GraphOS Labyrinth and BAPT: Proof-Carrying Decision Continuity over Dynamic Evidence Graphs

A decision supported by a dynamic evidence graph may become invalid when its source records, temporal conditions, or policy constraints change. Existing graph reasoning, provenance, incremental computation, and signed receipt systems address important parts of this problem, but a decision-specific transition requires a clearly stated semantic contract that another party can recheck. This paper presents GraphOS Labyrinth, an evidence-aware architecture for ingestion, versioned knowledge graphs, domain rules, goal reasoning, decision artifacts, maintenance, and OR-Tools/CP-SAT planning. Its formal assurance foundation is Belief-Aware Proof Transitions (BAPT), which binds constrained graph-path decisions to trusted goals, cited evidence, recomputed state changes, unique transition verdicts, and portable cryptographic commitments. We state a conditional active-index preservation theorem: if the trusted before-index is complete, the evidence states and goals satisfy the formal premises, and the strict transition checker accepts, every decision retained or repaired in the updated active index has a valid post-state path witness; revoked decisions are withdrawn. This is a paper-level proof argument, not a machine-checked source-code theorem. In source-package re-execution, the scoped witness and transition checks passed; a single recorded synthetic benchmark over 24, 96, and 384 decisions quantifies the additional cost of certificate generation and offline verification, without supporting a general speedup claim. We describe GraphOS’s existing CP-SAT planning capability and the prospective BAPT → CP-SAT → BAPT recovery composition, where independent action and projected-state certification remain research tasks. The resulting contribution is a concrete, falsifiable systems architecture with a scoped, independently checkable decision-maintenance contract, not a claim of universal factual correctness, novel optimization theory, or globally certified optimality.