IndisputableMonolith.CrossDomain.CrossPatternMatrix
The CrossPatternMatrix module defines algebraic entries for a cross-domain pattern structure in Recognition Science. Its central statement is the full turn identity 2 cubed times 45 equals 360 degrees. Researchers modeling the eight-tick octave or cross-domain interactions would cite these definitions. The module supplies direct definitions of the named pattern products and squares with no embedded proofs.
claimThe full turn satisfies $2^3 times 45 = 360$ degrees, realized through the pattern matrix whose entries are the products and squares $D_5^2$, $D_5 times 2^3$, $D_5 times gap$, $2^3 squared$, $2^3 times gap$, $gap squared$, $D_5 times 2^3 times cube$, and $D_5 times cube faces$.
background
Recognition Science places the eight-tick octave (period $2^3$) at T7 of the forcing chain. This module introduces the CrossPatternMatrix as the algebraic carrier for cross-domain pattern entries built from the D5 yardstick, the two-cube factor, and the gap term on the phi-ladder. The supplied doc-comment states the geometric closure: full turn equals $2^3 times 45$ degrees equals 360 degrees. All entries are expressed in native RS units where $c=1$.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the pattern-matrix definitions that support the T7 eight-tick octave and the geometric closure of the forcing chain. It feeds downstream cross-domain results that close the loop from the J-uniqueness fixed point to spatial dimension D=3.
scope and limits
- Does not contain any theorem statements or proofs.
- Does not import Recognition Science core modules beyond Mathlib.
- Does not define the explicit matrix layout or its eigenvalues.
- Does not address numerical evaluation of the entries.
declarations in this module (23)
-
theorem
D5_squared -
theorem
D5_times_2cube -
theorem
D5_times_gap -
theorem
twoCube_squared -
theorem
twoCube_times_gap -
theorem
gap_squared -
theorem
full_turn -
theorem
entries_distinct -
theorem
D_sq_times_cube -
theorem
D_times_double_cube -
theorem
cube_sq_plus_cube -
theorem
D_times_cube_faces -
theorem
D_sq_cube_faces_minus_gap -
theorem
cube_faces_squared -
theorem
face_pairs_minus_gap -
theorem
nine_is_D_sq -
def
matrixSize -
def
offDiagSize -
def
offDiagEntries -
theorem
offDiagEntries_eq -
theorem
offDiag_is_two_fourth -
structure
CrossPatternMatrixCert -
def
crossPatternMatrixCert