The declaration tripleProductCard in module IndisputableMonolith.Foundation.RSCoupledAxis is a Lean definition that computes a cardinality product for RS-independent axes.
(1) In plain English: it takes a structure RSIndependentTriple n (three finite axes, each of exact size n, tagged by distinct RS primitives such as jCost or phiLadder) and returns the product of the three axis cardinalities.
(2) Why it matters in Recognition Science: the module supplies infrastructure for cross-domain combination theorems. Two axes of the same cardinality are independent in RS only when tagged by different recognition primitives; tripleProductCard therefore gives the combinatorial count of states arising from three such independent axes.
(3) How to read the formal statement: def tripleProductCard {n : ℕ} (T : RSIndependentTriple n) : ℕ := @Fintype.card T.axis1.Ix T.axis1.finite * @Fintype.card T.axis2.Ix T.axis2.finite * @Fintype.card T.axis3.Ix T.axis3.finite. The @Fintype.card calls extract the size of each axis's index type Ix using the supplied finite instance; the result is therefore always n * n * n when the input satisfies the triple's cardinality equations.
(4) Visible dependencies or certificates: it depends on the inductive type RSPrimitive, the structure CoupledAxis, and the structure RSIndependentTriple. The theorem triple_card supplies the certificate that tripleProductCard T = n * n * n. Related declarations include RSDisjointSum3 and disjoint_sum_card.
(5) What this declaration does not prove: it establishes only a definitional cardinality computation and the equality to n³; it does not prove existence of any concrete RSIndependentTriple, does not derive physical constants or forcing theorems, and does not address whether such axes appear in nature or link to spacetime emergence.