The Complete TUS OS Executable Realisation — Technical Volume II

The Complete TUS OS Executable Realisation — Technical Volume II establishes the execution-level closure of the complete admissible protected TUS OS representation in the Answerability Calculus. Beginning from the exact protected representation and round-trip reconstruction proved in Technical Volume I, its governing result is the Complete TUS OS Executable Representation Theorem: TUS OS is an executable realisation of its constituted protected Answerability object. Technical Volume II does not alter the protected TUS OS organism, admissible parameter family, intrinsic fibred Answerability representation or representation maps established in Technical Volume I. Instead, it asks whether governed TUS OS execution is carried through that already-frozen representation as lawful Answerability discharge, while preserving terminal type, authority, resource, custody and occurrence identity. The executable core closes in three stages. Total-Disposition Soundness proves over the complete governed terminal TUS OS occurrence family that every represented terminal occurrence carries an actual Answerability execution occurrence with exact protected terminal semantics, preserved six-way terminal disposition, attained resource, custody and chargeable-support accounting. Fixed-Source Realised Completeness proves the converse on the independently constituted terminal-derivation-aligned comparison family for each fixed source execution instance. These directional results are then combined with an independently typed, target-record-free runtime correspondence to establish exact relational executable commutation: Δ̃A³⁴ ∘ R̃X³⁴ = F̃D³⁴,occ ∘ Δ̃T³⁴. Thus governed TUS OS execution followed by terminal-occurrence representation agrees exactly with representation-carried runtime correspondence followed by Answerability discharge at the proved relational occurrence scope. No fictitious pointwise runtime map or uniqueness assumption is introduced. The volume then determines the strongest lawful surrounding closure. Complete internal source-trace identity is not uniformly recoverable; instead, the paper identifies the finest representation-admissible recoverable complete-source-trace quotient and proves that every uniformly recoverable source-trace observable factors through it. The production analysis proves deterministic stagewise strongest-lawful production closure, while positively establishing that the stronger global native release order required for universal maximality is not constituted at Paper-10 scope. Claim-Authority Conservation proves that evidence identity, source role, Binding permission, production authority, claim ceiling, qualifications, unresolved conditions, custody and terminal disposition remain distinctly typed throughout lawful execution. Production may exercise, narrow, qualify, hold, block or withhold constituted authority, but may not manufacture evidence or authority absent from the source constitution. Candidate-level realised irredundancy is established for the exact twelve-member preregistered basis at its certified scope, while the Paper-9 recovery/non-recovery ledger is closed without resurrecting unavailable structure and the protected representation and execution laws restrict unchanged across admitted domain-content fibres. Every governed terminal derivation at the proved scope is further made proof-carrying through a finite protected discharge certificate, exhaustive finite checks and a deterministic verifier. Certification creates no authority, and verifier outcomes agree across the represented TUS OS and Answerability faces. Two independently constituted public pilot fibres then instantiate the unchanged representation, execution, authority and verification architecture; they are realised witnesses to the theorem stack, not premises from which it is defined. The final capstone closes the complete theorem stack under whole-object adversarial and regression analysis. Technical Volumes I and II together therefore establish exact protected-object representation and reconstruction together with governed terminal execution that is preserved, reflected and exactly commuting with Answerability discharge at the proved relational occurrence scope. Accordingly, at Paper-10 scope: A governed answer is realised as a constituted lawful discharge, and TUS OS exactly realises the complete protected structure constituting and governing that discharge at Paper-10 scope. The theorem boundary remains explicit. Paper 10 does not establish complete internal-trace identity, universal global maximality where the requisite order is absent, universal necessity, universal sufficiency or canonicity. The latter universal questions are reserved for Paper 11. At the scope proved here, Paper 10 Technical Volume II closes the executable-realisation problem for the complete protected TUS OS representation in the Answerability Calculus. Supporting mathematical papers This volume is Paper 10, Technical Volume II in the TUS OS quantum-operational research programme. Papers 1–9 establish the canonical qubit-state geometry, exact prepare–measure behaviour, global relational and predictive structure, complete-future and process-closure results, system-level Anchored Analog Quantum System recognition, contract-relative achievable-resource theory, structural classification of contract-induced resource transitions, the resource geometry of answerable inference, and finally the general typed Answerability Calculus governing lawful discharge, reduction, representation, repair, composition, activation, obstruction and conservation. Paper 10, Technical Volume I then returns that general theory to the complete TUS OS organism, independently constituting the admissible protected source object and intrinsic fibred Answerability comparison object and proving their exact forward representation and reverse reconstruction through the Complete Round-Trip Representation Theorem. The present volume takes that frozen representation as its starting point and closes the distinct execution-level problem, establishing soundness, realised completeness, executable commutation, trace and production-closure boundaries, claim-authority conservation, realised irredundancy, proof-carrying discharge, domain-parametric closure and realised pilot instantiation, culminating in the Complete TUS OS Executable Representation Theorem. Paper 1 — Canonical Tetrahedral Qubit-State Geometry in the TUS OS TriadXOR Completion, Receipt Verification and the Qubit-Geometric Semantic WitnessEstablishes the canonical tetrahedral geometry, unique XOR completion, exact qubit-SIC representation and centred-face trine geometry. Paper 2 — The TUS OS Operational CalculusClassical Construction of Exact Qubit Prepare–Measure Behaviour from a Receipt-Custodied Engine ArchitectureEstablishes exact full-carrier qubit prepare–measure behaviour from the deterministic classical engine under the declared Coordinate-Incidence Operational Harness. For each lawful foundation, the 64 six-bit carriers map to exactly 27 anchor-relative qubit preparations, while the separately declared face Harness gives the exact trine table. Paper 3 — From Finite Relational Structure to Qubit Operational FormAmbient Foundations, Canonical Subatlas, Exact Global Quantum Dimension, GUIDANCE Witness, Sequential Closure and Global Representation in TUS OSEstablishes the repeated-common-effect static Atlas, its exact minimum complex Hilbert dimension 4, exact carrier-reconstruction structure and deterministic predictive-state minimum 64 for the frozen complete principal future language. Paper 4 — Technical Volume I — Formal Foundations and the Complete-Future CorpusNative Contract, Statistical Discrimination and the Invariant Probability ModuleEstablishes the frozen complete principal terminal future-experiment language, complete statistical separation of distinct carrier pairs, exact parity-resolved discrimination results, complement reachability and the 33-dimensional rational invariant probability module. Paper 4 — Technical Volume II — Orthogonality, Process Closure and Native Triadic SynthesisEstablishes universal complement-support orthogonality and its propagation under exact common-CPTP dynamics, the resulting common-CPTP process bounds, recovery-complete LANDING and GUIDANCE results, exact 64-dimensional selected-line instrument/readout minima at their declared contracts, an exact classical–quantum hybrid construction, and the native structural/predictive quotient correspondence. The state-only common-CPTP minimum remains bounded within 32–64 rather than being fixed at 64. Paper 5 — TUS OS as an Anchored Analog Quantum SystemNative Witnesses, Predictive Synthesis, and Access-Contract Resource SeparationDefines Analog Quantum Views and Anchored Analog Quantum Systems, proves that TUS OS is a proper Anchored Analog Quantum System on its 64-input abstract canonical corpus, elevates the inherited structural/predictive correspondence into the Predictive Synthesis Identity Theorem, and composes the recognition, predictive, resource and downstream-conservation results into the TUS OS Anchored Analog Quantum System Theorem. Paper 6 — Contract-Relative Quantum Realisations of Classical ProcessesPredictive Compression, Vanishing Worst-Case Causal-State Transparency, and Finite-Dimensional BreakdownExtends the programme beyond the TUS-specific discovery corpus by formalising the contract-relative achievable-resource object (S,C,𝔐,ε) ⟼ Ach(S,C;𝔐,ε), and establishes three contract-relative resource phenomena: exact strict finite separation, incrementally unbounded finite separation across a family, and finite-resource breakdown. These are instantiated respectively by the TUS OS 4→64 separation, periodically modulated decay processes with finite memberwise realisations and growing prediction-to-transparency cost, and dual-Poisson finite-capacity breakdown for every positive uniform worst-case