IndisputableMonolith.Climate.DiurnalEightTick
The module establishes that the diurnal cycle consists of exactly eight phase positions drawn from the discrete 8-tick clock. Climate researchers applying Recognition Science to daily forcing would cite it to discretize solar input. The module supplies definitions for phase count, individual phases, bounds, noon alignment, 24-hour wrapping, a master function, and a certification theorem that imports the EightTick structure.
claimThe diurnal cycle is partitioned into eight phases at angles $0, 2^{-2}π, 2^{-1}π, 3·2^{-2}π, π, 5·2^{-2}π, 3·2^{-1}π, 7·2^{-2}π$, equipped with a master map from time to phase, a 24-hour wrap, and a certificate confirming exact agreement with the eight-tick cycle.
background
Recognition Science treats time as discrete with fundamental quantum τ₀ = 1 tick from the Constants module. The EightTick foundation supplies the core 8-tick cycle whose phases are 0, π/4, π/2, 3π/4, π, 5π/4, 3π/2, 7π/4; its doc-comment states that reality operates on this discrete clock. The present module imports those objects together with Cost and applies them inside the climate domain.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the eight-phase discretization required for any climate application of the eight-tick octave (T7). It directly implements the phase structure stated in the EightTick doc-comment and thereby links the forcing chain to diurnal observables. No downstream theorems are recorded yet.
scope and limits
- Does not model continuous-time evolution inside each phase.
- Does not incorporate seasonal or latitudinal dependence.
- Does not compute radiative fluxes or temperature fields.
- Does not compare the phase structure to observational records.