Finite Distinguishability Closure (FDC) v9 presents a finite structural closure framework based on six foundational constraints: Finite Distinguishability (FD), Non-Privileged Representation (NPR), Single Serial Ledger (SSL), Mapping Stability (MS), Distinction Preservation (DP), and Distinction Generation Exclusion (DGE). These are supplemented by one explicit Structural Closure Condition (SCC), the Minimal Closure-Core Specification Discipline (MCCS), and the Minimal Structural Readout Grammar (MSRG). The main construction yields four typed structural components: role layer: (nᵣ = 3), relational layer: (nₑ₄₋ = 11), phase layer: (n₇ = 9), address layer: (nₕ = 19). Their structurally independent closure-core inventory is N₂₎ₑ₄ = 3 + 11 + 9 + 19 = 42, with expansion basis C = 84. FDC v9 supersedes v8 by replacing the former Structural Operation Grounding (SOG) principle with three explicitly separated conditions: SCC for construction-phase closure-readiness, MCCS for stagewise specification discipline, and MSRG for readout-phase operation grammar. This separates the construction of the closure-core, the selection of component specifications, and the admissibility of arithmetic readout operations. The paper also records two structural readout routes. Route I gives the leading scalar skeleton ^ (I) 0 = Ncore nᵣ + nₑ₄₋ = 137, with rational correction terms evaluated in the appendix. Route II gives the distributed leading skeletons (^ (II) ₁, ^ (II) ₂, ^ (II) ₃) = (1836, 206, 3477). No empirical physical constants are used as inputs. Numerical comparisons with dimensionless physical quantities, including the inverse fine-structure constant and lepton/hadron mass-ratio-like readouts, are treated as downstream structural readout comparisons and are developed in companion works such as SCR. Within the broader MOF–FDC–PFC–SCR–AOH program: MOF supplies the eliminative/descriptive-closure foundation. FDC supplies the finite structural closure grammar. PFC gives a physical reading of closure and phase-flow structure. SCR records structural readouts and external numerical comparisons. AOH applies related closure/readout ideas to Hubble-scale and galactic-scale phenomena. This version should be read as the mathematical reference layer of the program. Its primary role is to define the finite closure-core, its dependency structure, and the admissible readout grammar. Physical interpretations and observational applications are developed only in companion works.
T Momose (Wed,) studied this question.