Sławomir Grzegorz Gątkowski

Minimal Nodal Complexity for Detecting the Primitive Middle Hodge Class on a Smooth Quadric Fourfold

This preprint studies a concrete generalized-Thomas-section benchmark on the smooth quadric fourfold Q^4. For the primitive middle Hodge class ζ=2[Π]−h^2 associated with a maximal plane Π, it proves—subject to independent verification and without a claim of novelty—that the minim...

Attainment of a Scale-Critical Vortex-Stretching Functional in Three Dimensions

This preprint studies a scale-critical variational functional associated with the nonlinear production of vortex stretching in three-dimensional incompressible Navier–Stokes flow. For divergence-free vorticity fields ω ∈ H1(ℝ3; ℝ3), the functional is defined by F(ω) = N(ω) / (ℰ(ω...

F–S–O: Observation Horizons, Task Recoverability, and Realization Cost

The Function–Structure–Operator (F–S–O) framing separates a specified task, a channel-to-state structure, and the operations available to a system. This note develops a finite-dimensional, first-order interpretation in which observation is represented by an explicit readout map....

Operational Transition Test (OTT): Experimental Crucible v0.2 - Frozen Prospective Protocol

This record contains the frozen prospective protocol for version 0.2.0 of the Operational Transition Test (OTT), developed to test whether a proposed operational criterion can distinguish genuine cross-level operational transitions from predictive compression, arbitrary aggregati...

When Output Becomes Infrastructure: Operational Compilation and a Falsifiable Test for Cross-Level Transitions

Scientific explanations routinely move between levels of organization, yet a change of level may represent either a genuine change in what a system or controller can operationally do or merely a useful redescription by an observer. We propose operational compilation: a lower-leve...

Operational Transition Test (OTT): Experimental Crucible v0.2 — Prospective Results (H1 = FAIL)

This record contains the prospective results of the Operational Transition Test (OTT) Experimental Crucible v0.2.0. The protocol, hypotheses, thresholds, benchmark families, development/evaluation split, resource accounting rules, and failure criteria were publicly frozen before...

Operational Transition Test (OTT): Experimental Crucible v0.3 — Prospective Reduced-VCX Results (H1–H4 PASS)

This record contains the prospective results of the Operational Transition Test (OTT) Experimental Crucible v0.3.0 — the reduced V–C–X criterion (scope-wide interventional validity ∧ robust control-cost compression ∧ attributable constrained operational expansion). The protocol,...

Operational Transition Test (OTT): Experimental Crucible v0.3 - Frozen Reduced-VCX Prospective Protocol

This record contains the frozen prospective protocol for version 0.3.0 of the Operational Transition Test (OTT) Experimental Crucible. Context. The v0.2 frozen protocol (DOI 10.5281/zenodo.22116064) was publicly timestamped before execution; its prospective run was then published...