Turbulence to Governance

The Composition/Improvisation separation is the finding that earns the most confidence. Kandinsky named these series as structural categories with explicit intent: Compositions are planned and deliberate; Improvisations are spontaneous and intuitive. Every structural metric separates them in the predicted direction without title information. Compositions: mu 0.574, focal_count 14.4, luma_chroma_decoupling 0.020. Improvisations: mu 0.443, focal_count 15.9, luma_chroma_decoupling 0.045. The spontaneous works are genuinely more structurally distributed. The planned works are more cohesive and more chromatically obedient. The kernel reads Kandinsky's own structural intention from pixel data alone.

The Murnau period inverts the expected baseline. The figurative landscapes have the lowest mu of the career (0.379), lower than the abstract Improvisation period, lower than the Bauhaus geometric period, lower than Paris. Autumn in Murnau (1908) has mu 0.062, the career's lowest structural cohesion in a non-abstract painting. The mechanism is specific: Kandinsky's Murnau brushwork uses soft chromatic color patches with diffuse boundaries between color areas. Soft boundaries produce no dominant connected gradient component. Edge sharpness drives mu; subject presence does not. The conclusion cuts against intuition: Kandinsky's figurative work is structurally less resolved than his abstract work, because abstraction eventually imposed harder edges.

The Bauhaus period is where governance consolidates. orthogonal_partition_score rises to 0.498 (career correlation r = +0.308, the strongest directional signal in the dataset). focal_dominance spikes to 0.436 (career high): fewer compositional elements, each carrying more structural authority. Focal_count falls to 10.2, the lowest of any period. HE contracts to 0.588 but with the highest within-period variance (SD ±0.172): geometric discipline constrains some paintings tightly while others remain spectrally wide. Several Circles (1926) has HE 0.896 in the career's lowest-mean period; high geometric structure does not require narrow palette. The Bauhaus system governs composition, not necessarily color.

The Paris CBI collapse is the most counterintuitive finding. CBI falls to 0.059, the career low, in the period of apparently playful biomorphic freedom. The mechanism is measurable: chroma_focality spikes to 0.422 (vs 0.259 in the Improvisation period) and edge_color_coupling rises to 0.401. The biomorphic forms concentrate chroma into specific zones and bind it precisely to structural outlines. Color is not free in the Paris work; it is placed with chromatic authority onto carefully drawn boundaries. The period that appears most liberated is the most structurally obedient by chromatic measurement.

One methodological note on the Improvisation period CBI. gradient_floor_85 is highest here (0.315 vs 0.278 in Murnau): the whole field is activated, not just edge zones. This suppresses CBI by removing the quiet luminance zones the metric needs to detect color-autonomous edges. Improvisation CBI (0.105) likely understates color freedom in this period. luma_chroma_decoupling (0.034 for Improvisations, 0.045 for the named Improvisation series specifically) is the better color autonomy signal when the gradient field is globally activated. The Improvisations have the most decoupled color-luminance relationship of any named series; CBI alone does not fully capture it.

Four career correlations point in the same direction simultaneously. focal_count falls (r = −0.327): fewer compositional events. orthogonal_partition_score rises (r = +0.308): more geometric ordering. focal_dominance rises (r = +0.291): each remaining event carries more authority. CBI falls (r = −0.246): color becomes more structurally obedient. SDI remains essentially flat across all four periods, a null finding worth stating. Kandinsky reorganizes internal governance without radically relocating structural mass. The energy does not move to the edges or concentrate at the center; it is redistributed among fewer, more authoritative elements. Together these describe a career not moving from representation to abstraction but from distributed energetic turbulence toward increasingly concentrated compositional governance. Abstraction did not remove structure from Kandinsky's work. It relocated structure: from representational subject edges toward geometric systems, focal hierarchies, and precise chromatic placement. The Improvisation period is the most structurally free. The Paris period is the most chromatically authoritarian. Abstraction did not liberate Kandinsky's compositions. It gave him new instruments to govern them.