Pith Number

pith:GTRD4GPY

pith:2010:GTRD4GPYOQC3VVGRT7OEHJGJMB

not attested not anchored not stored refs pending

Higher order scrambled digital nets achieve the optimal rate of the root mean square error for smooth integrands

Josef Dick

arxiv:1007.0842 v4 · 2010-07-06 · math.NA · math.ST · stat.CO · stat.TH

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GTRD4GPYOQC3VVGRT7OEHJGJMB}

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	2026-05-18T03:40:25.922188Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

34e23e19f87405bad4d19fdc43a4c96046c95a04405b81e4c4afaccf5d64985b

Aliases

arxiv: 1007.0842 · arxiv_version: 1007.0842v4 · doi: 10.48550/arxiv.1007.0842 · pith_short_12: GTRD4GPYOQC3 · pith_short_16: GTRD4GPYOQC3VVGR · pith_short_8: GTRD4GPY

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/GTRD4GPYOQC3VVGRT7OEHJGJMB \
  | 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: 34e23e19f87405bad4d19fdc43a4c96046c95a04405b81e4c4afaccf5d64985b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "55c35ef2d19021b0c19eda8801cdee040d6232f107b86e2fb054a439c2b9297c",
    "cross_cats_sorted": [
      "math.ST",
      "stat.CO",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2010-07-06T09:30:11Z",
    "title_canon_sha256": "537317c9443c25ac4df7ad259a9bd560185d67a2c4ad6a928a8562bc9342af7f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1007.0842",
    "kind": "arxiv",
    "version": 4
  }
}