IndisputableMonolith.ArtHistory.FibonacciInComposition
This module defines the golden section of unit length as 1/φ and supplies related properties for Fibonacci composition analysis in art history. It draws directly on the RS constants to embed the self-similar ratio into aesthetic contexts. Researchers linking Recognition Science structures to artistic proportions would cite these definitions when applying the phi-ladder to composition. The module consists of definitions and elementary lemmas on positivity and ratios.
claimThe golden section of unit length is $1/φ$.
background
The module sits in the ArtHistory domain of Recognition Science and imports the Constants module whose fundamental object is the RS time quantum τ₀ = 1 tick. It introduces the golden section as the division 1/φ together with basic facts on its sign and magnitude. These objects rest on the self-similar fixed point φ established in the upstream forcing chain.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the golden-division primitives that connect Fibonacci sequences in composition to the phi-based structures of Recognition Science. It supports later applications of the eight-tick octave and phi-ladder to aesthetic analysis. No downstream theorems are recorded yet.
scope and limits
- Does not treat specific artworks or artists.
- Does not derive φ from the forcing chain.
- Does not address non-unit lengths or higher dimensions.