Pith Number

pith:EZZC5TMQ

pith:2026:EZZC5TMQEVNFWD4IAWREBLSGIO

not attested not anchored not stored refs pending

Approximation of Functions: Optimal Sampling and Complexity

David Krieg, Mario Ullrich

Finite function evaluations impose strict information-theoretic limits on approximation accuracy.

arxiv:2602.02066 v2 · 2026-02-02 · math.NA · cs.IT · cs.NA · math.IT

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\usepackage{pith}
\pithnumber{EZZC5TMQEVNFWD4IAWREBLSGIO}

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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.

Claims

C1strongest claim

Many fundamental insights into the information-theoretic limits of function approximation from finite evaluations were obtained only recently.

C2weakest assumption

The discussion presupposes standard settings from optimal recovery and information-based complexity without detailing the precise function classes or norms under consideration.

C3one line summary

Survey of information-theoretic limits and optimal sampling for function approximation from finite evaluations, including nonlinear and adaptive measurements.

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-06-24T14:15:55.057913Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

26722ecd90255a5b0f8805a240ae46439e02e3d944adf53b2bd32c6890363403

Aliases

arxiv: 2602.02066 · arxiv_version: 2602.02066v2 · doi: 10.48550/arxiv.2602.02066 · pith_short_12: EZZC5TMQEVNF · pith_short_16: EZZC5TMQEVNFWD4I · pith_short_8: EZZC5TMQ

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/EZZC5TMQEVNFWD4IAWREBLSGIO \
  | 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: 26722ecd90255a5b0f8805a240ae46439e02e3d944adf53b2bd32c6890363403

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2ff737f1af7432427183b8d6d237ee5c8c2c9f96ba31a38eb10e75e218edf376",
    "cross_cats_sorted": [
      "cs.IT",
      "cs.NA",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-02-02T13:07:27Z",
    "title_canon_sha256": "dd3beade83f50c6d680452c0a189e34a480227de1f6fccf1cd17b8b06c092f92"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2602.02066",
    "kind": "arxiv",
    "version": 2
  }
}