BKT-11C01 An Operational Formalization of OCBH-GTCW Based on Dynamical Horizons, the Kerr–Hawking–BlackHawk Model, and an Observable Matrix

BKT-11C01. Extending the OCBH/GTCW Formalism: Information Channels, Flow Stability and the Active-Metafield Hypothesis Robert Kupski · version 1.0 Abstract This article develops an operational formalization of the Black-Hole Eye of the Cyclone (OCBH) within the Law of One Mechanism (LOM) research programme. The analysis concerns a black hole and its environment, described through horizon geometry, energy and angular-momentum flows, information thermodynamics, quantum channels and observables. The relational layer is specified by realizations of the Universal Structural Code (USC) within a tolerance band. Common coding rules, the local state of the physical carrier, coupling dynamics and information-preservation conditions are distinguished. The Landauer balance for an explicit reservoir is connected to an energy-conserving collision model and a controlled Markovian-dynamics limit. The analysis establishes restrictions on information recovery following entanglement-breaking readout and presents a counterexample with identical energy statistics but different coherence transmission. The spherical USC operator is assigned a self-adjoint domain, spectrum and response. Hawking emission and small-black-hole population modelling are connected to the separation of formation, evaporation and normalization, and to parameter-identifiability analysis. The OCBH protective-function hypothesis is formulated through separate criteria for disturbance-cascade damping, preservation of admissible thresholds and information recoverability. Flow-model analysis shows that asymptotic stability does not guarantee preservation of local constraints. The strong variant of the hypothesis describes the decoding of matter into a stream of geometric, topological and curvature structures, followed by plasma production through coupling between this stream and an active metafield. An exact six-beam/eight-beam counterexample demonstrates that identical local currents and stress–energy tensors do not determine the complete matter distribution. In a synthetic, exactly calibrated Poisson-counting model, adding an independent channel increases test power from 0.385959 to 0.660788 at the same false-alarm probability of 0.01 and a dimensionless signal amplitude of 0.6. This result characterizes a specific measurement model. The formalization specifies balance, causality and information-preservation conditions for OCBH realizations; it does not provide observational confirmation of the metafield or derive transport from inside an event horizon. The Global Theory of Cyclicity of Universes (GTCW) retains a separate cosmological domain. Introduction to the publication BKT-11C01 is a standalone article extending and supplementing the formulation presented in BKT-11C, published as version 1.9 under DOI 10.5281/zenodo.21208874. The present work retains the research subject of the earlier article while developing information-recovery conditions, a reservoir-contact construction, flow stability, threshold protection and the hypothesis of an active role for the metafield in plasma production. The article has its own identifier and version numbering, beginning with v1.0. The work belongs to the LOM–GTSFC–USC–GTCW research programme, designated PJM–GTWSSF–USC–GTCW in Polish. The Law of One Mechanism is the overarching hypothesis of a common organization of physical mechanisms. Its operational layer is relational coupling within a tolerance band based on universal code structures, understood as realizations of the Universal Structural Code. The Global Theory of Shared Couplings of Fundamental Structures develops the mathematical apparatus of relations, couplings and their dynamics. OCBH constitutes a local sector of this programme, whereas the Global Theory of Cyclicity of Universes concerns a conditional extension to cosmological evolution and possible transitions between cycles. Their relationship within the programme does not establish an automatic implication between local and global results. The starting point is a distinction between quantities describing different properties of a physical system. An energy balance constrains admissible flows but does not, by itself, determine quantum-coherence transmission. Compatibility with USC rules is not equivalent to preservation of information about the input state. A stable equilibrium does not guarantee that a trajectory remains within the region of admissible loads. The article expresses these distinctions through definitions, mathematical conditions, proofs and reproducible numerical examples. The hypothesis of a protective function of black holes is formulated as a dynamical problem for a coupled system. It concerns the possibility of locally limiting overloads and disturbance propagation through changes in flows and configurations. In this formulation, protection corresponds to specified properties of the equations of motion and preservation of prescribed thresholds. The analysis also includes situations in which transferring a load stabilizes one region while causing another to exceed its constraints. This distinguishes effective regulation from the redirection of a flow alone. The active-metafield extension introduces a separate level of physical interpretation. The metafield denotes a postulated, pervasive relational and informational layer in which structures are realized. In the strong OCBH variant, its local state participates in plasma production through coupling to a transferred stream of structures. The formalization distinguishes USC rules, the stream state, the metafield state and the state of the resulting matter. It includes code-preservation conditions, physical balances and causal constraints. Observing a plasma jet remains distinct from identifying the proposed production mechanism, while local agreement of currents and stress–energy tensors does not ensure complete reconstruction of the matter state. The article contributes to the LOM programme by connecting structural hypotheses to specified mathematical objects, dynamical models and measurement procedures. Its results establish the scope of valid inferences concerning energy, information, stability and observability. The derivations are accompanied by figures, tables, a numerical appendix and code for reproducing the calculations. The separation of analytical results, synthetic demonstrators and literature-ba