Four-Dimensional Intelligence Fields, Optimal Contraction Cycles, and Scalable Autonomous Learning- Self-Amplifying Novel RSI Method

Qhïunalūm is a self-contained mathematical and executable method for continuous four dimensional learning, interacting computational fields, and certified improvement of the proce dures used in later learning. Its state consists of coupled cells with two canonical pairs each. Dissipation reduces error, orthogonal transport redistributes it, and independently checked program identities permit changes to future synthesis and execution. The central field result permits nonlinear, state-dependent coupling while preserving the entire energy history of a prescribed local contraction cycle. When the same skew transport acts on the position and momentum channels, it factors into an orthogonal moving frame along each trajectory. Consequently, an optimal local endpoint lifts to an exact radial contraction of the whole interacting field, while retaining a state-dependent transport factor. This is a contraction relative to the declared target, not an assertion of incremental contraction between arbitrary trajectories. The graph transport has an explicit actuator cost; it is not a free control input. The continuous control theorem closes the exact attainability boundary in every even dimension. For frozen skew schedules with rotation cap ω and half-rank damping cap Γ > 0, the full-cap bound e−ΓT/2 is attainable at positive time if and only if Γ < 2ω and T ≥ π/ ω2 −Γ2/4. A block determinant and trace reduction sends arbitrary-dimensional mixing to a two-dimensional bounded-control return problem; the maximum principle supplies the sharp obstruction, and the explicit three-stage compiler attains every feasible horizon. An adjoint echo supplies an alter native cycle under faithful waveform replay. Exact rational checking validates rounded control programs separately from the ideal identities. Field-level volume bounds expose the total dissi pation required to contract an expanding number of independent error directions, and rule out uniform contraction of an infinite-dimensional linear field with a finite trace budget. Growth is assessed against unnormalized total error. The recursive component extends a certified program library across multiple generations. An ad mitted operation becomes available in later discovery. A separate exact checker verifies universal parameterized matrix identities, expected-source binding, and acyclic dependencies. A determi nant invariant gives an exponential lower bound on the number of primitive damping operations in the represented family, while a recursively growing description remains short. This is an im provement of the search representation within a specified language. An informed exact compiler is included as a stronger comparison. A work-account theorem states the conditions under which realized savings can fund further discovery without exceeding the fixed reference cost plus an explicit initial allowance. The manuscript also develops the earlier geometric foundation in full: exact recovery of Gaus sian directions through a positive-semidefinite face, recursive quotient closure, certified objec tive charts, optimally conditioned symplectic direction compilation, finite-algebra identities, and full-plane Hex boundary contracts. These results supply concrete objective families and state transformations for the learning architecture. The final release distinguishes written proofs, exact finite certificates, numerical integration, and bounded synthesis experiments. It provides a complete research method within its declared do mains. It does not infer general intelligence, open-ended capability acceleration, or a T9 outcome from the available results. The contribution is the precise contraction, interaction, recursive extension, and resource contracts together with their implementations; historical priority of the specific new constructions remains unestablished