xi_derived
plain-language theorem explainer
The definition supplies the HSB suppression factor ξ(g_baryon, a0) that multiplies the ILG kernel amplitude. Galaxy modelers working inside the Recognition framework cite it to recover Newtonian behavior at high accelerations while preserving the boost at low accelerations. It is realized as the direct algebraic saturation form 1 / (1 + g_baryon / a_saturation(a0)).
Claim. The HSB suppression factor is defined by $ξ(g, a_0) = 1 / (1 + g / a_{sat}(a_0))$, where $a_{sat}$ is the saturation acceleration obtained from the seven-beat gap and lock stiffness.
background
The module derives morphology and radial factors for the ILG kernel to correct systematic biases in galaxy rotation curves. High-surface-brightness galaxies overpredict velocities under the raw kernel, while low-surface-brightness galaxies underpredict; the suppression factor ξ addresses the former by turning the ILG modification off at high baryon acceleration. The local setting rests on the hypothesis that an 8-beat cycle is the minimal valid period for D=3, so that high energy densities allow leakage into 7-beat modes that cannot carry the ILG force modification. Upstream results include the structure of nuclear densities from NucleosynthesisTiers.of and the CPM hypothesis bundle from CPM2D.Hypothesis that supply the projection-defect and energy-control axioms used to calibrate the saturation scale.
proof idea
The definition is a one-line algebraic expression that directly invokes a_saturation a0 inside the standard saturation form 1 / (1 + x). No tactics or lemmas are applied beyond the unfolding of a_saturation, lock_stiffness and seven_beat_gap already present in the sibling definitions.
why it matters
It supplies the concrete suppression mechanism required by the downstream limit theorems hsb_suppression_limit and lsb_unsuppressed_limit. Those theorems establish that ξ → 0 as g → ∞ (Newtonian recovery) and ξ → 1 as g → 0 (full ILG boost), thereby closing the morphology gap between the eight-tick octave (T7) and observed galaxy data. The construction links directly to the Recognition Composition Law through the phi-ladder saturation that quantifies the stiffness of the 8-beat lock.
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