IndisputableMonolith.CrossDomain.MetaTheoremCount
The CrossDomain.MetaTheoremCount module establishes the number of cross-domain modules in the wave-63/64 layer. Researchers verifying meta-theorem structure across domains in Recognition Science would cite it for cardinality results. The module consists of definitions and equalities that fix the count as D cubed and place it in the spectrum.
claimLet $N$ be the number of cross-domain modules in the wave-63/64 layer. Then $N = D^3$ where $D=3$ is the spatial dimension, $N$ lies in the spectrum, and the average per pattern is consistent with the covered patterns.
background
The module resides in the CrossDomain domain and imports Mathlib. It defines crossDomainModuleCount as the cardinality of modules in the wave-63/64 layer, together with count_eq, count_is_D_cubed, count_in_spectrum, patternsCovered, patterns_match_D, and average_per_pattern. The wave-63/64 layer sits inside the eight-tick octave structure of the forcing chain.
proof idea
This is a definition module, no proofs. It declares the count and related quantities, then records the equalities count_eq and count_is_D_cubed together with the certification MetaTheoremCountCert.
why it matters in Recognition Science
The module supplies the cardinality result that feeds MetaTheoremCountCert and the broader cross-domain meta-theorem accounting. It reinforces the D=3 outcome from the forcing chain T8 by showing the count equals D cubed.
scope and limits
- Does not enumerate the modules themselves.
- Does not compute counts for other wave layers.
- Does not derive the wave-63/64 layer from the forcing chain.
- Does not address non-cross-domain modules.