fhelium.experimental.bootstrap.presets.exponential

Preconfigured full-slot callables using exponential-squaring reduction.

The versioned profile is documented for a configuration derived from Preset.slots32768_scale50_depth27_int64 with galois_generator=5. The factory composes public components; it does not certify encrypted range or application error.

exponential_depth_refresh_logn16_d16_v1

function View source

def exponential_depth_refresh_logn16_d16_v1(engine: Engine) -> FullSlotBootstrap: ...

Construct the versioned degree-16 exponential full-slot callable.

The composition uses two collapsed radix-2 stages in each transform, BSGS baby step 16, a degree-16 balanced-power exponential seed, repeated squaring for raw input bound $B=1024$, fused normalization $x=r/B$, and sine extraction by conjugation.

The documented configuration is derived from Preset.slots32768_scale50_depth27_int64 with galois_generator=5. The input occupies bootstrap.input_depth = engine.max_depth - 1. Entry preparation uses its actual scale; both resulting raw branch coordinates must lie in $[-1024,1024]$. The function does not enforce the deployment identity or encrypted range; FullSlotBootstrap checks structural-scale proximity, transform shape, and depth. Application tests must establish numerical suitability and depth budget. Online execution requires rotation, relinearization, and conjugation keys.

Parameters

• engine: Engine supplying slot count and Galois convention.

Returns

A full-slot callable configured for the supplied Engine.