Spectral Selection Rule AD: Fusion Category Structure Theorem and Uniqueness of Spectral Invariants at the Large Complex Structure Limit

This paper establishes, within the stable chamber C0 at the large complexstructure limit of the quintic Calabi–Yau threefold, a spectral filtration constraintfrom the chamber heart through a non-invertible ideal quotient to a semisimplefusion category, and separates the uniqueness of classification from already provedpropositions into a suspended hypothesis with explicit conditional depth and anexpiration date. The global dimension D2(S) is constrained by the necessarycondition of a finite product of Jones spectral factors 4 cos2(π/n); the standard rank4 category Sstd satisfies the exact identity D2 = 5+√5 = 4cos2(π/4)·4cos2(π/10),and the decomposition of its nontrivial spectral factors is unique over all ranges offactor number and n (Theorem 8.1); the original finite enumeration conclusion forn ≤ 60 and factor number ≤ 3 is its numerical verification layer. The semisimplecategory obtained via the Jnv quotient gives a compatible decomposition; theexclusion decision for other quotient types is registered as a finite enumeration tobe completed. The spectral invariants are separated at the definition level: thegeometric spectral invariant Zstd := χ/2 (mod 8) is given by the tangent bundleindex, and the system spectral invariant Zfull := ceff (mod 8) is given by the effectivecentral charge of the complete BPS branch; for the registered quintic input, Zstd = 4,Zfull = 6, and the difference is 2. The branch index gives a one-way correspondencefrom construction type to reading, not a circular criterion that infers constructiontype from reading. Error locking holds within the parameterized cascade model: theproduct of the three-chain effective exponents is 4/3, the deterministic bound at fixedparameters at δF = 1.2×10−3 is about 1.91×10−3, the simulated 97.5% quantileunder the registration protocol is about 2.76×10−3, and the locked value 2.8×10−3is the upward-rounded registered value of that quantile and does not constitute anupper bound at any arbitrary confidence level. Classification uniqueness is placed inparallel with H-Lift as the H-Class hypothesis; its conditional lifetime is determinedby the finite enumeration verification of rank 4, D2 = 5 +√5, fusion multiplicities∈ {0,1}, and pentagon residual ≤ 0.008. Chapter 8 narrows item by item thoseparts of the registered open boundaries that can be advanced with the tools ofthis paper: the semisimplification criterion for quotient types, the completeness ofthe quotient-type list at the level of Sstd itself, the ring-by-ring finite verificationkernel and the rank bound of the verification space for H-Lift. This paper doesnot use the necessary condition of the Jones filtration as a sufficient condition forclassification, does not extrapolate the numerical locking within the protocol to otherinput points, and does not state the label correspondence of the condensed-matteranalogy interface as a corollary of the Calabi–Yau computation.