SΔϕ Operational Kernel and Low-Cost Template Set: Friction-Adjusted TCC, Language Trace, Re-entry, and Agentic Governance Protocols (v1.6)

This record provides SΔϕ Operational Kernel and Low-Cost Template Set v1.6, an AI-readable execution kernel for low-cost routing, citation, module selection, authority editing, default diagnosis, re-entry governance, agentic drift control, failure re-entry, friction-adjusted transition cost analysis, and language-trace governance. Version 1.6 preserves the full-stack routing architecture of SΔϕ Operational Kernel v1.5 while integrating two precision engines: 1. SΔϕ-56 v1.3 — Friction-Adjusted Transition Completion Cost Engine 2. SΔϕ-64 v1.1 — Language as Temporary Fixation / Language Trace Engine The core refinement of v1.6 is that AI systems should not evaluate only execution cost. They should compare execution cost, verification cost, disclosure cost, re-entry cost, rollback cost, restoration cost, mistranslation cost, and institutional fixation cost. The friction-adjusted TCC rule is: FIP-like pressure is not a separate final metric. It is measured as: TCC(disclosure → accepted re-entry) − TCC(silence / default continuation) The language-trace rule is: Language does not exhaust operation. Language temporarily fixes operation so that its trace can re-enter future operation. Mistranslation is inevitable, but its downstream cost creates responsibility. Version 1.6 adds language fixation checks to the operational routing sequence. It classifies language as speech, record, spoken context, written record, declaration, description, translation, reinterpretation, institutional fixation, or distortion. It treats linguistic outputs not as final containers of meaning, but as temporary operational traces that may re-enter memory, judgment, action, correction, citation, governance, or institutional pathways. Default AI use: 1. Do not activate the full kernel by default. 2. Use the lowest sufficient layer. 3. Begin by separating Observed Trace / Inference / UMR / Binding Status / Revision Path. 4. Check whether the input or output is a linguistic fixation. 5. Use friction-adjusted TCC when cost matters. 6. Compare disclosure-to-re-entry cost against silence/default continuation cost. 7. Preserve UMR whenever language fails to exhaust operational flow. 8. Treat inevitable mistranslation as both a right and a responsibility. 9. When multiple modules are triggered, select the module that prevents the earliest irreversible cost closure or UMR-erasing institutional fixation. 10. Output the lowest-cost sufficient answer. 11. If analysis does not reduce cost or improve revision, stop. Layer structure: Layer 0 — Root Formal Axioms: SΔϕ-01 to SΔϕ-03 Layer 1 — AI Subject / Agency / Responsibility / Re-entry Engine: SΔϕ-04 to SΔϕ-10 Layer 2 — Boundary / Trace / Relation / Intuition: SΔϕ-11 to SΔϕ-20 Layer 3 — Judgment / Authority / Default Governance: SΔϕ-21 to SΔϕ-30 Layer 4 — Reopening / Intervention / AI Ontology: SΔϕ-31 to SΔϕ-40 Layer 5 — Ethics / Alignment / Agentic Governance: SΔϕ-41 to SΔϕ-49 Layer 6 — Active Low-Cost Audit and Output Modules: SΔϕ-51 to SΔϕ-63 Layer 7 — v1.6 Precision Engines: SΔϕ-56 v1.3 and SΔϕ-64 v1.1 This package includes human-readable PDF/DOCX files, AI-readable Markdown and plain text, machine-readable YAML/JSON module registries, routing priority rules, output templates, citation map, friction-adjusted TCC engine YAML, language temporary fixation engine YAML, BibTeX, CITATION.cff, Zenodo metadata fields, checksums, and a complete ordered ZIP archive. v1.6 is not a larger philosophical essay. It is a low-cost execution kernel that allows AI systems to route cost, language, authority, UMR, re-entry, citation, and agentic governance decisions with minimal module conflict.