IndisputableMonolith.Spiral.SpiralField
The SpiralField module supplies the geometric primitives for log-spiral structures under phi scaling in Recognition Science. Flight-geometry and turbine-model authors cite it for the J-cost measure, step ratios, and eight-tick neutrality predicates. As a pure definition module it introduces no theorems, only declarations that downstream files reuse directly.
claimThe module defines the logarithmic spiral path, the J-cost function obeying the Recognition Composition Law $J(xy)+J(x/y)=2J(x)J(y)+2J(x)+2J(y)$, step ratios, per-turn multipliers, and neutrality scores over eight-tick windows, all derived from the RS constant phi.
background
This module resides in the Spiral domain and imports only the RS time quantum tau_0 = 1 tick from Constants. It introduces the phi-ladder scaling, the J-cost defect measure that quantifies departure from self-similarity, sampled costs along discrete turns, and the eight-gate neutrality predicate that checks balance across the 2^3-tick octave. All objects remain purely geometric; no physical interpretation is attached.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the geometric layer for the spiral-field propulsion model. It directly feeds Flight.Geometry (phi-tetrahedral angles and log-spiral rotor paths), Flight.Schedule (8-tick control discipline reusing the neutrality predicates), and Flight.TeslaTurbine (modeling the 1913 bladeless turbine as a phi-spiral engine). It therefore anchors the geometric scaffolding that later connects to the eight-tick octave and D=3 spatial dimensions in the T0-T8 forcing chain.
scope and limits
- Does not assert any physical propulsion or turbine performance claims.
- Does not contain theorems or proofs; only definitions and predicates.
- Does not import mass formulas, alpha bands, or forcing-chain results.
- Does not address Berry creation thresholds or Z_cf values.