IndisputableMonolith.Cosmology.ScaleInvarianceSelectionCert
This module certifies scale invariance selection in cosmology by formalizing the Recognition Composition Law in inequality form. The law shows combined cost J(xy) + J(x/y) equals 2J(x)J(y) + 2J(x) + 2J(y), with costs controlled by individual J terms. Cosmologists using Recognition Science would cite it for selecting invariant structures. The module organizes this via imports from Cost and Constants without internal proof bodies.
claim$J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$, where $J$ is the cost function and the equality controls the cost of scale combinations by individual costs.
background
The module sits in the cosmology domain of Recognition Science, which derives all physics from one functional equation. It imports the RS time quantum τ₀ = 1 tick from Constants and cost structures from the Cost module. The supplied doc-comment states the RCL controls the cost of combining x and y by their individual costs, with sibling declarations such as rcl_equality, scale_change_cost, and log_space_symmetry providing supporting pieces.
proof idea
This is a definition module, no proofs. It structures the argument through sibling declarations that include rcl_equality, no_scale_change_is_free, and ScaleInvarianceCert to build the selection certificate.
why it matters in Recognition Science
The module supplies the scale invariance certificate that supports cosmological constructions in the Recognition framework. It directly encodes the RCL from the doc-comment and connects to the forcing chain via J-uniqueness (T5) and the phi fixed point (T6). With zero downstream uses listed, it functions as a foundational block for further cosmology work.
scope and limits
- Does not derive numerical values for constants such as alpha or G.
- Does not treat dynamical evolution or time-dependent scaling.
- Does not include data comparison or observational constraints.