Pith. sign in
module module low

IndisputableMonolith.Relativity.ILG.GWDerived

show as:
view Lean formalization →

Module collecting derived gravitational-wave results in the ILG sector of Recognition Science relativity. It packages wave-speed, polarization, and dispersion consequences that follow once the ILG effective metric and coupling are fixed. Relativity and phenomenology workers cite it for RS-native GW observables. Structure is a thin derivation layer over upstream ILG definitions rather than a free-standing axiomatic development.

claimDerived gravitational-wave quantities in the ILG framework: effective propagation speed $c_{\mathrm{GW}}$, polarization content, and dispersion relations implied by the ILG effective metric and Recognition-fixed couplings (with $c=1$, $\hbar=\varphi^{-5}$, $G=\varphi^{5}/\pi$ in RS-native units).

background

ILG is the Recognition Science treatment of gravity and relativistic kinematics inside the Relativity domain. The parent stack fixes the cost functional $J$ (T5), the golden ratio $\varphi$ as self-similar fixed point (T6), the eight-tick octave, and $D=3$ (T8), then specializes those constraints to an effective geometric description.

GWDerived sits above the core ILG metric and coupling definitions. It does not re-derive the Einstein or ILG field equations; it extracts wave-sector observables (phase speed, birefringence bounds, amplitude scalings) once those equations and the RS unit system are given. Constants appear in RS-native form so that GW predictions line up with the same $\varphi$-ladder used for masses and $\alpha$.

proof idea

This is a derivation module, not a single theorem. Typical pattern: import ILG effective metric and stress response; linearize about a background; read off the principal symbol for tensor perturbations; specialize to RS units and any ILG-specific coupling. Individual lemmas are short algebraic or PDE reductions; the module's value is the curated bundle of GW-facing corollaries rather than one deep existence proof.

why it matters in Recognition Science

Gives the Relativity stack concrete gravitational-wave handles that can be compared with LIGO/Virgo/KAGRA and pulsar-timing data without leaving the Recognition unit system. Downstream phenomenology and observational-bound modules use these derived speeds and polarizations to state RS-native constraints. Ties back to the forcing chain only indirectly: $c$, $G$, and the three-dimensional spatial setting are already fixed upstream (T8, RS constants), so GWDerived is an application layer, not a new forcing step.

scope and limits