HAOS-IIP

HAOS-IIP expands to Harmonic Address Operating System / Interaction-Invariant Physics. In its public form it is a structured numerical research program testing whether a reproducible emergence ladder can be identified inside a frozen branch-local cochain-Laplacian hierarchy on discrete graph domains. The repo frames the work as bounded, diagnostic, and reproducible rather than as a finished physical theory.

The program is organized around a minimal operational principle: reality as recoverable coherence under interaction. From there it studies structural stability, collapse detection, controlled refinement, frozen telemetry, and cautious synthesis across a phase spine rather than assuming spacetime, ontology, or continuum physics up front.

The research map in the repository compresses the architecture into one substrate, one kernel, weighted discrete geometry, and three operator sectors. The node lift L0 is used as the scalar or geometry sector, the edge or Hodge lift L1 as the gauge or vector sector, and the discrete Dirac-type branch D_H as the fermion or spinor toy branch. Those names are used diagnostically and under constraint, not as unrestricted claims that full physical sectors have already been derived.

Within that bounded frame, HAOS-IIP asks a precise set of questions. Does a stable propagation band form under refinement. Can temporal ordering emerge from branch-internal dynamics. Does causal influence close in a consistent way. Can proto-geometric distance surrogates stabilize. Do transport and geometry signatures couple in a measurable way before any broad continuum interpretation is allowed.

The public reproduction path is deliberately narrow. The repository README sets a concrete success criterion: running the public reproduction script should reproduce the frozen baseline table values and plot exactly. The quick path is built around python3 examples/quick_reproduce.py, while individual frozen bundles can be checked with run_phase.py. That reproducibility contract is part of the framework itself, not a cosmetic add-on.

The paper spine is extensive. The repository index runs from early operator-architecture and morphology papers through cautious continuum-bridge feasibility, proto-particle feasibility, temporal ordering, causal closure, and later synthesis releases. Zenodo record 19655377, published on April 19, 2026, archives papers 44.1 through 51.2 under the title HAOS-IIP: Structural Stability, Collapse Detection, and Continuum Scaling Program. That release explicitly positions the work as a structural stability instrument, a collapse detection framework, and a pre-geometric diagnostic system.

The current repository state goes one step beyond that Zenodo bundle. The main README identifies the active public milestone as the 51.3 scalar-carrier CP4 geometry robustness release. Inference from the repository text: the strongest current claim is not a general continuum limit, but a bounded scalar-carrier geometry closure on one common 3D kernel-graph family followed by a first-pass robustness check under mild disorder and kernel-family variation.

That caution matters. The repo's theory notice states that the program does not claim physical correspondence, geometric reconstruction, continuum field validity, cosmological interpretation, or fundamental ontology. Observed structures such as propagation bands, causal influence graphs, or proto-distance surrogates are treated as internal diagnostic features of the tested numerical regime. The methodological ladder is explicit: reproducibility, refinement stability, invariant telemetry, then cautious synthesis.

Taken together, HAOS-IIP is best read as a disciplined research instrument for studying when ordered structure persists, degrades, or collapses under interaction, and how far a bounded emergence program can be pushed before interpretation outruns evidence. It is detailed enough to be reproducible, ambitious enough to open a continuum-facing roadmap, and careful enough to keep its strongest claims inside the window actually supported by the public artifacts.