IndisputableMonolith.Stratigraphy.VarveThicknessFromJCost
This module defines the canonical summer/winter varve thickness ratio as the golden ratio φ derived from J-cost in Recognition Science stratigraphy. Geologists and physicists modeling periodic deposits via the phi-ladder would cite it to connect layer ratios to the self-similar fixed point. The module supplies definitions for varveCost and basic properties establishing the ratio equals φ and lies above one.
claimThe summer-to-winter varve thickness ratio equals $φ$, where $φ$ is the golden ratio fixed point of the J-cost function satisfying $J(φ) = φ$.
background
Recognition Science derives all structures from the J-cost function J(x) = (x + x^{-1})/2 - 1 obeying the Recognition Composition Law. Upstream, Constants supplies the fundamental time quantum τ₀ = 1 tick while Cost provides the J function and related cost definitions. This module applies those to varve formation in the stratigraphy domain, introducing varveSummerWinterRatio as the canonical ratio φ together with varveCost and the certificate VarveCert.
proof idea
This is a definition module, no proofs. It declares the ratio varveSummerWinterRatio and the associated cost varveCost, then records elementary properties such as the ratio exceeding one and lying inside the empirical band.
why it matters in Recognition Science
This module supplies the varve thickness ratio for the stratigraphy domain, extending the J-cost framework to geological records and supporting empirical checks against the phi-ladder. It connects to the eight-tick octave and the alpha band through cost-derived ratios, providing a concrete interface between the forcing chain and observable strata.
scope and limits
- Does not compute absolute varve thicknesses.
- Does not incorporate external geological forcings.
- Does not model non-periodic sediment layers.
- Does not simulate full T0-T8 forcing chain dynamics.