IndisputableMonolith.CrossDomain.TenFoldCombinations
This module defines 10-fold structure on a type T precisely when its cardinality equals 10, rewritten as the product 2·5. It supplies four concrete realizations (fingers, decimal digits, lumbar-sacral vertebrae, d-block elements) together with equicardinality and squaring lemmas. The definitions are used to exhibit 10-fold objects across independent domains inside the Recognition Science cross-domain layer.
claimA type $T$ satisfies $\mathsf{HasTenFold}(T)$ if and only if $|T|=10=2\cdot5$.
background
The module sits in the CrossDomain layer and introduces the predicate HasTenFold together with four named instances. Finger, DecimalDigit, LumbarSacralVert and DBlockElement are each shown to have cardinality 10. The auxiliary results ten_eq_two_D, tenfold_equicardinal and tenfold_squared record the algebraic consequences of writing 10 as 2·5.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the concrete 10-fold carriers that later cross-domain arguments rely on when they equate biological and chemical structures through the common cardinality 10=2·5.
scope and limits
- Does not assert a common physical origin for all listed 10-fold structures.
- Does not classify every possible type of cardinality 10.
- Does not relate the 10-fold predicate to the J-cost or phi-ladder.
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