Derivation of the Muon–Electron Mass Ratio from Finite-Resolution Closure: The Second Admissible Invariant of the IIM v3 Auditor State

This paper is a strict differential extension of the Invariant Information Measure (IIM v3) closure auditor framework. Within the finite-resolution closure at termination depth m* = 13, the auditor state admits exactly two independent invariant scalar residues under the non-privileged representation principle. The first invariant, corresponding to the symmetric aggregation mode, was previously identified with the proton–electron mass ratio. In the present work, we identify the unique remaining admissible invariant functional arising from the quotient-mode projection of the channel-register representation space and the interaction-graph automorphism symmetry. No new parameters, normalization choices, or closure rules are introduced. All structural constants and state variables are inherited unchanged from the published IIM v3 auditor state. Using the append-only invariant readout block applied to the already-fixed auditor state, the secondary invariant evaluates numerically to Iₛec ≈ 206. 768283 which coincides with the observed muon–electron mass ratio. This value is not introduced empirically but emerges as the inevitable structural readout of the second admissible invariant of the closure algebra. The audit procedure is fully reproducible by executing the public IIM v3 auditor code and appending the minimal readout block provided in this paper.