IndisputableMonolith.Cosmology.ScaleInvarianceSelectionCert
Module Cosmology.ScaleInvarianceSelectionCert supplies the Recognition Composition Law in inequality form to support scale invariance arguments in cosmology. It builds directly on the J-cost from the Cost module and the time quantum from Constants. The module organizes its content as a sequence of lemmas on scale changes, symmetries, and the final ScaleInvarianceCert.
claim$J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$, where the cost of combining $x$ and $y$ is controlled by their individual costs.
background
The module sits in the cosmology domain of Recognition Science and imports the fundamental time quantum τ₀ = 1 tick together with the J-cost definitions. Its doc-comment states that the Recognition Composition Law controls combination costs via individual J values. Sibling declarations introduce scale_change_cost, log_space_symmetry, no_scale_change_is_free, and the top-level ScaleInvarianceCert.
proof idea
This is a definition module, no proofs. The overall structure assembles lemmas that begin with rcl_equality, quantify costs under scaling, establish symmetry properties, and terminate at ScaleInvarianceCert.
why it matters in Recognition Science
The module supplies the RCL inequality required for cosmological scale invariance selection and connects to the J-uniqueness step in the T0-T8 forcing chain. It provides the inequality form that downstream cosmology constructions would cite when applying the phi-ladder or mass formulas. No used_by edges are recorded, indicating an intermediate block.
scope and limits
- Does not derive the RCL from the base functional equation.
- Does not compute numerical values for cosmological observables.
- Does not treat multi-body interactions beyond pairwise J-costs.
- Does not address time evolution or dynamics outside scale changes.