IndisputableMonolith.NavierStokes.EightTickDynamics
Module defines an abstract one-step discrete dynamics equipped with a defect functional, forming the base layer for eight-tick constructions in the Navier-Stokes domain. Researchers formalizing discrete fluid models cite it when building periodic iterations and defect-nonincreasing maps. The module imports the Patterns library to reuse the recognition composition law and declares sibling objects such as step8 and EightTickCertificate.
claimAn abstract one-step discrete dynamics equipped with a defect functional $D$ satisfying the recognition composition law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$.
background
The module sits inside the Navier-Stokes section of Recognition Science, which derives continuum equations from the unified forcing chain T0-T8. It imports the Patterns module, whose core supplies the J-cost functional and the recognition composition law. Local definitions include OneStepDynamics as the state-transition structure, step8 as the eight-tick iteration map, and EightTickCertificate as the object witnessing periodicity with non-increasing defect.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the discrete-dynamics layer that downstream siblings eight_tick_cycle_exists and eight_tick_minimal consume. It realizes the T7 eight-tick octave (period $2^3$) inside the Navier-Stokes setting and prepares the ground for the D=3 spatial dimension claim in the forcing chain.
scope and limits
- Does not prove existence of smooth solutions to the continuous Navier-Stokes equations.
- Does not incorporate boundary conditions or external forcing terms.
- Does not derive the phi-ladder mass spectrum or the alpha band.