), Paul Vitanyi (CWI & U. Amsterdam), Tao Jiang (McMaster U.)

arxiv:cs/9906008 v2 · 1999-06-04 · cs.CC · cs.DS

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XXZ7UK6E2TGSDHZAMAY7XHDPWU}

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	2026-05-18T02:28:29.753939Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdf3fa2bc4d4cd219f206031fb9c6fb50275affd238338032d56ae81637113ba

Aliases

arxiv: cs/9906008 · arxiv_version: cs/9906008v2 · doi: 10.48550/arxiv.cs/9906008 · pith_short_12: XXZ7UK6E2TGS · pith_short_16: XXZ7UK6E2TGSDHZA · pith_short_8: XXZ7UK6E

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/XXZ7UK6E2TGSDHZAMAY7XHDPWU \
  | 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: bdf3fa2bc4d4cd219f206031fb9c6fb50275affd238338032d56ae81637113ba

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a1467a3dd57b56dc9ea87c3811a76b269e0086829fdb4340b9d6b7ec47f4b464",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CC",
    "submitted_at": "1999-06-04T15:11:31Z",
    "title_canon_sha256": "9b1a2af1f8b9f1b80742b4f6ec45074ae5a81822fd511182d4b6380e3948d940"
  },
  "schema_version": "1.0",
  "source": {
    "id": "cs/9906008",
    "kind": "arxiv",
    "version": 2
  }
}