Pith Number

pith:MLUZGFWX

pith:2016:MLUZGFWXTIULYK7GGHP6IVMCXB

not attested not anchored not stored refs pending

Quicksort Is Optimal For Many Equal Keys

Sebastian Wild

arxiv:1608.04906 v4 · 2016-08-17 · cs.DS · math.PR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MLUZGFWXTIULYK7GGHP6IVMCXB}

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	2026-05-17T23:47:06.061908Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62e99316d79a28bc2be631dfe45582b8762a885d183a8c3aba486d7bb3b69c1c

Aliases

arxiv: 1608.04906 · arxiv_version: 1608.04906v4 · doi: 10.48550/arxiv.1608.04906 · pith_short_12: MLUZGFWXTIUL · pith_short_16: MLUZGFWXTIULYK7G · pith_short_8: MLUZGFWX

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/MLUZGFWXTIULYK7GGHP6IVMCXB \
  | 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: 62e99316d79a28bc2be631dfe45582b8762a885d183a8c3aba486d7bb3b69c1c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b266a8d1fcd833168dc2f385fa59e731efb79b824c481fc7538aba19e95ea874",
    "cross_cats_sorted": [
      "math.PR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2016-08-17T09:41:53Z",
    "title_canon_sha256": "193b9d4380a7bc9a3f8c12602aa43d5a6063ed9c81bc9d690b1628b4d00d916f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1608.04906",
    "kind": "arxiv",
    "version": 4
  }
}