Pith Number

pith:AO4QFRX2

pith:2011:AO4QFRX2WMK3CSR4N4KIPBPM32

not attested not anchored not stored refs pending

Lower Bounds for the Average and Smoothed Number of Pareto Optima

Luis Rademacher, Navin Goyal

arxiv:1107.3876 v1 · 2011-07-20 · 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{AO4QFRX2WMK3CSR4N4KIPBPM32}

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	2026-05-18T04:17:14.495830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

03b902c6fab315b14a3c6f148785ecde9c45a289778fefc53447ebcefdc3fcd6

Aliases

arxiv: 1107.3876 · arxiv_version: 1107.3876v1 · doi: 10.48550/arxiv.1107.3876 · pith_short_12: AO4QFRX2WMK3 · pith_short_16: AO4QFRX2WMK3CSR4 · pith_short_8: AO4QFRX2

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/AO4QFRX2WMK3CSR4N4KIPBPM32 \
  | 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: 03b902c6fab315b14a3c6f148785ecde9c45a289778fefc53447ebcefdc3fcd6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fec4a916b6d19be8ba13d3f331705f5aba574d15a0c0b61406dce61894aafaad",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.DS",
    "submitted_at": "2011-07-20T02:13:01Z",
    "title_canon_sha256": "2d1ee31ceafd826395ef54ee66f7ee48d245c78759f0b38f5eacf4ce21eaac0d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.3876",
    "kind": "arxiv",
    "version": 1
  }
}