This release presents an Open Specialist Assessment Version of a formal pressure test concerning selected commitments of Universal Recursive Dynamics (URD) and categorical, dependent, history-sensitive, and process-theoretic resources used to represent them without collapsing structural conditioning into temporal succession, constitution into restriction, or participant continuation into current-state identity. The investigation originated when the author recognized a possible structural correspondence between unresolved URD questions and split-idempotent/Karoubi resources encountered in Hefford and Wilson's work on hyper-decoherence from a causally indefinite process theory to quantum theory. The author is not a specialist in the mathematical fields employed and could not independently determine whether that apparent correspondence was mathematically substantive. Sustained human–AI inquiry was therefore used to translate the initial question into explicit definitions, candidate constructions, propositions, proofs, counterexamples, negative results, and unresolved formal obligations. The manuscript reports both positive and negative results. Split-idempotent/Karoubi machinery is retained as a resource for restriction and invariance but does not supply relation-priority or constitution; compatible-idempotent order does not by itself encode Paper-A structural conditioning. Dependent/displayed structures provide a bounded representation of specifiability dependence and display-relative polarity; an inductive-inductive witness supplies a limited joint-generation capability and a paper-local specification non-separability result. History-sensitive individuation, register, and continuation resist reduction to endpoint or current state, while the proposed Part III interface remains representational rather than derivational and retains explicit open obligations. The surviving formal material is released for independent specialist scrutiny. AI-assisted convergence is not treated as a substitute for disciplinary verification, and the author does not claim specialist mathematical competence sufficient to certify the formal results independently. In this assessment version, PROVED means that a result is claimed to follow from the stated assumptions by the proof or argument supplied, or is a directly used standard result; it does not imply prior independent specialist verification. Corrections, counterexamples, typing objections, provenance challenges, scope objections, and identification of prior mathematical formulations are specifically invited. A separate Technical Assessment Guide accompanies the manuscript so that readers may evaluate only the portions within their expertise.
This release presents an Open Specialist Assessment Version of a formal pressure test concerning selected commitments of Universal Recursive Dynamics (URD) and categorical, dependent, history-sensitive, and process-theoretic resources used to represent them without collapsing structural conditioning into temporal succession, constitution into restriction, or participant continuation into current-state identity. The investigation originated when the author recognized a possible structural correspondence between unresolved URD questions and split-idempotent/Karoubi resources encountered in Hefford and Wilson's work on hyper-decoherence from a causally indefinite process theory to quantum theory. The author is not a specialist in the mathematical fields employed and could not independently determine whether that apparent correspondence was mathematically substantive. Sustained human–AI inquiry was therefore used to translate the initial question into explicit definitions, candidate constructions, propositions, proofs, counterexamples, negative results, and unresolved formal obligations. The manuscript reports both positive and negative results. Split-idempotent/Karoubi machinery is retained as a resource for restriction and invariance but does not supply relation-priority or constitution; compatible-idempotent order does not by itself encode Paper-A structural conditioning. Dependent/displayed structures provide a bounded representation of specifiability dependence and display-relative polarity; an inductive-inductive witness supplies a limited joint-generation capability and a paper-local specification non-separability result. History-sensitive individuation, register, and continuation resist reduction to endpoint or current state, while the proposed Part III interface remains representational rather than derivational and retains explicit open obligations. The surviving formal material is released for independent specialist scrutiny. AI-assisted convergence is not treated as a substitute for disciplinary verification, and the author does not claim specialist mathematical competence sufficient to certify the formal results independently. In this assessment version, PROVED means that a result is claimed to follow from the stated assumptions by the proof or argument supplied, or is a directly used standard result; it does not imply prior independent specialist verification. Corrections, counterexamples, typing objections, provenance challenges, scope objections, and identification of prior mathematical formulations are specifically invited. A separate Technical Assessment Guide accompanies the manuscript so that readers may evaluate only the portions within their expertise.
This paper is an update of DOI: 10.5281/zenodo.18437917. It is intended for both human and AI reviewers; while the exposition is human-readable, the density and formal discipline are optimized for solver-based and machine-assisted review. The document will be modularized in future releases to focus on individual core aspects of the framework. This paper presents a falsification-focused evaluation of the Unified Resonance Model (URM) using an explicit solver-based methodology. Rather than proposing new physical laws or numerical predictions, the work tests whether URM’s core claims—regarding time, information, geometry, and record formation—survive structured challenge under a constrained execution protocol. Predictions and falsifiability claims are evaluated using a single-path solver that diagnoses admissibility across three stages: Possible (inference-free structure), Applied (execution under an explicit grammar), and Recorded (persistent, joinable records). Each claim is subjected to independent linguistic, mathematical, and geometric audits, ensuring that no temporal, causal, or outcome assumptions are introduced prior to record formation and that the possible domain remains untainted by actualized histories. The paper treats falsification as a methodological discipline rather than a defensive exercise. Predictions are classified as closed, conditionally closed, or open by design, with explicit criteria for what would constitute a genuine solver-consistent contradiction. Where claims remain open, this is shown to follow from a strict “no accrual” rule: outcomes depending on future record formation are not pre-booked. Several canonical tests are examined, including schema invariance, record-formation gradients, decoherence–recordability correlations, re-typing of the Quantum Zeno Effect, and parametric variation of execution grammar. Navier–Stokes behavior is analyzed as a representative case of infinite admissibility in the possible domain versus finite survivability under execution. No existing equations are modified, and no Millennium Problems are claimed as solved. The contribution is methodological: a documented procedure for running falsification through a formal solver and DSL, functioning as a laboratory for structural admissibility and realizability rather than numerical simulation.
Abstract We present Kunato Core Ver.5.0.0, a general framework for ontological admission, typed representation transport, empirical identifiability, effective-structure validation, and provenance-preserving epistemic state transition. The framework addresses a recurrent inferential problem across mathematical physics, statistical inference, inverse problems, effective theories, information theory, complex systems, quantum theory, and scientific realism: mathematical definability, empirical adequacy, model identification, and physical realization are distinct achievements and must not be silently promoted into one another. Kunato formalizes this separation through the constraint Formal(M) AND Emp(M; O) DOES NOT IMPLY Ontic(M). No representation receives automatic ontological privilege. Finite observation provides a first source of non-identification. Distinct formal models can agree exactly on a finite empirical record; in particular, uncountably many models can be constructed that coincide on any prescribed finite set of sample points. This establishes non-uniqueness within the relevant formal model class without promoting mathematical alternatives into claims about distinct physical causal histories. Finite measurement precision is treated through fibers of explicit resolution maps rather than by identifying metric neighborhoods with equivalence classes. The framework further distinguishes finite-dimensional state spaces from finite-state ontologies: finite-dimensional complex Hilbert spaces can contain a continuum of pure-state rays, whereas finite operational distinguishability requires additional assumptions such as a uniform positive separation scale on a compact state space. For stochastic observations, Kunato separates distributional identifiability, asymptotic inference, finite-sample discrimination, and zero-error identification. Positive overlap between competing observational laws prevents zero-error discrimination from the corresponding finite record. Increasing statistical evidence can therefore strengthen discrimination without automatically supplying an ontological realization warrant. Identification within a declared candidate class likewise remains conditional on that class and does not establish that physical reality belongs to it. The mathematical core is a typed property-transport calculus. Given a representation map Phi: X -> Y and a property P: X -> Z, P factors through Phi precisely when P is constant on every fiber of Phi. Equivalently, the kernel equivalence relation induced by Phi is contained in the kernel equivalence relation induced by P. This criterion separates state identification from property identification: a non-injective representation may fail to recover individual source states while still determining every property invariant on its fibers. Representation types, identified by their induced fiber equivalence relations, are organized by refinement within the complete lattice of equivalence relations on X. This provides a common mathematical structure for coarse-graining, quotient representations, projections, information loss, recoverability, and comparison of effective descriptions. Refinement is a partial order, so representations may also be incomparable. Effective structures consequently require property-specific transport warrants. Compression of a unitary parent operator, for example, need not preserve unitarity or normality. Conversely, non-normality alone does not entail a non-real spectrum, irreversibility, non-Markovianity, or absence of characteristic timescales. Observable symmetry, effective geometry, statistical regularity, entropy, information structure, temporal scales, and other representation-dependent properties cannot be transported automatically to a parent ontology. Kunato operationalizes these restrictions through methodological admission protocols. The Metric Admission Protocol regulates inference from effective metric structure to fundamental geometry. The Statistical-Invariant Admission Protocol separates existence of a mean from typicality, concentration, and self-averaging. The Timescale Admission Protocol distinguishes observed decay and hazard structure from claims about fundamental temporal dynamics. The Informational-Semantic Admission Protocol constrains inference from probability, entropy, information geometry, and semantic structure to latent ontology. The Criticality Admission Protocol separates phenomenological scaling from stronger claims of critical structure by requiring appropriately scoped diagnostics such as finite-size behavior, exponent stability, data collapse, robustness analysis, and negative controls. These protocols are methodological admission criteria rather than asserted laws of nature. Ontological admission is governed by differentiated semantic, fit, identification, scope, realization, revocation, and provenance warrants. These warrant types prevent empirical fit, interpretation, candidate-class identification, physical realization, and evidential history from being collapsed into an undifferentiated notion of support. Epistemic judgments are represented as contextual and versioned states, allowing changes in evidence, candidate classes, semantics, scope, and warrants to be reconstructed as explicit state transitions rather than hidden revisions. A central distinction is that UNRESOLVED is not REJECTED. Failure to establish an adequate promotion warrant blocks the requested inference but does not establish falsity or nonexistence. Rejection requires an independent refutation condition. Revocation acts on claims and accepted epistemic states while retaining their provenance; it does not imply any operation on authors or other persons. Self-application closes the framework. Continuum models, discrete models, cellular automata, XOR-based constructions, effective theories, quantum representations, and Kunato itself receive no exemption from the admission rules. Failure to identify a continuum ontology does not identify a discrete ontology, empirical adequacy of a constructive model does not establish its fundamental realization, and formal validity of Kunato does not confer physical ontological status on Kunato. The framework therefore entails neither a privileged fundamental model nor ontological nihilism. Not identified does not imply false, and not admitted does not imply nonexistent. Kunato Core Ver.5.0.0 provides a unified formal and computational vocabulary for ontological admission, finite-data non-identification, finite-record discrimination, inverse problems, coarse-graining, property factorization, representation refinement, effective dynamics, statistical invariants, temporal inference, information-theoretic interpretation, criticality assessment, model-class identification, provenance, epistemic-state revision, and scientific realism. Its objective is not to determine a preferred ontology by methodological fiat, but to make the inferential boundaries between representation, observation, identification, and physical realization explicit and auditable. The framework is summarized by four constraints: no hidden epistemic transition; no hidden ontological promotion; no untyped representational transport; and no self-exemption. Its terminal methodological principle is: no representation receives automatic ontological privilege.
Description QSTH M.1B is the operational continuation of QSTH M.1A, Genealogy of Alpha-I-Dim and Equations E1–E10. M.1A established the algebraic genealogy of the reference Alpha-I-Dim construction and identified effective entropy S_eff and the structural parameter κ(Γ) as imported quantities whose physical meaning could not be supplied by algebra alone. M.1B addresses that open requirement by constructing a first explicit finite operational framework for structural configurations, equivalence, representation, statistical measure, dynamics, entropy and independent classification. The study defines typed relational configurations with a decidable admissibility predicate and equivalence under relabelling; constructs a faithful incidence representation; distinguishes representational equivalence, physical equivalence and indistinguishability under a limited readout; and states the conditions under which deterministic and probabilistic dynamics descend consistently to configuration classes. A finite operational statistical entropy is then constructed from a prespecified state space, measure and readout. Independently, a dynamical classifier based on closed recurrent sectors is introduced, together with an audit of exact charge protection versus finite escape time. The central integration result is deliberately restrictive. The independently defined sector count is not a universal entropic coefficient for Equation E10. The same entropy may coexist with different sector structures, while genuine internal degrees of freedom may increase entropy without creating an additional recurrent sector. The independent test is therefore allowed to reject the proposed identification rather than being normalized to reproduce it. Accordingly, the formal mathematical and statistical stage B1-B7 is complete within its declared domain, while physical horizon identification, M-independence and the continuation to E11+ remain open. This publication does not claim a new universal constant, a microscopic theory of horizon entropy, or empirical confirmation of QSTH. Its contribution is an auditable operational framework, explicit counterexamples, reproducible finite tests, and a precise boundary between mathematical construction and physical identification. A separate companion study, QSTH M.1B-SR1, examines whether a richer spectral response can provide a conditional bridge between an independently defined observable and the thermal entropy of specified interface carriers.
Recursive Collapse Field Theory (RCFT): Foundations, Derivations, and Implications for Quantum Structure, Version 2.0 is the revised and recontextualized second edition of the first public RCFT publication, originally released on 16 May 2025. The 2025 paper introduced the originating generative architecture of the research program that later developed into Structura Reditus. Its central inversion was that collapse need not be treated only as termination, destruction, or failure, but may instead generate difference, structure, memory, bifurcation, recursive reentry, and metastable form. That first formulation expressed these ideas through a nonlinear stochastic field grammar involving the symbolic excitation field ε(x,t)\varepsilon(x,t), recursive drift, collapse amplification, the Weft Process, collapse dominance, recursive proper time, symbolic entropy, glyphic attractors, recursive resonance, and proposed applications to quantum structure, gravitation, cognition, and cross-domain dynamics. Version 2.0 preserves the 2025 publication as a frozen historical source object rather than silently rewriting it in the language of the mature corpus. Its equations, terminology, claims, evidence posture, ambitions, and original intent remain historically intact. The purpose of this edition is instead to determine what was structurally born in that first paper, what later survived under stronger formal conditions, what required repair or retyping, what remains exploratory, and where RCFT now belongs within the completed architecture of Structura Reditus. The edition reconstructs the lineage by burden rather than by vocabulary alone. Recursive reentry is distinguished from the later formal object Reditus, defined as admissible return through collapse under declared conditions. Generative collapse is placed within Generative Collapse Dynamics (GCD). RCFT is retyped as the disciplined exploratory function responsible for candidate generation before freeze; UMCP carries evaluation; ULRC carries preservation of meaning, translation, critique, refusal, and contact. The earlier claim of one universal recursive field equation across domains is repaired into a stronger methodological architecture based on domain-specific Tier-2 closures without requiring mechanism identity. Not every first-edition construction receives present authority. The Weft Process, collapse-dominance ratio, recursive proper time, symbolic entropy, glyph conditions, quantum-collapse proposal, black-hole memory model, cognition mapping, and related structures are preserved under explicit statuses such as returned with constraint, retyped, notation-reassigned, repaired, open, not established by Version 1, or preserved as exploratory. This edition therefore does not replace the first RCFT paper or retroactively canonize it. It returns to the originating source under the architecture that its own unresolved pressures helped generate. Corpus placement: Reditus is the object; Structura Reditus is the field; GCD is the foundational theory; Tier-1, Tier-0, and Tier-2 govern authority; UMCP evaluates; RCFT explores; ULRC preserves meaning and contact. DOI: 10.5281/zenodo.22473173
Paper 7 of 11 — A General Theory of Answerability The eleven-paper TUS OS mathematical research programme Abstract This paper develops a structural theory for classifying how representation-resource requirements change when the operational obligation imposed on an independently fixed native system is lawfully strengthened. Building on the contract-relative resource law of Paper 6, it asks which source-level features of a strengthening determine or constrain the resulting resource transition. The theory fixes the native system, weak and strong contracts, realisation category, tolerance and charged resource before optimisation. A finite-baseline gate requires the weak contract to possess a finite-resource realisation, preventing pre-existing category nonrealisability from being misclassified as a strengthening-induced transition. The source-level object is a Contract Distinction System (CDS), which records the native configurations challenged by the stronger obligation, required distinctions or recovery targets, success rules, inspection boundaries and interface/commonality structure. Semantic challenge refinement and CRC cofinal/refinement equivalence control dependence on alternative finite challenge presentations. A Certified Observability Transport Theory (COTT) then maps licensed source-level facts into necessary resource lower bounds inside a fixed representation category and tolerance regime. The resulting directed finitary demand profile supports two distinct mechanisms. Internal divergence occurs when a single strengthened contract contains finite restrictions of arbitrarily large certified demand and can therefore exclude every finite-resource strong realisation in the declared category. Family divergence occurs when every member of a parametrised family remains finitely realisable while the additional resource induced by strengthening grows without bound across the family. Lower recognition is kept logically separate from upper-side existence: bounded certified demand is not treated as an existence theorem, and finite regimes require independent construction, compactness/gluing or another valid upper certificate. Conditional on finite baseline feasibility, the resulting pointwise classifier distinguishes resource-neutral, strict finite, finite-resource breakdown and UNRESOLVED transitions, with incrementally unbounded finite separation carried separately as a family-scaling modifier. Several exact witnesses separate these regimes. With three native labels, the same coarse distinction graph K3, representation category, Hilbert-dimension resource and discrimination threshold fixed, changing only interface commonality produces an exact minimum-dimension transition from 2 to 3 throughout 2/3 < τ ≤ 1/2 + √3/4. Thus interface structure can itself be representation-resource-bearing. For the canonical TUS OS target, the complete static Atlas has exact minimum Hilbert dimension 4, whereas recovery-complete selected-line instrument access has exact minimum 64, giving an exact strict-finite transition 4→64. The weaker state-only common-CPTP problem remains unresolved within 32≤d≤64, demonstrating that the stronger interface theorem cannot be transferred backward through a forgetful map. For periodically modulated decay processes, every finite member remains finitely realisable while the contract-induced capacity gap diverges with family size. For the fixed dual-Poisson process, every positive worst-case transparency strengthening eliminates all finite-resource strong realisations in the declared autonomous one-copy classical–quantum category. A synthetic Countable Pairwise Identity Ladder supplies a cross-interface internal-divergence test, while the Fanizza–Lumbreras–Winter result marks the separate outer boundary of baseline category nonrealisability. Together, the results establish that operational observability is a resource-bearing input to quantum realisability without being invariably resource-increasing. Resource transition depends on the typed structure of the operational obligation—not merely native-state count, predictive-state cardinality, distinction count or coarse distinction graph. Supporting General Theory Programme This paper is Paper 7 in the TUS OS quantum-operational and Answerability research programme. Building on Paper 6’s contract-relative resource theory, it develops operational observability and a structural classification of contract-induced resource transitions, distinguishing resource-neutral, strict finite, finite-resource breakdown and unresolved pointwise outcomes, with family divergence carried separately as a family-scaling modifier while separating lower-bound certification from constructive realisability. Papers 8–9 then move to Answerability as a generic mathematical object, developing the resource geometry of answerable inference and the Answerability Calculus; Paper 10 proves the protected and executable realisation of TUS OS within that calculus; and Paper 11 closes the programme with A General Theory of Answerability, establishing Structural Identity, Recognition, the canonical mandatory protected core, and lawful Realisation Freedom. 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 exact contract-relative regimes: strict finite separation, unbounded finite separation and finite-capacity breakdown. These are instantiated respectively by the TUS OS 4→64 separation, the periodically modulated decay 2→N exact prediction-to-transparency separation, and dual-Poisson finite-capacity breakdown for every positive uniform worst-case transparency threshold. Paper 7 — Operational Observability and Contract-Induced Resource Transitions in Quantum RealisabilityStructural Classification, Family Scaling, and Finite-Resource BreakdownDevelops the structural classification theory for contract-induced representation-resource transitions. It introduces the Contract Distinction System (CDS) as a representation-independent source description of the additional distinctions, recovery targets, challenge structure and interface/commonality obligations introduced by lawful contract strengthening; semantic challenge refinement and CRC cofinal/refinement equivalence to control presentation dependence; and a Certified Observability Transport Theory (COTT) that maps licensed source-level structure into necessary category- and tolerance-specific resource lower bounds. The resulting directed finitary-demand theory separates internal divergence within one fixed strengthened contract from family divergence across finitely realisable members, while keeping lower recognition logically independent from upper-side construction or compactness/gluing. Conditional on finite baseline feasibility, the pointwise classifier distinguishes resource-neutral, strict finite, finite-resource breakdown and UNRESOLVED transitions, with incrementally unbounde
Paper 4 (Technical Volume II) of 11 — A General Theory of Answerability The eleven-paper TUS OS mathematical research programme Abstract TUS OS Paper 4 — Technical Volume II: Orthogonality, Process Closure and Native Triadic Synthesis completes the two-volume technical development of Paper 4. Technical Volume I fixed the 64-state carrier, complete terminal future corpus, parity-separated complement-reachability structure and invariant probability module. This volume closes the remaining questions of universally forced support orthogonality, native composition, representation closure, LANDING, GUIDANCE and downstream synthesis correspondence at their explicitly declared scopes. For every finite-dimensional exact common-effect representation, Atlas complement effects force complementary carrier states to have orthogonal supports. In every exact common-CPTP realisation, common-word complement reachability propagates this orthogonality backwards by trace-distance contractivity. The resulting provenance-certified graph is G_prov ≅ K₃₂^even ⊔ K₃₂^odd, with ω(G_prov) = srk⊥(G_prov) = 32. Hence every admitted common-CPTP predictive representation has persistent Hilbert dimension at least 32. An explicit 64-dimensional diagonal construction supplies an exact upper-bound realisation, establishing 32 ≤ d_CPTP^min ≤ 64. The 1,024 cross-parity pairs remain unclassified by the certified forcing route. Accordingly, neither the complete universally forced support-orthogonality relation nor the exact common-CPTP minimum within this interval is determined. The paper then constructs a total, source-separated and non-circular conservative native whole-Triad object. Semantic equality erases custody identity, while a distinct provenance fibre preserves exact source, occurrence, relation and certificate custody. The construction is triadically governed at the input-incidence level, but its conservative semantic output is exactly decomposable and its generated relational layer is pairwise-generated. At this scope, native synthesis is therefore a relationally enriched constrained concatenation rather than an irreducible ternary semantic state. On the abstract canonical corpus, the structural quotient has exactly 64 singleton classes and is canonically isomorphic to the complete deterministic predictive carrier system. No predictive merger is possible: the minimum deterministic unifilar realisation has exactly 64 states. This carrier-faithful target exposes an exact static–dynamic separation. The inherited dimension-four static Atlas representation admits no affine or linear descent for the principal or continuation maps, whereas the 64-sector diagonal construction realises them by fixed CPTP channels. Exact LANDING state-only closure satisfies 32 ≤ d_L,state^min ≤ 64, while recovery-complete selected-line instrument access forces and attains d_L,instr^min = 64. An explicit 32-state complement-orbit memory construction also gives an exact classical–quantum hybrid with the certified four-dimensional quantum component. LANDING further admits factorised two-step process-comb and exact relational representations, showing that neither non-Markovian process memory nor irreducibly relational form is necessary for existence at the canonical scope. GUIDANCE is classified separately. Its selected-line future language distinguishes every non-complement pair, and exact line and endpoint instruments attain their declared recovery contracts. Deterministic GUIDANCE line observation can be nondemolition and jointly compatible with LANDING. The GUIDANCE and LANDING endpoint transformations are sibling same-start updates and cannot be serialised on a single carrier without changing their meanings. An exact no-feedback sidecar instrument instead returns the authoritative LANDING successor together with the GUIDANCE receipt. Joint LANDING–GUIDANCE compatibility therefore closes at the canonical scope without adaptive feedback, hidden carrier lookup or source-role inversion. Finally, the native-to-emitted correspondence is formalised as a custody relation and a lawful status-constrained subrelation, rather than as an asserted deterministic projection. The active-v1 profile yields a total 106-class correspondence census with no material-loss, unjustified-field or unresolved class. One authenticated Pilot 2 package supplies an unrestricted realised witness (ω_P2, s_P2) ∈ C_lawful ⊆ C_cust, reproduced by a separately written reconstruction together with the release-verification controls. This establishes one admitted instance of custody-closed native-to-emitted synthesis. The results concern exact finite mathematical and operational models under frozen access, recovery and resource contracts. The certified same-parity graph is a proved universal subgraph of the full forced-orthogonality relation; cross-parity forcing remains unclassified, no universal 64-way support-orthogonality result is established for the full common-CPTP representation class, and the exact common-CPTP minimum remains open within 32–64. Stronger recovery-complete selected-line access contracts are separately shown to require dimension 64. Likewise, the conservative native object is triadically governed, source-sovereign and non-circular, but no irreducible three-lane semantic degree of freedom is claimed at that scope. The paper makes no claim of global all-runs correspondence, truth of external domain claims, physical quantum execution, quantum advantage, production Domain Binding or activation of a production Technical Synthesis policy. Supporting General Theory Programme This technical volume is Technical Volume II of Paper 4 in the TUS OS quantum-operational and Answerability research programme. Building on Technical Volume I’s complete-future corpus, native contract, admissibility framework, and statistical discrimination theory, it develops process-forced orthogonality, process closure, LANDING/GUIDANCE results, native Triadic synthesis, and the associated process-resource bounds. Paper 5 then organises the resulting structure through the theory of Anchored Analog Quantum Systems; Papers 6–7 extend the programme through contract-relative quantum realisation, resource separation, operational observability, and contract-induced resource transitions; Papers 8–9 develop generic Answerability theory and calculus; Paper 10 proves the protected and executable realisation of TUS OS; and Paper 11 closes the programme with A General Theory of Answerability, establishing Structural Identity, Recognition, the canonical mandatory protected core, and lawful Realisation Freedom. 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 under one foundation-defined tetrahedral-SIC Harness, 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 OSExtends the local prepare–measure construction to the complete family of completed foundations and the canonical TUS OS subatlas. It establishes exact carrier-reconstruction structure, the repeated-common-effect static Atlas with exact minimum complex Hilbert dimension 4, 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 ModuleFixes the formal native domain, complete principal terminal future-experiment language and one-common-word experiment class. It establishes complete statistical separation of distinct carrier pairs, the exact parity-resolved pairwise total-variation optimum, exact complement reachability and the 33-dimensional rational invariant probability module that provides the formal complete-future foundation for the process analysis of the present volume. Technical Volume II imports these results without modification. Paper 4 — Technical Volume II — Orthogonality, Process Closure and Native Triadic SynthesisEstablishes universal complement-support orthogonality and its backward propagation under exact common-CPTP dynamics, yielding the provenance-certified same-parity graph and the bound 32 ≤ d_CPTP^min ≤ 64, with cross-parity forcing and the exact state-only common-CPTP minimum remaining unresolved. It further establishes the native structural/predictive quotient correspondence; exact LANDING and GUIDANCE process, readout and compatibility results; exact 64-dimensional minima for recovery-complete LANDING selected-line instrument access, recovery-complete GUIDANCE selected-line readout and the stronger GUIDANCE joint-instrument contract; an exact four-dimensional-quantum-plus-32-state-classical hybrid construction; joint LANDING–GUIDANCE compatibility without adaptive feedback; and one authenticated custody-closed realised native-to-emitted synthesis instance. 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 corp