Compatible Role-Occupancy Closure for the Neutrino Propagation Role Complex

Compatible Role-Occupancy Closure for the Neutrino Propagation Role Complex Universal Compatible-Occupancy Lifting, Carrier-Semantic Descent, and Terminal Over-Residue This paper develops the role-occupancy layer of the Neutrino Carrier Prediction arc. It takes the exact PCR-4 carrier-survivor quotient as fixed input and asks two distinct questions: whether every surviving carrier class admits a complete internally compatible role-occupancy architecture; and whether those compatible realizations collapse to a unique terminal physical carrier. The analysis separates internal factorization, carrier-semantic identity, and terminal Role-Occupancy Closure. These are different resolutions and cannot be identified merely because they describe the same propagation complex. Universal compatible-occupancy lifting For each PCR-4 survivor, the paper constructs a nonempty role-bearing core from mandatory witness paths. Witness-preserving normalization produces a finite partially ordered set of admissible factorizations. Maximal factorizations retain all required factor blocks, constitutive maps, source interfaces, continuation data, and failure records. Every factor block has a nonempty role-standing signature, and every maximal factorization admits a complete assignment satisfying: pointwise eligibility (E₅); global compatibility (J₅); complete role-core coverage; preservation of the PCR-4 common-cone structure; the declared internal grammar and witness contracts. Consequently, every PCR-4 carrier survivor has at least one complete compatible internal occupancy assignment: Σ⁵ᵢₙₜ(x) ≠ ∅ for every x ∈ 𝔖ν⁽⁴⁾. The internal occupancy object therefore satisfies the universal lower bound: |𝔒⁵ᵢₙₜ| ≥ |𝔖ν⁽⁴⁾| ≥ 2. This is a positive universal lifting theorem. It shows that the surviving carrier classes are not merely formal survivors: each supports at least one complete compatible role-bearing factorization within the declared PCR-5 grammar. Carrier-semantic descent Internal factorization is deliberately finer than physical carrier identity. A single parent carrier may admit several incomparable maximal factorizations, and these alternatives are retained at the internal level. The carrier projection quotients factorization alternatives over one parent: 𝔖ν,car⁽⁵⁾ := im(π̄car) = 𝔖ν⁽⁴⁾. This prevents internal factorization multiplicity from being mistaken for multiple physical carriers. At the bounded reference corpus, the law-only Weinberg carrier and the constructive full-rank active Standard Model plus three-νᴿ carrier remain distinct because their parent carrier traces are inequivalent. The cross-corpus analysis therefore retains the lower bound: |𝔖ν,car⁽⁵⁾[K₊]| ≥ 2. Low-energy matching may identify propagation kernels, effective residues, or numerical observables, but it does not erase differences in primitive carrier traces, source incidence, retained-resolution continuation, or failure domains. Terminal Role-Occupancy Closure The terminal carrier-resolution target contains one complete carrier role: R⁵ₜₑᵣₘ = {r_cₐᵣ(Tνosc)}. The terminal eligibility relation and compatibility predicate are formed independently after carrier-semantic descent. The resulting live terminal residue is the surviving carrier-semantic residue itself: |Residue⁵ₜₑᵣₘ[K₊]| ≥ 2 > 1 = |R⁵ₜₑᵣₘ|. A compatible terminal realization would require a bijective role-covering assignment from the one-element role set onto the complete live residue. Because the residue contains at least two distinct carrier classes, no such bijection exists: Σ⁵ₜₑᵣₘ = ∅, Σ⁵ₜₑᵣₘ[K₊] = ∅. The complete terminal certificate therefore yields: ¬RealizationLicensed(𝒞⁵ν,ₜₑᵣₘ, T⁵ν,ₜₑᵣₘ). The terminal diagnosis is over-residue: compatible carrier realizations exist, but the separately declared one-role terminal target does not close to a unique licensed carrier residue. Interpretation of the endpoint The result is a strict lower bound, not an exact two-carrier theorem. The paper does not claim that exactly two physical carriers exist. A future singleton theorem would require one of three developments: failure of an upstream premise; a lawful equivalence of the surviving carrier traces; an explicitly enlarged target carrying genuinely new ultraviolet-sensitive standing information. Alternative factorizations, low-energy matching, post hoc preference, or numerical agreement cannot supply that collapse by themselves. Scope and realization boundary The theorem is exact relative to the PCR-1–PCR-4 imports, the finite PCR-3 source scope, the independently generated PCR-5 internal grammar, the declared terminal carrier-resolution target, and the bounded reference corpus. The internal factorization-sensitive quotient is not the terminal physical carrier quotient. Internal multiplicity does not automatically imply carrier multiplicity, while distinct carrier traces remain distinct after factorization alternatives are collapsed. The paper does not assert an exact two-carrier result, a unique ultraviolet completion, a complete physical terminal realization, or the exclusion of future target extensions with genuinely new source information. Role in the PCR programme PCR-5 converts the PCR-4 survivor result into a compatible-occupancy theorem and then tests terminal carrier closure. It proves universal nonempty internal occupancy while showing that the present one-role terminal target remains over-resolved by the surviving carrier-semantic residue. Its principal contribution is the clean separation of: compatible internal role occupancy; carrier-semantic identity; terminal role coverage; terminal physical realization. Keywords compatible role occupancy; neutrino propagation; PCR-5; Role-Occupancy Closure; carrier-semantic residue; maximal factorization; terminal compatibility; neutrino carrier; oscillation structure; Weinberg operator; right-handed neutrino; effective field theory; ultraviolet completion; terminal over-residue; AASC