module module high

`IndisputableMonolith.CrossDomain.CardinalitySpectrum`

The CrossDomain.CardinalitySpectrum module asserts that spatial dimension equals three in the Recognition Science framework. Researchers deriving D from the forcing chain T0-T8 would cite it to anchor cross-domain cardinality results. The module assembles sibling definitions and equalities such as Dspatial and three_is_Dspatial to realize the T8 step from the eight-tick octave.

claim$D_{spatial} = 3$

background

The module sits in the CrossDomain section and focuses on cardinality spectrum analysis. It introduces Dspatial as the spatial dimension together with Dconfig, twoFace, gap45, eightTick, and cubeFaces, plus their equality forms. These objects connect to the unified forcing chain where T7 sets the eight-tick octave and T8 forces three spatial dimensions. The module imports Mathlib and states the central equality 3 = D_spatial in its documentation.

proof idea

this is a definition module, no proofs

why it matters in Recognition Science

The module supplies the dimensional constraint D = 3 required by T8 in the forcing chain. It feeds parent results on the phi-ladder mass formula and constants such as G = phi^5 / pi that presuppose three spatial dimensions. The doc comment directly records the equality that closes the cross-domain cardinality argument.

scope and limits

Does not derive the forcing chain steps T0-T7.
Does not extend to temporal or higher dimensions.
Does not compute numerical values for alpha or G.
Does not invoke the Recognition Composition Law.

declarations in this module (36)

def Dspatial L26
def Dconfig L27
def twoFace L28
def gap45 L29
def eightTick L30
def cubeFaces L31
theorem eightTick_eq L33
theorem gap45_eq L34
theorem cubeFaces_eq L35
theorem three_is_Dspatial L40
theorem four_is_2sq L43
theorem five_is_Dconfig L46
theorem six_is_cubeFaces L49
theorem seven_is_cube_minus_one L52
theorem eight_is_2cube L55
theorem ten_is_2_D L58
theorem twelve_is_D_4 L61
theorem fifteen_is_3_D L64
theorem sixteen_is_2_fourth L67
theorem twentyfive_is_Dsq L70
theorem fortyfive_is_gap L73
theorem sixtyfour_is_2sixth L76
theorem seventy_is_choose_8_4 L79
theorem oneTwentyFive_is_Dcubed L82
theorem twoSixteen_is_six_cubed L85
theorem twoFiftySix_is_power_of_2cube L88
theorem threeSixty_is_tick_gap L91
theorem threeOne25_is_D_fifth L94
theorem eleven_check L99
theorem thirteen_is_fib_7 L103
def rsSpectrum L107
theorem rsSpectrum_length L110
theorem rsSpectrum_pairwise_lt L113
theorem rsSpectrum_bounded L116
structure CardinalitySpectrumCert L119
def cardinalitySpectrumCert L133