This release presents a structured series of research papers forming the HAOS-IIP (Harmonic Address Operating System / Interaction-Invariant Physics) program, focused on detecting structural stability and collapse in evolving systems. The work develops a minimal, testable framework based on the principle: reality = recoverable coherence under interaction Rather than assuming predefined geometry or spacetime, the program studies how ordered structure persists, degrades, or collapses under repeated interaction and refinement. Included Papers (44.1–51.2) This release contains the following documents: 44.1 — Minimal Scaling Sketch for a Proto-Continuum Effect 45.1 — A Minimal Structural-Stability Oracle Based on Frozen HAOS-IIP Telemetry 46.1 — HAOS-IIP Master Synthesis (Program-Level Compression) 47.1–47.2 — Cluster-Scale Dependence of Coupled Transport–Geometry Signatures in Interaction Graphs 48.1 — Scalar Continuum Control and Harmonic-Coexact Sector Roadmap 49.1 — From Recoverable Coherence to Harmonic Operator Construction and Continuum-Stability Roadmap 50.1–50.3 — Foundations Synchronization and Post-Validation Release Series 51.1–51.2 — Active-Branch Closure, Clean Baseline Identity, and Holonomy-Split Family Resolution Core Contributions Definition of recoverable coherence as a minimal physical diagnostic Identification of collapse without fragmentation (frozen hierarchy regime) Introduction of persistence-based stability metrics and the k* critical point Empirical detection of pre-break structural signatures Evidence of transport–geometry coupling in interaction graphs Initial pathway toward continuum scaling and coarse-graining without assuming spacetime Program Position This release represents a post-foundations validation stage, where: core operators are fixed structural signals are tested across regimes early continuum-feasibility behavior is explored The work does not claim a complete physical theory.It establishes a constrained, falsifiable diagnostic layer intended for: refinement testing cross-domain validation eventual continuum interpretation Scope The HAOS-IIP program is currently positioned as: a structural stability instrument a collapse detection framework a pre-geometric diagnostic system Further development will focus on: scaling behavior under refinement coarse-graining invariance mapping to effective continuum observables Keywords (paste in Keywords field) interaction-invariant physicsstructural stabilitycollapse detectionrecoverable coherencegraph dynamicscontinuum scalingcoarse-grainingnetwork systemstransport geometrypre-geometric models Copyright Copyright (C) 2026 Tomislav Rupić https://tomislav-rupic.com/