Decoupled Entropic-Geometric Planning (DEGP): Verified Conditioning and a Measured Contact-Prediction Boundary in Latent World Models

Gradient-based latent space planning faces a fundamental trade-off: maintaining high-entropy representations for robust perception under domain shift often yields ill-conditioned manifolds that destabilize trajectory optimization. DEGP introduces a framework designed to isolate gradient interference between representation learning and control dynamics via strict architectural separation. However, empirical evaluation demonstrates that structural decoupling alone is insufficient for closed-loop planning (0/50 per condition; 0/200 total), uncovering a fundamental information-usability gap driven by contact-conditional predic-tion errors and cost signal suppression. The gap is not closed by retraining the encoder to be more decodable: a trained encoder whose T-pose decodability matches DEGP’s (R2=0.686) still yields a predictor that captures essentially no contact-conditioned movement (CDR = 0.046, versus the frozen random encoder’s 0.060). To delineate these operational limits, we provide analytical proofs establishing guaranteed spectral bounds on the predictor’s Ja-cobian under distribution shifts. Furthermore, we validate DEGP across manipulation tasks, ntroducing a telemetry-based runtime contract that quantifies the operational boundaries where geometric conditioning preserves planning stability.