IndisputableMonolith.Cost.Ndim.Octave
This module defines uniform phase shifts indexed by octaves within the N-dimensional reciprocal cost framework. It extends the scalar kernel lifting from the Core submodule to handle periodic eight-tick structures. The module contains only definitions and no theorems or proofs.
claimThe module supplies the uniform phase shift function $f(k)$ for octave index $k$, together with trajectory maps that satisfy $f(k+8)=f(k)$ over the eight-tick cycle.
background
The module sits in the Cost domain and imports the Core submodule, whose doc-comment states that it defines the multi-component reciprocal cost by lifting the scalar kernel through a weighted log aggregate. This supplies the J-cost and defectDist primitives used for N-dimensional extensions. The octave index directly references the eight-tick period (T7) in the forcing chain, where phase is required to be uniform.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The definitions supply the phase and trajectory objects required by the eight-tick octave step (T7) of the UnifiedForcingChain. They prepare periodic structures that later feed into D=3 spatial constructions and the Recognition Composition Law. No downstream theorems are recorded in the current dependency graph.
scope and limits
- Does not prove any periodicity identities.
- Does not assign explicit numerical values to the phase shift.
- Does not connect phase to the phi-ladder mass formula.
- Does not treat dimensional reduction or Berry threshold.