HAOS-IIP Phase-I - Frozen pre-geometry can organize, but it does not bind.

This preprint presents the Phase I results of the HAOS-IIP program, an exploratory numerical framework aimed at mapping the minimal dynamical conditions under which organized structure can emerge on a discrete interaction substrate prior to the introduction of geometric or spacetime assumptions. Using a frozen kernel-induced cochain operator architecture, a systematic diagnostic ladder (Stages 0–18) investigates single-packet behavior, collective interactions, coarse-grained basin formation, and candidate mechanisms for emergent composite binding. Across scalar extensions, relational feedback, phase-synchronization tests, and minimal retarded-interaction pilots, the architecture consistently supports localized ordering and metastable morphology but fails to produce scale-robust composite stabilization or self-generated geometric capture. The central boundary result of Phase I is therefore: Frozen pre-geometry can organize, but it does not bind. This finding establishes an architectural limit of static linear substrates: without dynamical back-reaction in the interaction kernel itself, emergent relational geometry and persistent binding do not arise. The work reframes negative outcomes as structural constraints, providing a mapped pre-geometric regime space rather than a search for tuned success cases. The paper concludes by defining the transition to Phase II, in which the interaction kernel becomes a bounded dynamical degree of freedom. This regime shift opens a falsifiable path toward testing whether minimal substrate back-reaction can generate stable composite structures while preserving the diagnostic discipline developed in Phase I. The HAOS-IIP repository accompanies the preprint as an open numerical atlas of emergent morphology in discrete interaction systems.