Pith Number

pith:PDA6E56Q

pith:2026:PDA6E56QWAIHMTWAIDN7KWLGEX

not attested not anchored not stored refs resolved

Sampling pseudospectrum for data-driven matrices

Caroline Wormell

A sampling pseudospectrum estimator lets users test statistically whether eigenvalues from finite data are genuine or sampling artifacts.

arxiv:2605.15234 v1 · 2026-05-13 · math.NA · cs.NA · math.SP · math.ST · stat.CO · stat.TH

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\pithnumber{PDA6E56QWAIHMTWAIDN7KWLGEX}

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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

The estimator ˆP(λ), which can be obtained by reprocessing our finite data sample, allows us to test statistically for the location of the true eigenvalues and gives a rigorous way to assess whether extracted patterns are signal or noise.

C2weakest assumption

The central premise that reprocessing the finite data sample yields an unbiased estimator for the sampling pseudospectrum of the underlying infinite-data operator, without additional assumptions on the distribution of sampling errors or the structure of the true operator.

C3one line summary

Introduces a sampling pseudospectrum P(λ) and estimator ˆP(λ) obtained by reprocessing finite data to statistically test the location of true eigenvalues versus sampling artifacts in data-driven matrices.

References

31 extracted · 31 resolved · 1 Pith anchors

[1] A Collatz-Wielandt characterization of the spectral radius of order-preserving homogeneous maps on cones 2011 · arXiv:1112.5968

[2] Ergodic theory, dynamic mode decomposition, and computation of spectral properties of the koopman operator.SIAM Journal on Applied Dynamical Systems, 16(4):2096–2126, 2017 2096

[3] Arnold.Random dynamical systems 1998

[4] VivianeBaladi.Dynamical zeta functions and dynamical determinants for hyperbolic maps. Springer, 2018 2018

[5] Rayleigh-bénard convection.Contemporary Physics, 25(6):535–582, 1984 1984

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:47.622621Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78c1e277d0b010764ec040dbf5596625d18e2d514ba670659ab949cbda585530

Aliases

arxiv: 2605.15234 · arxiv_version: 2605.15234v1 · doi: 10.48550/arxiv.2605.15234 · pith_short_12: PDA6E56QWAIH · pith_short_16: PDA6E56QWAIHMTWA · pith_short_8: PDA6E56Q

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/PDA6E56QWAIHMTWAIDN7KWLGEX \
  | 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: 78c1e277d0b010764ec040dbf5596625d18e2d514ba670659ab949cbda585530

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5464a6de77cf430893f238a843d354916e5caeec8f2875dd454697e6826ac150",
    "cross_cats_sorted": [
      "cs.NA",
      "math.SP",
      "math.ST",
      "stat.CO",
      "stat.TH"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2026-05-13T18:25:15Z",
    "title_canon_sha256": "efad13aa568b04dbdbc493876ccd6ebc41beeae76155bcc6d5324e747400c7b6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15234",
    "kind": "arxiv",
    "version": 1
  }
}