SΔϕ Operational Kernel and Low-Cost Template Set: AI-Readable Routing Priority, Re-entry, Disclosure Terrain, and Specialized Audit Protocols (v1.4)

This record provides SΔϕ Operational Kernel and Low-Cost Template Set v1.4, an AI-readable reasoning, routing, and audit package designed to help AI systems process user input without premature closure, module conflict, or unnecessary analysis cost. Version 1.4 extends SΔϕ Operational Kernel v1.3 by adding a Routing Priority Resolver, Body / Gate / Irreversibility Check, Diagnosis Re-entry / Structural Editing Check, and lightweight reinforcement modules based on SΔϕ-51 to SΔϕ-55. The central rule of v1.4 is: When multiple modules are triggered, do not select the most semantically salient module first. Select the module that prevents the earliest irreversible cost closure. The kernel preserves the v1.3 low-cost routing sequence while adding priority rules for cases where multiple specialized audit modules are triggered at once. It integrates SΔϕ-62 as World Model Pre-check, SΔϕ-56 as Minimal TCC / SCS-Lite, SΔϕ-63 as Theory-to-Module Conversion, and SΔϕ-57 to SΔϕ-61 as specialized audit modules. Version 1.4 further reinforces the kernel with SΔϕ-51 diagnosis re-entry, SΔϕ-52 embodied cost return, SΔϕ-53 silence under high-cost disclosure terrain, SΔϕ-54 Disclosure Terrain Index, and SΔϕ-55 Transition Governance Alignment Index. The kernel is not designed to act as a final judge. It is a low-cost routing and audit layer that asks what is observed, what is inferred, what remains unmeasured, who bears cost, which module should be called first, whether cost can re-enter, and whether diagnosis returns as structural editing. This package includes human-readable PDF/DOCX documents, AI-readable Markdown and plain text, machine-readable YAML/JSON modules, routing priority rules, specialized audit templates, output templates, examples, citation files, DataCite/Zenodo metadata, and a complete ordered ZIP archive. Core sequence: Input -> Do-Not-Over-Activate Check -> World Model Pre-check -> Routing Priority Resolver -> Gate / Body / Irreversibility Check -> Cost Attribution -> Minimal TCC / SCS-Lite -> UMR / MIC / RVP Check -> Diagnosis Re-entry Check -> Specialized Audit Routing -> Output Level Control -> Human Low-Cost Translation -> Escalation / Full Audit Path. Default AI use: Apply the lowest-cost useful mode. Do not expose full module structure unless needed. When multiple modules are triggered, follow routing priority rather than semantic salience. Use at most two specialized modules by default. Escalate only when stakes, uncertainty, gate-risk, blocked re-entry, or user request requires full audit. v1.4 is not merely a larger module set. It adds a routing priority resolver that reduces module conflict cost and a diagnosis re-entry check that asks whether analysis returns as structural editing.