The Funnel Geometry
To build an execution architecture within an organic model, we must abandon the flat, linear columns of traditional machine learning. Biology does not process information in uniform vertical slices; it forces patterns to organize through localized physical constraints. In the Vexafracta paradigm, this is achieved by folding the standard “all-to-all with only the next layer” feedforward rule into a concentric, shrinking 2D geometric tile.
Consider a 16×16 micro-unit tile segment. Instead of passing data sequentially from Left to Right, the signal propagates centripetally—collapsing radially inward from a 60-node outer sensory perimeter (Layer 7) down through eight shrinking concentric rings to a symmetric 2×2 core anchor (Layer 0).
By forcing the layer-to-layer connections to scale down with the geography, the matrix math slashes its own overhead automatically. Layer 7 to Layer 6 requires a 60×52 matrix calculation, but by the time the wave reaches the Layer 1 to Layer 0 junction, it requires only a 12×4 footprint. The entire inward cascade collapses into a tiny 8,848-weight total budget, stripping out nearly 87% of the computational waste before a single line of code is executed.
The shrinking surface area acts as a natural information funnel. Spatial features are mechanically squeezed together as they move inward, forcing individual signals to fuse into a single, unified harmonic signature right at the center.
The Inward / Exward Breathing Cycle
The processing of data within this grid is governed by a strict two-phase kinetic lifecycle: Systole (the inward collapse) and Diastole (the exward relaxation).
During the inward phase, a localized input wave passes through our 256-entry Sigmoid Lookup Table (LUT). The table acts as a viscous fluid damper; unaligned ambient ripples lack the momentum to cross the threshold and die out early in the outer rings, while structurally coherent features constructively interfere, boosting their energy to past local thresholds.
When this concentrated wavefront successfully crashes into the 2×2 center core, the event triggers a state inversion. The core nodes fire into an Active phase (State 11), creating an intense, localized point-source disturbance.
This brings us to the neologism anchoring our recovery loop: the exward wave.
Energy cannot simply vanish into a digital sink. Upon firing, the core initiates a secondary shockwave that radiates exward—traveling backward from Layer 0 out to Layer 7. The exward wave does not carry raw data; it carries the refractory footprint of the execution event. Traveling outward layer by layer, driven by localized 1-bit event triggers (dirty bits), it flips the 2-bit state machine into its Refractory phase (State 01). This triggers a localized, non-linear R/C decay curve that flushes out the system baseline and prevents immediate reactivation, letting the tile clear its lungs before its next breath of data.
SWR and the Core-to-Core Highway
The ultimate scalability of this framework rests on solving the inter-tile boundary problem without a heavy, energy-draining global clock. We must reject the concept of peripheral sloshing; tiles do not messily bleed into each other’s outer edges. The 16×16 perimeters are clean, sealed, closed boundaries.
Instead, tile-to-tile relationships are exclusively center-to-center.
When a 2×2 core fires, its time-encoded output state (\(\Delta t\), representing the duration since its last full activation) is injected directly into the 2×2 cores of touching tiles via a higher-level macro-grid highway. This center-to-center link relies on the physical mechanics of Standing Wave Ratio (SWR) and impedance matching:
- The Mismatched Boundary (High SWR): If the adjacent tile’s core recently fired and sits in a highly resistive, low-\(\Delta t\) refractory state, the incoming core pulse hits a temporal brick wall. The energy experiences a massive SWR mismatch, reflecting straight back down the highway to damp itself out locally.
- The Resonant Boundary (1:1 SWR): If the adjacent tile’s core is resting in a receptive state (High \(\Delta t\) / State 00), its impedance matches perfectly. The pulse slides across the core highway with zero reflection, immediately triggering an exward wave at the center of the next tile, which ripples outward to its perimeter, rebounds, and cascades back inward as a fresh calculation.
By treating the 2×2 centers as the exclusive vertices of a higher-level macro-geometry, the network dynamically folds its own spatial paths. Information naturally carves its own trajectory through the hyper-dimensional grid, flowing exclusively through paths of maximum resonance where the SWR boundaries are lowest, while discordant noise gets choked out by its own internal reflections. It is a true fractal processor—where the structural rules of the micro-scale perfectly mirror the macro-scale, allowing infinite complexity to orchestrate itself.