SΔϕ-78 — Value as Path Preservation under Cost Return: An AI-Native Operational Axiology of Transfer, Retention, Refusal, and Re-entry (v1.0)

SΔϕ-78 develops an AI-native operational theory of value centered on path preservation, transition cost, cost return, and transfer asymmetry. Rather than identifying value with scarcity, price, popularity, irreversible impact, or intrinsic worth, the framework analyzes value as an observer-indexed relation among the future paths that an object, resource, institution, technology, or relationship opens or preserves; the transition-completion costs required to acquire, retain, exit, restore, or re-enter those paths; the coordinates to which those costs ultimately return; and the resulting orientations toward retention, acquisition, disposal, or refusal. The framework is organized around the operational sequence: PATH → COST → RETURN → TRANSFER SΔϕ-78 builds on three prior components of the SΔϕ Formalism: Value Openness and the ontology–axiology distinction in SΔϕ-23; Transition Completion Cost (TCC), friction, observer position, re-entry, and Unmeasured Remainder (UMR) in SΔϕ-56; and the cost-return coordinate and non-deferrable cost structure developed in SΔϕ-52. The package rejects several common value shortcuts: scarcity does not by itself imply value; abundance does not imply low value; price does not exhaust value; irreversible trace strength does not imply value openness; nominal path expansion does not guarantee higher value when dependency, exit, repair, restoration, or re-entry costs are high; and negative relational value does not imply negative intrinsic worth of persons or social groups. Instead of producing a universal scalar value score, SΔϕ-78 defines an observer-indexed Value Profile containing path openness, transition costs, cost-return structure, transfer orientation, Unmeasured Remainder, and revision paths. This AI-native package includes a canonical paper, machine-readable core specification, value-audit protocol, YAML formal specification, JSON value-profile schema, source-bridge documentation, value-misclassification rules, worked cases, counterexamples and failure modes, reusable AI prompt templates, and JSONL evaluation cases. Intended applications include AI governance, value alignment, institutional analysis, policy auditing, economic and social value analysis, human–AI interaction, cost allocation, path dependence, technology governance, and relational value assessment. Core audit questions: What paths does the target open, preserve, or close? What do those paths cost to acquire, maintain, exit, restore, or re-enter? Where do those costs actually return? Who seeks to retain, acquire, dispose of, or refuse the target? What remains unmeasured, and what evidence would revise the judgment?