IndisputableMonolith.Architecture.GoldenSectionInProportion
The module defines the golden ratio as the aesthetically preferred aspect ratio in Recognition Science. It introduces objects including preferredAspectRatio, proportionCost, and GoldenSectionCert along with basic properties such as non-negativity and band membership. Researchers modeling aesthetic proportions from the J-cost function would reference these definitions. The module consists of definitions and elementary lemmas.
claimLet $r$ be an aspect ratio and $C(r)$ the associated proportion cost. The preferred aspect ratio equals the golden ratio $phi$ satisfying $phi=1+phi^{-1}$, with $C(phi)$ minimal (zero at ideal), $C(r)geq0$ for all $r$, and $phi$ inside the aesthetic band.
background
The module sits in the Architecture domain. It imports the fundamental RS time quantum $tau_0=1$ tick from Constants and cost structures from the Cost module. Definitions center on the preferred aspect ratio as the golden ratio, the proportion cost function derived from J, and the GoldenSectionCert that verifies ideal properties. The setting identifies self-similar fixed points as aesthetically optimal proportions.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the golden ratio definitions that support aesthetic applications in the Recognition framework. It connects to the phi forced as self-similar fixed point in T6 of the UnifiedForcingChain. No direct parent theorems appear in the used_by relations.
scope and limits
- Does not derive the golden ratio from the forcing chain T0-T8.
- Does not connect aspect ratios to mass formulas or spatial dimensions.
- Does not address time-dependent or dynamic proportions.
- Does not prove uniqueness beyond the listed properties.