Quotient Orthogonality & Admissibility
Abstract
We discharge the two prongs of next-steps.md sub-targets 2.3 (Quotient Orthogonality and Invisibility) and 2.4 (Admissibility) for the canonical Burnol/Blaschke defect object used in the vol5 conditional theorem . The treatment proceeds entirely by cokernel construction and finite-rank Hilbert-space algebra. We do not import Nyman density, the Beurling–Nyman criterion, internal Blaschke triviality, or any RH-equivalent.
For sub-target 2.3 we construct by taking the orthogonal-to-representable predicate to be exactly the Nyman/Yoneda image and exploiting the cokernel rule that -realised representables are annihilated by the projection onto . For sub-target 2.4 we prove the three opaque atoms , , and by parameterising over a single three-field admissibility introduction package, each field of which is a finite-rank Hilbert-space-algebraic input lifted to the canonical defect via regularised (resolvent-strong) convergence rather than raw operator-norm convergence.
Artifacts
Vol6.QuotientOrthogonalityAdmissibilityhaskell/paper-05-quotient-orthogonality-and-admissibility/Main.hsVol6.Obstruction.AdmissibilityObstructionStatus & Obstructions
The principal theorem is conditional on inhabiting the named obstruction type. The obstruction module precisely characterizes the missing Vol5 introduction rule. No new sorry, admit, axiom, or opaque is introduced in Vol6.