Pith Number

pith:UWXOYYPK

pith:2026:UWXOYYPKG4YIFUCNK537VYEQR4

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Limitations of LTI Koopman Modeling for Nonlinear Control Systems

Johannes Heeg, Karl Worthmann

Nonlinear control systems admit exact LTI Koopman models only if they are affine linear, under mild controllability and full-state observables.

arxiv:2604.25290 v2 · 2026-04-28 · math.OC

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\usepackage{pith}
\pithnumber{UWXOYYPKG4YIFUCNK537VYEQR4}

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Record completeness

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4 Citations open

5 Replications open

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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

assuming a mild controllability condition and full-state observables, the dynamics of the underlying control system must be affine linear

C2weakest assumption

The mild controllability condition together with the choice of full-state observables

C3one line summary

Exact LTI Koopman models for controllable nonlinear systems with full-state observables must have affine-linear dynamics.

Receipt and verification

First computed	2026-05-29T01:05:10.616032Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a5aeec61ea373082d04d5777fae0908f2c19f62a48f67796327a0ed2c5ffb309

Aliases

arxiv: 2604.25290 · arxiv_version: 2604.25290v2 · doi: 10.48550/arxiv.2604.25290 · pith_short_12: UWXOYYPKG4YI · pith_short_16: UWXOYYPKG4YIFUCN · pith_short_8: UWXOYYPK

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/UWXOYYPKG4YIFUCNK537VYEQR4 \
  | 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: a5aeec61ea373082d04d5777fae0908f2c19f62a48f67796327a0ed2c5ffb309

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1603fa765ebfbb0430c982636930060f675ef0e56a878f6d1cc08547b1b1b1d9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2026-04-28T06:54:02Z",
    "title_canon_sha256": "611025988060a21730fde05fd7dc57317f156d37477c5795851e82d40c6fb440"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.25290",
    "kind": "arxiv",
    "version": 2
  }
}