High-Dimensions Governing Low-Dimensions: Axiomatic 10.7 cm Solar Radio Flux Prediction Based on Dimensional Approximation

By applying a Topological Inference method that leverages high-dimensional constraints to progressively approximate the Low-Dimensional Manifold Projection, this framework aligns closely with the instrumental noise floor (MAE ≈ 0.85 sfu) during Solar Minimum and stable transition phases. This is not a conventional data-fitting model. Using a Dimensional Approximation approach, we bridge unobservable high-dimensional laws and 3D solar observations. By reconstructing the High-Dimensional Causal Backbone, the system identifies the deterministic anchors of solar activity. Compared to standard F10.7 models (NOAA SWPC, NRC Canada), where resolution bottlenecks occur, our high-dimensional approach achieves higher fidelity, matching the physical observation limits of modern radiotelescopes for approximately 65% of the solar cycle. Framework Performance by Physical Environment: Deterministic Domain (Solar Minimum / Stable Phases; 15.5% coverage)During periods of high topological coherence, the model achieves an MAE of 0.85 ± 0.04 sfu, converging with the thermal noise floor of the DRAO radiotelescope—establishing a practical precision benchmark beyond typical operational baselines. Inertial Domain (General Transition Phases; 49.5% coverage)The system maintains error bounds largely within ±3.0 sfu. By tracking macroscopic solar momentum, we eliminate divergent “rolling errors” common in AI or standard operational models, ensuring causal consistency in the F10.7 trend. Absolute Horizon (Solar Maximum / Eruptive Phases; ~35% coverage)During violent solar activity, the high-dimensional manifold undergoes topological rupture. Instead of producing unreliable stochastic guesses, the framework enacts a Topological Veto, calculating a 7.92-day Causal Re-coupling Period, the time required for the system to settle back into a predictable, deterministic state. Summary: Within its defined stable domains, this framework approaches the physical limits of solar radio flux predictability. It effectively separates predictable from chaotic regimes without unscientific data smoothing. Reproducibility: All mathematical derivations are closed-loop. Fully executable Python source code and standardized datasets are provided for immediate, zero-barrier verification.