Observable Performance Does Not Fully Reflect Adaptive System Organization: A Multi-Level Analysis of Gait Dynamics Under Occlusal Constraint

Understanding adaptive biomechanical systems requires distinguishing observable performance, static multivariate representation, longitudinal displacement, and internal approximation of observed change. This study introduces Level 5, which examines whether the M1-M2 transformation observed in a single-subject gait dataset can be approximated within a selected PCA representation. Gait was recorded with instrumented insoles in a participant with Parkinson's disease under six occlusal observational probes during two sessions eleven weeks apart. A simplified feed-forward neural network was trained to approximate M2 PC1-PC2 coordinates from M1 coordinates, occlusal-probe descriptors, and the longitudinal-transition indicator. In the core analysis aligned with Level 4, the model preserved the Euclidean centroid-displacement hierarchy dOC3 < dONL < dOC2.5. In the extended six-probe analysis, it preserved the broad structure of the exploratory ordering. Held-out M2 and leave-condition-out analyses provided internal tests beyond the full-dataset fit, while a within-session analysis described probe positions relative to ONL. The term predictive is used only in a restricted methodological sense. The model does not provide prospective clinical prediction, patient-level forecasting, or generalization to unseen individuals. Occlusal conditions are treated as observational probes applied during measurement, not as continuous causal drivers of longitudinal evolution. The findings are exploratory, retrospective, representation dependent, and non causal. They do not establish causal occlusal effects, validated viability thresholds, therapeutic superiority, distinct physiological states, or generalizable predictive validity.

Observable performance is commonly used to characterize biological systems, yet aggregated outputs may remain insufficient for uniquely resolving observational conditions, and richer multivariate representations may retain substantial ambiguity. This article proposes a representational bootstrap framework for adaptive biological systems. Bootstrap is used in a methodological and epistemological sense, not as statistical resampling. New analytical levels emerge when the active representation becomes insufficient for the question under investigation. The framework comprises five successive levels: observable performance, conceptual dynamic organization, exploratory multivariate representation, observed longitudinal centroid displacement, and internal approximation of observed displacement. Three previously reported gait-occlusion studies are used as a methodological case sequence rather than as new experimental evidence. The revised first study showed persistent static representational non-identifiability: neither the scalar score nor the exploratory embedding uniquely resolved the occlusal probes. The second study shifted the question toward M1-M2 centroid displacement in a common PCA representation. The third examined whether that observed representation-dependent transformation could be internally approximated by a simplified supervised model. The contribution is not a new algorithm, clinical protocol, or dataset. It is the formalization of a bootstrap methodology in which persistent explanatory insufficiency motivates reformulation of the scientific question and the emergence of progressively more adequate representations.

Cerebral Palsy (CP) is a neurological disorder of movement and the most common cause of lifelong physical disability in childhood. Approximately 75% of children with CP are ambulatory, and accurate gait assessment is central to preserving walking function, which deteriorates by mid-adulthood in a quarter to half of adults with CP. The Rodda and Graham classification system quantifies sagittal-plane gait deviations using ankle and knee z-scores derived from 3D Instrumented Gait Analysis (3D-IGA), but 3D-IGA is expensive and limited to specialized centers, while observational assessment shows only moderate inter-rater agreement. We developed a markerless gait analysis pipeline that quantifies Rodda and Graham knee and ankle z-scores directly from single-view clinical gait videos. Across 1,058 bilateral limb samples from 529 trials of 152 children (88 male, 63 female; age 12.1 $\pm$ 4.0 years; 60 distinct primary diagnoses, cerebral palsy the most common at $n=54$), the sagittal-view model achieved $R^2 = 0.80 \pm 0.02$ and CCC $= 0.89 \pm 0.02$ for knee z-scores and $R^2 = 0.57 \pm 0.02$ and CCC $= 0.72 \pm 0.02$ for ankle z-scores against 3D-IGA. Binary screening for excess knee flexion achieves AUROC $= 0.88$, correctly identifying 83% of affected children, and applying Rodda and Graham rules yields $43 \pm 1$% 7-class accuracy with macro-AUROC $= 0.78 \pm 0.01$, ankle prediction error remaining the primary bottleneck. Beyond cross-sectional screening, continuous z-scores support longitudinal trajectory tracking across visits, providing a quantitative substrate for monitoring disease progression and treatment response unavailable from observational scales. These results demonstrate the feasibility of video-based z-score estimation, excess-flexion screening, and longitudinal trajectory tracking as a path toward scalable, objective gait assessment in low-resource clinical settings.