patterns_match_D
The declaration records that the cross-domain layer covers exactly five universality patterns. Researchers verifying the meta-theorem count lower bound cite this equality to confirm the structural inventory of C1-C28. The proof reduces directly to reflexivity on the constant definition of patternsCovered.
claimThe number of universality patterns covered by the cross-domain theorems equals $5$, where the patterns are the $D=5$ instances, the eight-tick octave $2^3=8$, $J$-positivity, the phi-ladder, and the gap45 ceiling.
background
Module C28 supplies the meta-count for the cross-domain layer of Recognition Science, enumerating 27 prior theorems (C1-C27) plus the count itself. patternsCovered is defined as the natural number 5, standing for the five universality patterns: D=5 instances, 2^3=8, J=0, phi-ladder, and gap45. The upstream definition of patternsCovered supplies the value directly, while the modules list from Masses.Manifest provides the broader inventory context for the layer.
proof idea
The proof is a one-line wrapper that applies reflexivity to the definition of patternsCovered, which expands to the constant 5.
why it matters in Recognition Science
This theorem populates the patterns_covered field inside metaTheoremCountCert, which aggregates count_eq, count_is_D_cubed, and count_in_spectrum to certify the meta-count. It closes the structural claim that the cross-domain layer contains a quantifiable number of joint theorems, aligning with the T7 eight-tick octave and T6 phi fixed-point landmarks in the T0-T8 forcing chain.
scope and limits
- Does not compute the total number of cross-domain modules.
- Does not derive the reported average of 5.4 modules per pattern.
- Does not address physical interpretations of the five patterns.
- Does not connect to the mass ladder or Berry creation threshold.
Lean usage
def exampleCert : MetaTheoremCountCert := { count := count_eq, count_is_cube := count_is_D_cubed, patterns_covered := patterns_match_D, count_in_spectrum_range := count_in_spectrum }formal statement (Lean)
64theorem patterns_match_D : patternsCovered = 5 := rfl
proof body
Term-mode proof.
65
66/-- Each pattern produces multiple cross-domain modules. Average: 27/5 = 5.4. -/