Pith Number

pith:MW3MIDWO

pith:2013:MW3MIDWO73MDCWRDJOSTE4VKAH

not attested not anchored not stored refs pending

Lower bounds for the integration error for multivariate functions with mixed smoothness and optimal Fibonacci cubature for functions on the square

Dinh D\~ung, Tino Ullrich

arxiv:1311.1563 v2 · 2013-11-07 · math.NA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MW3MIDWO73MDCWRDJOSTE4VKAH}

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	2026-05-18T03:00:49.103710Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

65b6c40ecefed8315a234ba53272aa01c1a14e34a110c385b68a3e013b29e6be

Aliases

arxiv: 1311.1563 · arxiv_version: 1311.1563v2 · doi: 10.48550/arxiv.1311.1563 · pith_short_12: MW3MIDWO73MD · pith_short_16: MW3MIDWO73MDCWRD · pith_short_8: MW3MIDWO

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/MW3MIDWO73MDCWRDJOSTE4VKAH \
  | 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: 65b6c40ecefed8315a234ba53272aa01c1a14e34a110c385b68a3e013b29e6be

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "90e1e2ac313de5d60c73d3078e377c921023ef12f17a71b7c5555d64d9686660",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2013-11-07T03:14:32Z",
    "title_canon_sha256": "e482f32c9608e65d32c9746deebd63eafab18d52797dc63cd7dc851b0360b70a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.1563",
    "kind": "arxiv",
    "version": 2
  }
}