SΔϕ-26 AI-READABLE Package — Irreversibility as Restoration Cost Explosion (v1.0)

<p> This record provides the AI-readable structured package for <em>SΔϕ-26 — Irreversibility as Restoration Cost Explosion: Minimal Fixation Conditions after Pre-detection (v1.0)</em>. </p> <p> SΔϕ-26 defines irreversibility not as metaphysical finality or absolute impossibility of reversal, but as restoration cost exceeding the threshold of practical return. A transition becomes irreversible when return remains formally conceivable yet is no longer practically selectable within the operative system. </p> <p> The package extends SΔϕ-25 by clarifying when a latent or newly registered difference becomes fixed as an event. Event fixation occurs not merely because something happened, but because low-cost return has closed. In this framework, the world is not divided between absolutely reversible and absolutely irreversible transitions, but between low-cost return and cost-exploded fixation. </p> <p> Restoration cost is formalized as <code>C_restore(t) = f(E, T, I, N, M)</code>, where <code>E</code> denotes energetic or material cost, <code>T</code> temporal cost, <code>I</code> informational reconstruction cost, <code>N</code> network propagation cost, and <code>M</code> memory or interpretive residue cost. The practical return threshold is denoted by <code>θ</code>. </p> <p> The core conditions are: <code>Reversible iff C_restore(t) &lt; θ</code>; <code>Irreversible iff C_restore(t) ≥ θ</code>; and <code>Fixation(e) iff C_restore(e) ≥ θ</code>. Full eventhood is defined as <code>Eventhood = detected difference + irreversible fixation</code>. </p> <p> SΔϕ-26 separates formal reversibility from practical reversibility. A prior state may remain logically describable or computationally representable while lacking any economical path of return. Therefore logical reversibility, computational reversibility, and actual restoration must be distinguished. </p> <p> The package also addresses digital and virtual environments. Digital systems may appear reversible because deletion, copying, editing, and rollback are technically possible; however, replication, distributed observation, logs, external systems, and interpretive memory may increase restoration cost. Thus deletion does not necessarily equal restoration, and rollback does not necessarily restore the total prior world-state. </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; restoration cost axioms; minimal definitions; formal versus practical reversibility notes; restoration cost model; event fixation model; eventhood as detected difference plus fixation; cost components E/T/I/N/M; digital and virtual irreversibility notes; low-cost return closure notes; minimal examples; diagnostic regimes; 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 metaphysical finality theory, a claim that reversal is logically impossible, a claim that all changes are irreversible events, a claim that digital rollback restores the total prior world-state, a claim that deletion equals restoration, moral theory of consequence, or legal finality doctrine. SΔϕ-26 fixes only minimal restoration-cost and event-fixation dynamics after pre-detection. </p>