IndisputableMonolith.CrossDomain.TenFoldCombinations
The CrossDomain.TenFoldCombinations module defines ten-fold structure on a type precisely when its cardinality equals 10, which factors as 2 times 5. Researchers applying Recognition Science to biological or decimal systems would cite the module for its concrete realizations. The module consists entirely of definitions and equicardinality statements with no proof bodies.
claimA type $T$ has ten-fold structure if and only if $|T| = 10 = 2 · 5$.
background
The module sits in the cross-domain layer of Recognition Science and introduces the predicate that a type carries ten-fold structure exactly when its cardinality is 10. It supplies concrete instances: Finger, DecimalDigit, LumbarSacralVert, and DBlockElement, each shown equicardinal to 10. Additional statements record that 10 equals 2 times D and that the ten-fold property is preserved under squaring.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the ten-fold definitions that cross-domain applications of the Recognition Science framework rely on when mapping numerical patterns onto biology and decimal systems. It stands upstream of any later use of 10-fold structure in the phi-ladder or octave constructions.
scope and limits
- Does not derive physical constants or mass formulas.
- Does not reference the forcing chain T0-T8 or RCL.
- Does not connect ten-fold structure to J-uniqueness or phi.
- Does not address spatial dimension D = 3.
declarations in this module (16)
-
def
HasTenFold -
inductive
Finger -
inductive
DecimalDigit -
inductive
LumbarSacralVert -
inductive
DBlockElement -
theorem
finger_is_10 -
theorem
digit_is_10 -
theorem
lumSac_is_10 -
theorem
dBlock_is_10 -
theorem
ten_eq_two_D -
theorem
tenfold_equicardinal -
theorem
tenfold_squared -
theorem
tenfold_times_D -
theorem
ten_as_two_halves -
structure
TenFoldCombinationsCert -
def
tenFoldCombinationsCert