Finite Distinguishability Closure (FDC): Axiomatic Structure and Non-Fitted Numerical Readouts (v5.1)

This record documents version v5.1 of the Finite Distinguishability Closure (FDC) framework. FDC is an axiomatic construction based on three primitive principles:- Finite Distinguishability (FD)- Non-Privileged Representation (NPR)- Single-Serial Ledger (SSL) In addition, the present formulation employs explicit admissibility conditions for structure-preserving transformations:- Distinction Preservation (DP)- Mapping Stability (MS)- Distinction Generation Exclusion (DGE) These conditions define the class of admissible morphisms under which finite distinguishability closure is studied. Within this framework, a finite closure structure is constructed and analyzed. Under the stated admissibility constraints, the construction leads to: - A finite structural inventory (including a total distinguishability count)- A dual-basis expansion structure- Two distinct scalar readout schemes (Route I and Route II)- A finite termination of the expansion hierarchy All numerical values presented in this record are obtained through explicit structural constructions and finite computations. No empirical constants are used as inputs. This version (v5.1) is released for priority and archival purposes. Further refinement of the axiomatic hierarchy and proof structure is ongoing.