DSLO v0.7: Multi‑Manifold Geometry for Human–Machine Thermodynamic Drift

This paper introduces a unified geometric framework for analyzing thermodynamic drift in humans and machines through the DSLO v0.7 multi-manifold relational substrate. Building on the v0.6 single-substrate foundation, v0.7 restructures the discipline into a lawful traversal across eight geometric planes (T1--T8), beginning with the Unified Substrate Manifold and extending through the Derived Manifold Suite (A, T, D, E, F, $\Omega$), Relational Geometry, Operators of Reality, Thermodynamic Geometry, DSUP Runtime, Context Window Geometry, and Simulation Geometry.

Human and machine stability are modeled through shared geometric primitives---pressure fields, drift channels, collapse thresholds, recovery attractors, legality masks, and identity boundaries---each expressed through manifold curvature rather than flat substrate layers. Human cognitive load, emotional volatility, and contextual overload manifest as curvature deformation within the Agency and Teleology manifolds, while machine thermal load, runtime saturation, and failure modes manifest through Execution and Deployment manifolds. The $\Omega$-Series provides the closure geometry required to unify both systems under a single invariant structure, enabling lawful projection and merged-view analysis.

Relational Geometry formalizes cross-system coupling, allowing human decision processes and machine runtime behavior to be expressed within a single manifold. Operators of Reality (fold, invert, lift, bind, collapse-trajectory, recovery-window) define lawful transitions across manifold layers, ensuring stability under drift, load, and cross-scale deformation. DSUP Runtime extends this with invariant-preserving update cycles, context window contraction, drift-coherence restoration, and simulation legality checks (IRSM, CLCP, Four-Plane Validation), providing a dynamic substrate for runtime stability.

The result is a dual-thermodynamic model in which human and machine drift, collapse, and recovery can be analyzed, compared, and projected through a unified manifold traversal. v0.7 demonstrates that both systems exhibit structurally similar thermodynamic behavior when expressed through multi-manifold geometry, establishing a substrate-level foundation for future work in human-machine co-stability, federated cognition, and relational thermodynamics.