module module moderate

`IndisputableMonolith.CrossDomain.RecognitionGenerators`

The RecognitionGenerators module asserts that {2, 3, 5} forms the smallest generating set for the spectrum. Researchers working on cross-domain spectral structure in Recognition Science cite it when selecting minimal bases for phi-ladder decompositions. The module collects sibling definitions for G2, G3, G5 and assorted decomposition maps but contains no proofs.

claimThe set $S = {2, 3, 5}$ is the smallest generating set for the spectrum.

background

Recognition Science derives physics from the Recognition Composition Law together with the J-uniqueness fixed point and the forced eight-tick octave. This module resides in the CrossDomain section and supplies generators tied to the prime factors that appear on the phi-ladder. It prepares spectral objects used in arguments that reach D = 3 and the alpha inverse interval.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the minimal generators required by downstream cross-domain results. It fills the spectral foundation that later connects to the T7 octave and the mass formula on the phi-ladder. No parent theorem appears in the current dependency graph.

scope and limits

Does not contain theorem statements or proof bodies.
Does not import core Recognition Science modules beyond Mathlib.
Does not define the spectrum object itself.

declarations in this module (25)

def G2 L41
def G3 L42
def G5 L43
theorem four_decomp L47
theorem six_decomp L48
theorem seven_decomp L49
theorem eight_decomp L50
theorem ten_decomp L51
theorem twelve_decomp L52
theorem fifteen_decomp L53
theorem sixteen_decomp L54
theorem twentyfive_decomp L55
theorem fortyfive_decomp L56
theorem seventy_decomp L57
theorem oneTwentyFive_decomp L58
theorem twoSixteen_decomp L59
theorem twoFiftySix_decomp L60
theorem threeSixty_decomp L61
theorem threeOneTwentyFive_decomp L62
theorem generators_minimal L67
theorem primorial_product L72
theorem second_primorial L76
theorem third_primorial L77
structure RecognitionGeneratorsCert L79
def recognitionGeneratorsCert L92