IndisputableMonolith.Engineering.PhantomCoupledGWAntennaSensitivity
The module defines the carrier frequency of a phantom-coupled gravitational wave antenna as 5φ Hz in RS-native units along with the associated sensitivity function and certification objects. Engineers and physicists applying Recognition Science to detection hardware would cite these results when evaluating antenna response near the phi-ladder scale. The module consists of a sequence of definitions and lemmas establishing carrier positivity, sensitivity positivity, and strict anti-monotonicity.
claimCarrier frequency $f_c = 5phi$ Hz. The sensitivity function $S(f)$ is positive and strictly anti-monotonic in frequency offset from $f_c$, with certification object PhantomCoupledGWAntennaSensitivityCert.
background
The Constants module supplies the fundamental RS time quantum τ₀ = 1 tick. The Cost module supplies the J-cost function J(x) = (x + x^{-1})/2 - 1 used to measure defect distances on the phi-ladder. This engineering module applies those primitives to define a phantom-coupled GW antenna whose carrier sits at 5φ Hz, introducing sensitivity as a function of deviation from carrier together with the required positivity and monotonicity statements.
proof idea
This is a definition module. It introduces the carrier frequency, sensitivity function, and certification theorem through a chain of definitions followed by lemmas that establish carrier positivity, sensitivity positivity, and strict anti-monotonicity using algebraic properties imported from the Cost module.
why it matters in Recognition Science
The module supplies the concrete sensitivity model for phantom-coupled GW antennas and feeds the one-statement certification gw_antenna_one_statement. It places the carrier at the 5φ scale, linking the phi-ladder fixed point (T6) and eight-tick octave (T7) to an engineering application while remaining inside the Recognition Composition Law framework.
scope and limits
- Does not derive gravitational wave emission or propagation equations.
- Does not compute numerical sensitivity values outside the defined carrier band.
- Does not address quantum noise or detector limits beyond the J-cost model.
- Does not claim experimental validation against LIGO or other instruments.