Pith Number

pith:IGGJGF2E

pith:2019:IGGJGF2EQDWFL2CK3VHFWFGI4A

not attested not anchored not stored refs pending

A Detailed Analysis of Quicksort Running Time

Doron Zeilberger, Shalosh B. Ekhad

arxiv:1903.03708 v1 · 2019-03-09 · math.PR · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{IGGJGF2EQDWFL2CK3VHFWFGI4A}

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	2026-05-17T23:51:41.200378Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

418c93174480ec55e84add4e5b14c8e017ca4df081a967247044a364d555a472

Aliases

arxiv: 1903.03708 · arxiv_version: 1903.03708v1 · doi: 10.48550/arxiv.1903.03708 · pith_short_12: IGGJGF2EQDWF · pith_short_16: IGGJGF2EQDWFL2CK · pith_short_8: IGGJGF2E

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/IGGJGF2EQDWFL2CK3VHFWFGI4A \
  | 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: 418c93174480ec55e84add4e5b14c8e017ca4df081a967247044a364d555a472

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5ddc69a3d1c0150f1604a728526385db4e373480fe3e4c6290b66183094783eb",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2019-03-09T00:40:35Z",
    "title_canon_sha256": "79ee8139f275b99ed9bf9d709fb7801f704991f63fcb87fdadf1a158af247474"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1903.03708",
    "kind": "arxiv",
    "version": 1
  }
}