frcBridgeCert
The declaration assembles the lattice FRC bridge certificate by packaging three results: FRC holds on the RS lattice for every finite volume profile, an explicit bound on that FRC exists, and the lattice result closes any abstract conditional completion route to regularity via direction constancy. Researchers working on Navier-Stokes regularity through Recognition Science lattice cutoffs would cite this certificate. The construction is a direct definition that wires three upstream theorems into the FRCBridgeCert structure with no additional sub
claimThe lattice FRC bridge certificate is the structure whose fields are: for every finite volume profile $s$, the RS lattice FRC condition holds; for every finite volume profile $s$, a lattice FRC bound exists; and for any conditional completion route and profile, if the RS lattice FRC condition implies the route's FRC hypothesis then the route yields regularity for the profile.
background
This module closes the logical loop between the lattice φ-ladder cutoff and the conditional-completion route for Navier-Stokes regularity. On a finite RS lattice the normalized vorticity ratio is automatically finite-volume controlled, supplying a finite recognition-cost bound that feeds into the abstract route FRC to injection damping to direction constancy to rigid rotation veto to regularity. The PDE steps remain external; only the exact logical bridge is formalized here.
proof idea
The definition constructs the FRCBridgeCert structure by direct assignment. The frc_on_lattice field receives the theorem frc_holds_on_RS_lattice, which reduces to finiteVolume_Jcost_bound. The frc_exists_bound field receives frc_holds_on_RS_lattice_exists. The conditional_loop field receives lattice_regular_via_direction_constancy, which applies close_conditional_loop to the supplied route.
why it matters in Recognition Science
This certificate supplies the complete logical closure package for the lattice-to-conditional bridge. It feeds the φ-ladder cutoff result directly into the hypothesis interface of the conditional Navier-Stokes regularity paper. In the Recognition Science framework it relies on T5 J-uniqueness and T6 phi fixed point to control recognition cost on the eight-tick lattice, completing the T0-T8 forcing chain step for the Navier-Stokes domain.
scope and limits
- Does not prove regularity for the continuous three-dimensional Navier-Stokes equations.
- Does not apply to infinite domains or non-finite volume profiles.
- Does not verify the PDE-specific steps inside the conditional route.
- Does not compute explicit numerical values for the recognition cost bounds.
formal statement (Lean)
165def frcBridgeCert : FRCBridgeCert where
166 frc_on_lattice := frc_holds_on_RS_lattice
proof body
Definition body.
167 frc_exists_bound := frc_holds_on_RS_lattice_exists
168 conditional_loop := fun route profile hFRCBridge =>
169 lattice_regular_via_direction_constancy route profile hFRCBridge
170
171end
172
173end FRCBridge
174end NavierStokes
175end IndisputableMonolith