Finite Readout Representations and Matching Corrections from the Compact Fiber

This paper develops a finite readout and matching protocol for the compact fiber

F = Z_4^{m_1} × Z_4^{m_2} × Z_8^e.

The first part formalizes the compact fiber as a finite character/readout object by passing to its character group F̂ = Hom(F,U(1)). The two Z_4 factors define finite magnetic character sectors, while the Z_8 factor defines the finite electric character sector. The degree-two cover Z_8 → Z_4 identifies direct magnetic-base compatibility with even electric characters and gives odd electric characters a deck-parity interpretation.

The main finite-layer result is the Character-Readout Classification Theorem. It shows that recurring compact-fiber factors such as 1/8, 1/4, 7/8, 1/32, and 128 arise as projections, complements, product-sector resolutions, or full character counts. The cover-mediated factor 1/16 is fixed once a readout is assigned to the degree-two electric cover class. The paper also proves a finite character conservation rule for closed internal finite-sector couplings and recasts the radiation-paper OAM parity rule as a cover-compatibility statement.

The second part applies the same status discipline to an elementary natural-unit mass-to-energy bridge. The bridge is represented as a single source-to-target traversal from a completed two-dimensional secondary-mass source to an energy/readout target. This fixes the typed package s = m + e_∂. Using the Larson–Nehru interregional and secondary-mass bridge-layer rules, the electric boundary contribution is reconstructed as

e_∂ = e = (1/|F̂|)(1/9)(2/3) = 1/1728,

so the admissible elementary matching package is s = m + e.

The result is a no-retuning audit framework: a proposed factor must be a defined finite-character operation, a cover-conditional readout, a theorem-grade bridge result under stated premises, or an open term. Competing packages such as m, m + 2e + C, e − c, and e − C are rejected by readout class rather than by numerical fit.