IndisputableMonolith.Relativity.ILG.GWDerived
GWDerived derives gravitational wave structures in the ILG extension of Recognition Science. It maps the J-function and phi-ladder onto tensor wave propagation in three dimensions. The module collects definitions linking the forcing chain T0-T8 to wave observables. It organizes derived structures without internal proofs.
claimMain objects include the wave strain $h_{ij}(t, x)$ obeying the wave equation derived from the Recognition Composition Law $J(xy) + J(x/y) = 2J(x)J(y) + 2J(x) + 2J(y)$, with speed fixed at $c=1$ and modes set by the eight-tick octave.
background
Recognition Science derives physics from one functional equation. The J-cost is $J(x) = (x + x^{-1})/2 - 1$, satisfying the RCL, with phi the self-similar fixed point. This module introduces ILG definitions for gravitational waves under the relativity domain, using T7 eight-tick octave and T8 D=3 from the unified forcing chain.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies definitions feeding parent theorems on relativistic wave predictions. It advances the chain from T8 D=3 to observable gravitational effects, supporting derivations of constants such as alpha in (137.030, 137.039).
scope and limits
- Does not solve the wave equation for specific sources.
- Does not derive energy flux or polarization details.
- Does not address matter interactions or quantum corrections.
- Does not include numerical simulations or data comparisons.