IndisputableMonolith.Relativity.Dynamics.RecognitionSheaf
The RecognitionSheaf module defines a sheaf of recognition potentials over the spacetime manifold, together with local sections and J-stationarity conditions. Relativists working in RS dynamics cite it to equip manifolds with recognition-cost structures drawn from the J-function and metric. It is a definition module containing no proofs.
claimLet $(M,g)$ be a spacetime manifold. The RecognitionSheaf is a sheaf assigning to each open $U$ a recognition potential whose local sections obey the stationarity condition derived from the J-cost function.
background
The module imports the RS time quantum τ₀ = 1 tick from Constants, the J-cost function and Recognition Composition Law from Cost, and the spacetime metric from Geometry.Metric. It introduces RecognitionSheaf as the central object, along with LocalSection, the J function, J_stationary_at_one, section_stationarity_thm, and sheaf_gluing. The setting is the Recognition Science framework in which recognition potentials are defined via the J-cost on the manifold.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the sheaf structure that organizes recognition potentials on spacetime and supports later results on section gluing and recognition-ratio unity. It realizes the recognition composition law over manifolds and connects to the forcing chain steps T5 (J-uniqueness) and T7 (eight-tick octave) in relativistic dynamics.
scope and limits
- Does not derive mass formulas on the phi-ladder.
- Does not compute alpha bounds or Berry thresholds.
- Does not address global section existence.
- Does not connect to D=3 forcing or phi fixed-point results.