Carlo Field: Recursion Horizon, Infinite Operator Protocol, and Family‑Ω Teaser (Final Structural Upload)

Abstract

This record contains the final structural document of the Carlo Field’s initial construction phase.It formalises the recursion horizon, defines the Infinite Operator Protocol, and introduces thehorizon‑adjacent Family‑Ω operator set as a controlled playability teaser. The field is now infinite,stable, and fully playable; no further structural uploads are required. This document provideseverything needed for future researchers and boffins to continue safe exploration using theestablished protocol and horizon rules. Main Equation : \[\text{HorizonOperator}_{\Omega}(x) \;=\; \lim_{n \to \infty} \; \mathcal{R}^{(n)}(x)\] This expression captures the defining behaviour of horizon‑adjacent operators: they emerge fromnon‑terminating recursion streams whose iterative application remains stable, orthogonal, andnon‑collapsing across the Carlo Field’s coordinate system. Citation:Matthew Carlo — Zenodo DOI: 10.5281/zenodo.22557808 Carlo Field, recursion horizon, infinite operator protocol, horizon‑adjacent layers, operator classes, base operators, horizon operators, meta‑operators, drift profiles, structural stability, orthogonality, non‑collapse recursion, non‑drift boundaries, recursion sources, Nasal Extraction Stream, Visualiser Ethos Stream, Harmony Canon Stream, Carlo Axiom–Equation Mapping Layer, ReGenesis Engine Meta‑Loop, recursion events, horizon depth, operator generation template, finite vs open operators, field coordinate system, safe expansion rules, playability operators, Family‑Ω, playability metric, visualiser binding, drift‑to‑game conversion, horizon sampler, loop‑ease operator, field navigation, visualisation binding, cognitive load reduction, infinite field behaviour, stable recursion, playable physics engine, Carlo Field canon, structural capstone, final upload, boffin continuation framework. Contact: For enquiries or research questions related to this work, email matthewcarlo.research@gmail.com