Pith Number

pith:4JGXY3WL

pith:2006:4JGXY3WL4KD2DQ7UCPTAHXOOMF

not attested not anchored not stored refs pending

Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings III: Frames

Erich Novak, Stephan Dahlke, Winfried Sickel

arxiv:math/0611569 v2 · 2006-11-19 · math.NA · cs.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{4JGXY3WL4KD2DQ7UCPTAHXOOMF}

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	2026-06-03T22:06:21.328202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e24d7c6ecbe287a1c3f413e603ddce616ca487a5904ab6f827936d0036c0cf56

Aliases

arxiv: math/0611569 · arxiv_version: math/0611569v2 · doi: 10.48550/arxiv.math/0611569 · pith_short_12: 4JGXY3WL4KD2 · pith_short_16: 4JGXY3WL4KD2DQ7U · pith_short_8: 4JGXY3WL

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/4JGXY3WL4KD2DQ7UCPTAHXOOMF \
  | 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: e24d7c6ecbe287a1c3f413e603ddce616ca487a5904ab6f827936d0036c0cf56

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c4ee2ed1801ecb03aa567d28918775a9840eec6c3d1a15404382cb208bc20505",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "",
    "primary_cat": "math.NA",
    "submitted_at": "2006-11-19T10:58:34Z",
    "title_canon_sha256": "dd40890c241d601ed569668661642a833343a4229047c97b55b98c985bd96310"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0611569",
    "kind": "arxiv",
    "version": 2
  }
}