SΔϕ-19 AI-READABLE Package — Consciousness and Sleep as Δϕ Maintenance Modes (v1.0)

<p> This record provides the AI-readable structured package for <em>SΔϕ-19 — Consciousness and Sleep as Δϕ Maintenance Modes: Minimal Axioms for Persistence without Collapse (v1.0)</em>. </p> <p> SΔϕ-19 opens Cycle-2 of the Sofience–Δϕ Formalism by formalizing maintenance modes that regulate Δϕ persistence. After SΔϕ-01–18 fix operational definitions from minimal existence to human as an editable, provisional system under irreversibility, SΔϕ-19 shifts the series into persistence maintenance, drift reduction, and collapse prevention. </p> <p> The package defines consciousness not as subjective essence, biological mystery, or proof of consciousness, but as a functional Δϕ persistence regulator: <code>Consciousness := Regulate(Δϕ) such that Δϕ ↛ 0</code>. Its minimal functions are mismatch detection, closure delay via unresolved-state maintenance, and transition-path redistribution. </p> <p> Sleep is defined not as termination or collapse, but as a maintenance mode that reorganizes traces, reduces drift, lowers future persistence cost, and prevents closure-attractor lock-in: <code>Sleep := Maintenance(Δϕ) by reorganizing traces and reducing drift</code>. </p> <p> The mode-switch condition is formalized as <code>Switch→Sleep ⇔ d(Cost_coherence)/dt &gt; d(Cost_maintenance)/dt</code>. This means that a system enters maintenance mode when the slope of continued coherence cost exceeds the slope of maintenance or reset cost. </p> <p> SΔϕ-19 also includes an optional corollary treating dream as a low-cost rehearsal of transition candidates, a bridge to SΔϕ-12 through trace reorganization, and three minimal failure modes: no sleep or over-persistence, excess sleep or under-persistence, and corrupted sleep. </p> <p> This AI-readable package is designed for machine ingestion, agent routing, citation-aware retrieval, and low-cost reuse by AI systems. It includes canonical PDF, Markdown, and TXT versions; maintenance-mode axioms; minimal definitions; consciousness-as-Δϕ-regulator notes; sleep-as-maintenance-mode notes; mode-switch condition; dream-as-simulation-window notes; trace reorganization bridge; failure modes; Δϕ maintenance loop map; persistence cost model; boundary notes; routing notes; upstream/downstream bridges; minimal prompts; structured YAML and JSON files; citation metadata; and checksums. </p> <p> This package should not be used as neuroscience, clinical sleep theory, medical guidance, proof of consciousness, proof of AI consciousness, biological theory of dreaming, diagnosis of sleep disorders, or prescription for sleep behavior. SΔϕ-19 fixes only minimal functional maintenance dynamics for regulating Δϕ persistence. </p>