IndisputableMonolith.Cosmology.ScaleInvarianceSelectionCert
The ScaleInvarianceSelectionCert module certifies scale-invariant cost structures for cosmology by encoding the Recognition Composition Law and its consequences under scaling. Cosmologists working from recognition axioms to derive invariant quantities would cite it when selecting models that preserve J-cost under dilation. The module organizes its content as a sequence of supporting definitions on equality cases, scale-change costs, and log-space symmetry.
claim$J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$, with the net cost of any scale change controlled by the individual J-values of the factors.
background
The module sits in the cosmology domain and imports the RS time quantum τ₀ = 1 tick together with the J-cost framework. It treats the Recognition Composition Law as the governing algebraic relation that controls how costs combine under multiplication and division. Supporting objects include rcl_equality, scale_change_cost, no_scale_change_is_free, and log_space_symmetry, which together prepare the ScaleInvarianceCert.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the scale-invariance certificate required for cosmological applications of the forcing chain, directly implementing the RCL equality that appears in the T5–T8 landmarks. It therefore feeds any later derivation that selects dimensionally consistent cosmologies from recognition principles.
scope and limits
- Does not derive numerical values for constants.
- Does not address non-scale-invariant sectors.
- Does not contain the full forcing chain from T0.