IndisputableMonolith.Spiral.SpiralField
SpiralField supplies the logarithmic spiral paths, J-cost functions, step ratios, and eight-gate neutrality predicates for Recognition Science flight models. It is imported by the Geometry, Schedule, and TeslaTurbine modules in the Flight domain. The module is a pure definitions collection built on the RS constant φ and the time quantum from Constants, with no internal theorems.
claimThe module defines the log-spiral $r(\theta) = a \phi^{\theta/(2\pi)}$ under $\phi$-scaling, the J-cost $J(x) = (x + x^{-1})/2 - 1$, per-turn multipliers, and eight-gate neutrality scores on the phi-ladder.
background
Recognition Science derives geometry from the forcing chain (T5 J-uniqueness, T6 phi fixed point, T7 eight-tick octave). The Constants module supplies the RS time quantum $\tau_0 = 1$ tick. SpiralField introduces sibling definitions: Params for spiral parameters, logSpiral for the geometric path, Jcost as the recognition cost function, stepRatio and sampledCost for discretization, eightGateNeutral and neutralityScore for the 8-window predicates, perTurnMultiplier, and ELStationary.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module feeds the purely geometric layer of Flight.Geometry (phi-tetrahedral angles and log-spiral rotor paths), the 8-tick control surface of Flight.Schedule, and the spiral engine model of Flight.TeslaTurbine. It supplies the phi-derived primitives required by the Recognition Science propulsion scaffold.
scope and limits
- Does not assert physical realizability or forces.
- Does not compute numerical flight trajectories.
- Does not derive mass or energy formulas.
- Does not extend beyond the eight-tick structure.