Accessibility Geometry Reference Stack: Reference B - Accessibility Derivative Register

Accessibility Geometry Reference Stack — Reference B: Accessibility Derivative Register v0.5 defines the derivative and trajectory layer of the Accessibility Geometry framework. Where Reference A — Accessibility Variable Register defines the primary state variables of observer accessibility modeling, Reference B asks how those variables move over time. It introduces a controlled vocabulary for first-derivative behavior, second-derivative behavior, acceleration signatures, warning trajectories, collapse patterns, recovery indicators, and preliminary Human TAWS logic. The register uses stable plain-text derivative notation for reliable PDF, word processor, repository, and plain-text rendering. Core derivative variables include accessibility velocity, coherence velocity, reconstructability velocity, integration velocity, projection horizon velocity, audit bandwidth velocity, reorganization capacity velocity, scalar harmony velocity, observer impedance velocity, recursive closure velocity, recovery margin velocity, and constraint preservation velocity. This version develops a provisional compound-warning taxonomy for observer-state trajectories, including: Quiet Descent Zeno Capture Panic Horizon Collapse False Coherence Recovery Reindexing Unbounded Expansion Constraint Collapse Impedance Spiral Fragmentation Drift Emergency Descent The paper also introduces Human TAWS as a proposed terrain-awareness-and-warning-system analogue for observer systems. Human TAWS is intended as an exploratory warning architecture for detecting narrowing future-space, collapsing projection horizon, reduced audit bandwidth, increasing recursive closure, shrinking recovery margin, and degraded constraint preservation before full system failure occurs. Reference B is positioned within the broader Accessibility Geometry stack. Accessibility Geometry distinguishes possible futures from accessible futures. Reference A defines the state variables used to describe that accessibility landscape. Reference B defines the movement of those variables through time. Logical Aliveness provides the minimum observer-system threshold for history-informed future-state navigation, while Reference B describes how such navigation expands, contracts, accelerates, destabilizes, recovers, or approaches collapse terrain. This work remains exploratory. The derivative variables, warning signatures, and Human TAWS logic introduced here are not clinical diagnostic tools, legal standards, engineering certifications, or validated empirical predictors. They are provisional modeling constructs intended to support future simulation, calibration, toybox investigation, Human TAWS development, Genesis ODE integration, and multi-scale observer dynamics research. Keywords Accessibility Geometry; Accessibility Derivatives; Accessibility Derivative Register; Observer Systems; Future-State Navigation; Human TAWS; Terrain Awareness Warning System; State Gradients; Warning Trajectories; Collapse Signatures; Recovery Signatures; Quiet Descent; Zeno Capture; Panic Horizon Collapse; False Coherence; Recovery Reindexing; Unbounded Expansion; Constraint Collapse; Impedance Spiral; Fragmentation Drift; Emergency Descent; Logical Aliveness; Multi-Scale Observer Dynamics; Projection Horizon; Audit Bandwidth; Reconstructability; Integration; Reorganization Capacity; Scalar Harmony; Observer Impedance; Recursive Closure; Recovery Margin; Constraint Preservation; Coherence Dynamics Laboratory; Genesis ODE; Systems Theory; Cybernetics; Synthetic Observer Systems