IndisputableMonolith.Foundation.Gap45Degeneracy
The Gap45Degeneracy module defines Gap-45 regions by their synchronization period and landscape flatness in the Recognition Science foundation. Researchers analyzing the eight-tick octave and spatial dimension forcing cite these structures when examining degeneracy on the phi-ladder. The module supplies a collection of definitions and supporting lemmas on divisibility and flatness without deeper derivations.
claimA Gap-45 region consists of a synchronization period $s$ satisfying $8|s$ and $45|s$, together with landscape flatness $f>0$. The construction gap45_from_lcm produces such regions from least common multiples, and larger $s$ yields flatter landscapes.
background
The module sits in the Foundation domain and introduces Gap45Region as the central object, characterized by sync period and landscape flatness according to the module documentation. It draws on the Recognition Composition Law and phi-ladder conventions from upstream forcing-chain results. Sibling definitions cover gap45_from_lcm, sync_factorization, eight_divides_sync, fortyfive_divides_sync, landscapeFlatness, flatness_at_360, flatness_pos, gap45_creates_flat_landscape, and larger_sync_flatter.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies Gap-45 region definitions that feed the T7 eight-tick octave and T8 D=3 steps of the UnifiedForcingChain. It supports flatness analysis required for the self-similar fixed point and phi-ladder mass formulas downstream.
scope and limits
- Does not establish existence of Gap-45 regions in physical data.
- Does not derive numerical values for alpha or G.
- Does not address Berry creation threshold or Z_cf.
- Does not connect to mass-rung formulas on the phi-ladder.