IndisputableMonolith.Relativity.Dynamics.RecognitionSheaf
This module defines the Recognition Sheaf as a sheaf of recognition potentials over the spacetime manifold. RS-relativity researchers cite it when moving from local J-cost sections to global structures via gluing. It is a definition module whose content rests on imported metric, cost, and constant primitives.
claimLet $M$ be a spacetime manifold equipped with the metric of the imported geometry module. The Recognition Sheaf $\mathcal{R}$ is the sheaf that assigns to each open $U \subseteq M$ the set of recognition potentials whose J-cost satisfies stationarity at unity.
background
The module imports Constants (defining the RS time quantum $\tau_0 = 1$ tick), the Cost module (supplying the J-cost function), and the Metric module (providing the spacetime geometry). Recognition potentials are sections whose local behavior is governed by the J function $J(x) = (x + x^{-1})/2 - 1$. The sheaf structure encodes how these potentials glue consistently across overlapping open sets of $M$.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the sheaf foundation required for dynamics in the relativity domain. It positions the Recognition Composition Law and J-stationarity conditions on the manifold, preparing for later results on section stationarity and sheaf gluing listed among its siblings.
scope and limits
- Does not prove existence of global sections.
- Does not fix the manifold dimension or signature.
- Does not derive the phi-ladder mass formula.
- Does not invoke the eight-tick octave or D=3.