IndisputableMonolith.Physics.NonlinearDynamicsFromRS
The NonlinearDynamicsFromRS module encodes period-doubling cascades from Recognition Science, with the explicit target that doubling reaches period 8. Dynamical systems researchers linking fundamental physics to chaos would cite it for the T7 octave step. The module consists of type definitions and certificates that build directly on the imported Cost module.
claimPeriod-doubling reaches the target $2^3=8$ in the Recognition Science framework.
background
Recognition Science derives all physics from one functional equation whose forcing chain (T0-T8) produces T7, the eight-tick octave of period $2^3$. This module imports IndisputableMonolith.Cost, which supplies the J-cost function used throughout the framework, and introduces sibling declarations that realize the period-doubling route to that octave.
proof idea
This is a definition module, no proofs. It defines BifurcationType, periodDoublingTarget_8, equilibrium, and NonlinearDynamicsCert to encode the period-doubling target at 8.
why it matters in Recognition Science
The module supplies the period-doubling objects required by T7 in the UnifiedForcingChain. It therefore supports any later derivation that invokes the eight-tick octave to obtain D=3 or other physics results, although no downstream uses are recorded yet.
scope and limits
- Does not derive the Feigenbaum constant or scaling ratios.
- Does not model continuous-time flows or specific physical systems.
- Does not prove stability or uniqueness of the period-8 orbit.
- Does not connect to the mass ladder or fine-structure constant.