IndisputableMonolith.Foundation.UniversalForcing.Strict.Modular
The module defines strict modular realizations for moduli n>1, extending the ordered integer case. Researchers building categorical hooks in the Recognition Science forcing chain would cite these definitions. It consists of cost functions on Z/nZ together with arithmetic equivalence lemmas to LogicNat.
claimFor $n>1$, the cost $\ ext{zmodCost} : \\mathbb{Z}/n\\mathbb{Z} \\to \\mathbb{R}$ satisfies self-symmetry and the arithmetic equivalence $\\text{strictModular_arith_equiv_logicNat}$ to the canonical LogicNat surface; the realization is $\\text{strictModularRealization}(n)$.
background
The module belongs to the Strict subhierarchy of UniversalForcing and imports the Ordered module, whose doc states it supplies strict ordered realization on $\mathbb{Z}$ with equality cost and unit translation. It introduces modular cost functions (zmodCost and its symmetry/self lemmas) on finite quotients $\mathbb{Z}/n\mathbb{Z}$ for $n>1$, preserving the equality-cost structure while preparing the carrier for categorical abstraction.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
It supplies the modular step that the downstream Categorical module imports to construct the strict categorical/Lawvere-style realization hook whose carrier is the canonical LogicNat NNO surface. The module therefore closes the ordered-to-categorical transition inside the universal forcing chain before any refinement to full Mathlib category-theory NNO API.
scope and limits
- Does not treat moduli $n\le 1$.
- Does not refine to full category-theory NNO API.
- Does not address non-strict or probabilistic costs.
- Does not link to mass ladder or physical constants.