IndisputableMonolith.Relativity.Dynamics.RecognitionSheaf
RecognitionSheaf defines a sheaf of recognition potentials over spacetime manifolds in the RS framework. It builds local sections and stationarity conditions from the J-cost and metric geometry. RS-relativity researchers cite the module when assembling global structures from local recognition data. The module consists of definitions and supporting theorems with no complex proofs.
claimThe recognition sheaf $R$ is a sheaf of recognition potentials over the spacetime manifold $(M,g)$, whose local sections satisfy the stationarity condition derived from the $J$ cost function.
background
The module sits in Relativity.Dynamics and imports Constants (for the RS time quantum τ₀ = 1 tick), Cost (for the J function), and Geometry.Metric (for the underlying manifold). It introduces RecognitionSheaf as a sheaf of recognition potentials together with LocalSection, the J function, J_stationary_at_one, section_stationarity_thm, and sheaf_gluing.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
RecognitionSheaf supplies the sheaf infrastructure that supports section_stationarity_thm, local_section_eq_global, recognition_ratio_unity, and sheaf_gluing inside the RS-relativity development. It links the J-cost to manifold geometry and advances the forcing chain toward unified dynamics.
scope and limits
- Does not derive explicit curvature or metric components.
- Does not address the phi-ladder or mass formula.
- Does not close the full T0-T8 forcing chain.