HAOS-IIP: Structural Stability, Collapse Detection, and Continuum Scaling Program (Papers 44.1–51.2)

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 physics
structural stability
collapse detection
recoverable coherence
graph dynamics
continuum scaling
coarse-graining
network systems
transport geometry
pre-geometric models

Copyright

Copyright (C) 2026 Tomislav Rupić

https://tomislav-rupic.com/