Distinct Representation Does Not Imply Complementary Decision Power

bstract. A time series can be read through several detectors: local amplitude (window variance), ternary occupancy (aWCM state-geometry reader), and ternary transition run-bias (a WCM state-dynamics reader). Starting from aconjecture that the polynomial discriminant of a windowed series would supply a reader complementary to WCM, weran a pre-registered chain of falsification gates. Four results survive. (i) The discriminant is not an independent reader:it is a re-parametrization of window variance (Spearman rho = 0.879), and once its amplitude prefactor is removed itloses to plain window statistics and is unstable under representation changes. (ii) Occupancy and transition areseparable reader channels: interventions move them with distinct, asymmetric preference, and their coupling is anoblique (not orthogonal, not identical) rho = 0.5-0.7 across geological, biological, physical and physiological data. (iii)That separability is a property of dynamical regime: increasing state persistence binds the two channels (coupling rises)and erodes the independent controllability needed to define the intervention geometry, whereas true sinusoidal periodiccarrier has the opposite effect (coupling falls and inverts). (iv) In an out-of-sample EEG seizure task with a frozendecision rule, distinct readers did not produce distinct failures: their error sets coincided. We conclude thatrepresentation space, reader space, and decision space must be kept separate: reading different structure does not byitself confer complementary detection power. Synthetic results are reproducible with numpy-only scripts andvalue-preserving nulls. ※ The license for codes is AGPL3.0-or-later Data: CHB-MIT EEG (PhysioNet, ODC-BY, Guttag 2010); Bird Song Database(National Museum of Nature and Science, Japan, CC BY 4.0, Hamao 2025);Stanford Thermoacoustic Instability Dataset (doi:10.25740/fs912pm2448,CC BY-NC-SA 4.0, non-commercial use); JMA unified earthquake catalogue.