Pith Number

pith:KQPSVYRI

pith:2026:KQPSVYRICKYVTEMTOREI7QOUBV

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Subspace Pruning via Principal Vectors for Accurate Koopman-Based Approximations

Dhruv Shah, Jorge Cort\'es

A hybrid principal-vector pruning framework refines Koopman subspace invariance with error bounds and rank-one update efficiency for lifted linear prediction.

arxiv:2605.13135 v1 · 2026-05-13 · eess.SY · cs.SY

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Claims

C1strongest claim

We establish the geometric equivalence between consistency-based methods and principal-vector pruning, and build on this insight to introduce a hybrid strategy that balances between multiple and single principal vector pruning for improved numerical stability and scalability.

C2weakest assumption

That the principal angles between a candidate subspace and its image under the Koopman operator provide a sufficient and refinable measure of invariance error that can be systematically reduced by pruning without losing essential dynamical information.

C3one line summary

A hybrid principal-vector pruning framework refines Koopman subspace invariance with error bounds and rank-one update efficiency for lifted linear prediction.

References

50 extracted · 50 resolved · 1 Pith anchors

[1] We construct a transformation matrixT∈R s×(s−k) by padding Ewith zeros to align with the originals-dimensional space: T= E 0k×(s−k) .(25)

[2] We then perform a QR decomposition ofCas C=Q CRC,(26) whereQ C ∈R s×(s−k) is orthogonal andR new =R C ∈ R(s−k)×(s−k) is the new upper triangular factor

[3] The matricesW new andR new are a valid QR decomposition ofKU new, i.e., KU new =W newRC

[4] We employ these eigenfunctions as the ground truth for evaluating the accuracy of the pruning algorithms

[5] Note that kernel EDMD performs the orthogonal projection using the kernel inner product, which is different from the standard L2(µX)inner product used in our other examples

Formal links

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Receipt and verification

First computed	2026-05-18T03:08:57.602853Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

541f2ae22812b159919374488fc1d40d59d80228d1561c09036763c8601e47e8

Aliases

arxiv: 2605.13135 · arxiv_version: 2605.13135v1 · doi: 10.48550/arxiv.2605.13135 · pith_short_12: KQPSVYRICKYV · pith_short_16: KQPSVYRICKYVTEMT · pith_short_8: KQPSVYRI

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KQPSVYRICKYVTEMTOREI7QOUBV \
  | 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: 541f2ae22812b159919374488fc1d40d59d80228d1561c09036763c8601e47e8

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f56663f0735ea4992d17ac3b9b93369378cd1698da5b0bf77a5dfdb3bbb2caa4",
    "cross_cats_sorted": [
      "cs.SY"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "eess.SY",
    "submitted_at": "2026-05-13T08:04:38Z",
    "title_canon_sha256": "8a411ea5a9d6daa8ed39621a4d125d2b68ae5d78072fc876712f867bac2b7eb7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13135",
    "kind": "arxiv",
    "version": 1
  }
}