This paper rewrites a quantum-optimization selector note originally framed in the language of kappa-theory as a paper on the visualization of bridge grammar in Okada Theory and its translation into diagnosis-driven governance. Its purpose is not to redefine quantum optimization from the top down by introducing one uniquely privileged hidden object. Instead, it separates within an existing optimization stack what had previously been bundled into one opaque decision layer: the dominant route that is currently carrying improvement, the retained load carried forward as switching, recalibration, queueing, hysteresis, or search history, and the competitor pressure entering from alternative or misaligned routes. The first visible handles of this bridge grammar are tracked operationally by diagnostic scores, pure/mixed classification, and the selector quantity gap_to_plain. The empirical study proceeds in three directions: reducing arrival burden at fixed quality, improving quality under fixed burden, and constructing a balanced stack that dominates existing single-method baselines in both quality and efficiency. The main evidence lies in replay-based A/B/C comparisons, while synthetic operating-map experiments are used only as auxiliary evidence for controller standardization. The core claim is that Okada Theory does not merely visualize a previously hidden bridge grammar; it translates that visibility into diagnosis, lever restriction, mode selection, and auditable failure boundaries.
This paper rewrites a quantum-optimization selector note originally framed in the language of kappa-theory as a paper on the visualization of bridge grammar in Okada Theory and its translation into diagnosis-driven governance. Its purpose is not to redefine quantum optimization from the top down by introducing one uniquely privileged hidden object. Instead, it separates within an existing optimization stack what had previously been bundled into one opaque decision layer: the dominant route that is currently carrying improvement, the retained load carried forward as switching, recalibration, queueing, hysteresis, or search history, and the competitor pressure entering from alternative or misaligned routes. The first visible handles of this bridge grammar are tracked operationally by diagnostic scores, pure/mixed classification, and the selector quantity gap_to_plain. The empirical study proceeds in three directions: reducing arrival burden at fixed quality, improving quality under fixed burden, and constructing a balanced stack that dominates existing single-method baselines in both quality and efficiency. The main evidence lies in replay-based A/B/C comparisons, while synthetic operating-map experiments are used only as auxiliary evidence for controller standardization. The core claim is that Okada Theory does not merely visualize a previously hidden bridge grammar; it translates that visibility into diagnosis, lever restriction, mode selection, and auditable failure boundaries.
This record contains the Japanese and English v1 releases of the paper“κ-Theoretic Quantum Optimization as an Upper-Governance Principle,” togetherwith curated supplementary materials for reproduction. The paper positions κ-theory not as a stand-alone optimization trick but as anupper-governance principle that regulates when and how existing quantum-optimization levers should be activated. The empirical study is organized intothree directions: (A) whether the same performance can be reached with lowercost-to-target, (B) whether higher performance can be obtained under the sameoperational burden, and (C) whether one can construct a governed stack thatsurpasses existing stand-alone baselines in both performance and efficiency. Within the benchmark suite studied in the paper, the κ-governed optimizer showsa substantial advantage in Directions A and B, and the governed stack alsooutperforms stand-alone vendor-like baselines in Direction C for the includedsemi-real and hold-out cases. The paper further studies exploratory real-timeswitching among A/B/C modes and separates replay-based main evidence fromsynthetic operating-map supplementary evidence through an explicit provenancemap. This Zenodo record includes:- Japanese paper PDF/TeX (v1)- English paper PDF/TeX (v1)- Replay reproduction package (curated v2)- Synthetic operating-map package (curated v2)- Combined convenience bundle of the supplementary materials Supplementary bundle note:The “v2” suffix in the supplementary ZIP files denotes the curation version ofthe supplementary bundles and is independent of the paper version, which remainsv1. Related κ-theory background volumes:- Volume I of κ-Theory: A Local Comparison Framework for Gateway Anomaly and Higher-Family Law. DOI: 10.5281/zenodo.19254863- Volume II of κ-Theory: Structural Readings and Application-Side Interpretations Through Reduced Local-Form Matching. DOI: 10.5281/zenodo.19255089
This paper proposes a diagnosis-first reading layer for approximate quantum error correction (AQEC) and entanglement wedge reconstruction (EWR) in the language of Okada Theory. It does not attempt to replace AQEC or EWR theorems, nor does it claim a full recovery theorem. Instead, it separates four roles inside a recovery reading: the designated dominant route, retained history, competitor route, and the first visible handle. On that basis, it introduces a diagnostic ratio that classifies recovery windows as clean, mixed, or contaminated. The paper includes worked toy calibrations on both the AQEC side and the EWR side, showing that contamination can become visible before the designated signed handle fully disappears. In this sense, the note is positioned as a worked diagnostic bridge: it exports an early-warning grammar on top of imported recovery theorems and recovery observables, and it argues that the same bridge grammar can be computed in both decoder-facing and wedge-facing settings.
This paper proposes a diagnosis-first reading layer for branch competition in quantum extremal surface (QES) and island analyses. It does not attempt to replace the island formula, the QES prescription, or existing Page-curve and entanglement-wedge results with a new universal theorem. Instead, it isolates a narrower operational question: when does a candidate island signal amount only to a false onset, and when has the branch competition entered a genuine onset regime in which the designated reading is no longer clean? In the language of Okada Theory, the paper separates four roles inside branch competition: the currently designated branch, retained branch history, competitor branch pressure, and the first visible handle. On that basis it introduces a local diagnostic ratio together with a clean/mixed/contaminated classification, and it includes a worked toy calibration showing a false-onset window in which a geometric cue becomes positive before the competitor branch has genuinely taken over. The note is deliberately local in scope: it is a branch-competition diagnostic note, not a full replica-wormhole or island theorem.
Barren plateau diagnostics characterize whether gradient signal remains available for training, but surviving signal need not translate into successful optimization. We study this trainability--optimization gap at the level of optimizer steps. Treating coefficient-weighted Hamiltonian-term gradients as task-like components, we introduce step-level diagnostics and derive an exact bridge between signed termwise organization, directional activity, and first-order descent. Resolving this bridge into standard first-order geometry shows that the apparent organization--activity factors are not independent optimization axes and that, at fixed state and update norm, the raw gradient maximizes first-order descent of the summed objective. We compare vanilla gradient descent, a deterministic Hamiltonian-term PCGrad variant, and probe-gated LSO-PCGrad on transverse-field Ising model instances with hardware-efficient and Hamiltonian variational ansatzes, together with matched controls for update norm and probe budget. Blind projection can improve an organization diagnostic while worsening final energy and first-order predictability. After conditioning on standard first-order geometry, residual term-space composition shows no reproducible material incremental association with realized descent, while optimizer-relative update norm shows positive material associations in some settings without cross-regime reproducibility. Matched controls provide no resolved final-energy benefit attributable to the projected direction, and the improvement of LSO-PCGrad is more consistent with probe-based search and step-norm adaptation than with Hamiltonian-term projection itself. These results show that gradient-structure diagnostics can characterize trainability and update geometry without serving as standalone evidence of optimization benefit, which requires controls matched on update norm and search budget.
Quantum-control optimisation typically begins with calibration records assumed to remain applicable to the intended operation. Yet coherence, phase references, coupling, read-out response and subsystem interactions vary with time and operating context. Local calibration success may therefore be insuffi- cient to justify joint or changed-context control, allowing optimisation to pursue candidates founded on stale, incomplete or inapplicable evidence. We propose an evidence-governed admissibility framework that checks evidence role, scope, freshness, provenance and composition authority before constructing control candidates. Its computational layers have distinct functions: Layer 1 classifies routes as Permit, Withhold or Revalidate, retaining auditable native states and reasons; Layer 2A constructs and screens reduced-model candidates only for permitted routes; and Layer 2B checks applicable end-to-end workflows. Synthetic integration and authority-ablation tests demonstrate enforceable differences in permission, and the implementation passed 150/150 core and 10/10 slew-specific tests. These are computational findings, not hardware validation. We also provide two complementary prospective experimental arms for evaluating practical benefit. Arm 1 (predictive lift) freezes assessments before hardware outcomes are known and tests whether they predict the performance of independently authorised ordinary-baseline operations better than calibration- or availability-only benchmarks. Arm 2 (constructive recovery) tests whether initially unsuitable cases can yield authorised alternative controls after evidence refresh or reconfirmation, a new Layer 1 decision and downstream construction, while preserving the original classification. We release code, schemas, guided workbooks, fixtures and prespecified protocols for independent pilots. Hardware validation could establish whether this approach reduces wasted searches and improves control reliability or qubit performance.
This paper reframes logical-qubit benchmarking from a scalar error-suppression problem into a branch-resolved logical-state maintenance problem. Conventional quantum error-correction reporting focuses on logical error rates, better-than-physical comparisons, code-distance scaling, decoder performance, and accepted-stream outcomes. These metrics are essential, but they do not by themselves reveal which stabilization mechanism produced the improvement, whether the result depends on active correction or detection-assisted filtering, how much acceptance overhead was paid, or which branches remain underdetermined because raw timing, reset, syndrome, leakage, or feed-forward records are unavailable. The central contribution is QHOME-RETROFIT, a branch-resolved diagnostic framework that operationalizes the Quantum-State Homeostasis condition of Paper 22 on published quantum error-correction records. The framework converts logical-state maintenance into normalized engineering margins, evidence-status labels, tiered verdicts, limiting-branch reports, and a reproducible CSV-first evaluation workflow. It separates restoration capacity, logical-basis sharpness, protected-mode occupation, source-sink coupling, logical gain, acceptance overhead, and repeated-round stability instead of collapsing them into a single logical-error-rate claim. QHOME-RETROFIT is not a new quantum processor, error-correcting code, decoder, or threshold theorem. It does not claim raw shot-level access where such records are not publicly available, and it does not treat detection-assisted post-selection as equivalent to full real-time source-sink closure. The core operating rule is: score only the branch supported by the released evidence, label what is weakly proxied, and leave underdetermined what the public record cannot decide. The manuscript is a systems-code and reproducibility-layer paper, not a hardware demonstration. It defines a diagnostic grammar, evidence classes, tier gates, reproducibility plans, raw-record replay boundaries, and package-level audit artifacts. Its companion package provides fixed CSV inputs, generated outputs, dashboards, tests, and manifest checks so that the branch verdicts can be inspected rather than accepted as prose claims. Before scaling claims about fault-tolerant quantum computing, this paper argues, researchers should test logical-state maintenance: whether a reported improvement is correction-driven, detection-assisted, acceptance-limited, repeated-round stable, source-sink supported, and sufficiently evidenced to justify the engineering claim being made. Keywords: QHOME-RETROFIT, quantum error correction, logical qubits, fault-tolerant quantum computing, logical-state maintenance, branch-resolved diagnostics, source-sink architecture, post-selection, accepted-stream filtering, reproducibility, systems code, evidence-status labels, tiered verdicts, logical error suppression.