Pith Number

pith:S6CDWYEG

pith:2016:S6CDWYEG2NIKNS5FWCRJPRZDD3

not attested not anchored not stored refs pending

Counting Zeros in Random Walks on the Integers and Analysis of Optimal Dual-Pivot Quicksort

Clemens Heuberger, Daniel Krenn, Helmut Prodinger, Martin Aum\"uller, Martin Dietzfelbinger

arxiv:1602.04031 v2 · 2016-02-12 · math.CO · 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{S6CDWYEG2NIKNS5FWCRJPRZDD3}

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	2026-05-18T01:15:06.311192Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

97843b6086d350a6cba5b0a297c7231ef4e1d84520987bb48cf03f32c7bd2ee5

Aliases

arxiv: 1602.04031 · arxiv_version: 1602.04031v2 · doi: 10.48550/arxiv.1602.04031 · pith_short_12: S6CDWYEG2NIK · pith_short_16: S6CDWYEG2NIKNS5F · pith_short_8: S6CDWYEG

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/S6CDWYEG2NIKNS5FWCRJPRZDD3 \
  | 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: 97843b6086d350a6cba5b0a297c7231ef4e1d84520987bb48cf03f32c7bd2ee5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a25068e256e38b0d5f2c9edb6181ae9faf5d265522b2615e6c5f126b196213e3",
    "cross_cats_sorted": [
      "cs.DS"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2016-02-12T12:34:37Z",
    "title_canon_sha256": "1bc41b39f54f108b78c784be4ce729b5ffa42df6453152722d1ad382169922e7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1602.04031",
    "kind": "arxiv",
    "version": 2
  }
}