IRMT XVII - Compact Determinant Closure and the Finite Charged-Lepton Triplet

Paper XVI of the Information Relational Manifestation Theory program audited whether the response–connection law required by the charged-lepton construction follows from the microscopic substrate dynamics. It concluded that it does not. The relation was retained as the minimal constitutive endpoint of the effective theory, and the construction of Paper XV was accordingly reclassified as a highly constrained conditional effective model rather than a microscopic theorem. Paper XVI left three logically distinct paths: accept the constitutive law, introduce new microscopic protection structure, or derive a deeper packet action. The present paper reports that the second and third paths were both taken, and that the constitutive endpoint has been closed within a declared finite and countable domain. The closure is not a repair of the local route audited in Paper XVI. It replaces that route entirely. The mechanism converts Paper XVI’s own compact-phase obstruction into the instrument of closure. A globally smooth periodic scalar on a compact phase circle cannot possess a nonzero constant derivative; the exact compact completion therefore carries an integer winding record. Once the winding record is admitted, three independent structural requirements — cross-dimensional unitary equivariance, orthogonal direct-sum compatibility, and elementary-record normalization — reduce the space of admissible response-to-current transformations from eighty-one real dimensions to two, then to one, then to none. The surviving transformation is the identity, and the unique linear oriented current in that class is The corresponding lock action has stationary equation exp(iΘ𝒟) = exp(iΩDW,𝒟 ,𝒟) and Hessian equal to the identity on the determinant-line coordinate space, so the common and relative channels acquire equal unit coefficients without a separately normalized ratio. The identity intertwiner, the unit lift coefficient, and the compact phase normalization — three of the eight items Paper XVI listed as underived — follow from this classification rather than from assumption. The mixed-wedge obstruction is removed by a different argument. When the protected projectors are treated as completed retained records, admissible future events intertwine each projector individually, and the second exterior power then preserves the determinant-line subspace and the mixed-wedge sector separately. The cross block vanishes identically, B = 0, Aeff = A − B C⁻¹ B† = A, so the effective determinant-line metric is protected exactly rather than suppressed numerically. The quantitative decoupling requirement of Paper XVI, ≳ 421.9, is therefore not met; it ceases to apply. We recompute that threshold independently and reproduce it to 421.948, together with the Paper XVI mixed-wedge audit values ‖BHsupp‖ = 0.2801773320 and ‖BHsupp‖² = 0.0784993374, in order to establish that the two papers describe the same object under different admissibility conditions. Conditional on the closure, the charged-lepton chain becomes a finite numerical prediction. With the Fermi constant as the sole empirical import and no charged-lepton mass used anywhere, the packet scale is Epacket = 1882.648719 MeV and the triplet is (0.510861466, 105.630987, 1776.506871) MeV, against measured (0.510998950, 105.6583755, 1776.86) MeV. The three deviations are −0.0269%, −0.0259% and −0.0199%. A single common rescaling of Epacket by +0.0242% reduces all three residuals below 0.0044%, and the predicted square-root mass ratios agree with measurement to 4.9 × 10⁻⁶ and 3.5 × 10⁻⁵. We report this decomposition as a diagnostic that localises any required correction in the scale bridge rather than in the Koide geometry. It is not a second prediction, and the common factor is a one-parameter post-hoc fit. The result is therefore closure relative to a disclosed premise bundle, not unconditional derivation. The premises are: the winding-record completion of the compact phase; cross-dimensional naturality of the response transformation; elementary-record normalization; the supplied support generator and signed curvature ; and, for the protection theorem, restriction to the admissible retained-record tangent space. The last of these is the load-bearing and most contestable assumption in the paper, and we state its exact scope and its retirement condition explicitly. Interacting continuum protection, the microscopic origin of the packet support generator, and the extension of this mechanism to the quark and neutrino sectors remain open.