IndisputableMonolith.Engineering.CorticalNeuromodulationDevice
This module defines the carrier frequency and supporting parameters for a cortical neuromodulation device in Recognition Science units. It fixes the frequency at 5φ Hz and supplies positivity, band, and bound lemmas for carrier, pulse spacing, and entrainment confidence. Engineers applying RS to neuromodulation cite it for device specification and certification. The module consists of definitions plus short lemmas establishing the required inequalities.
claimThe cortical-column carrier frequency equals $5φ$ Hz. Pulse spacing and entrainment confidence are positive reals with entrainment confidence bounded in $(0,1]$ and strictly anti-monotonic in the carrier.
background
The module imports the RS time quantum τ₀ = 1 tick from Constants and the J-cost machinery from Cost. It introduces carrier frequency, pulse spacing, and entrainment confidence as concrete engineering quantities tied to the phi-ladder. These quantities are required to satisfy positivity and unit-interval constraints before the device certificate can be formed.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies a concrete device-level realization of the phi fixed point and eight-tick octave, feeding the CorticalNeuromodulationDeviceCert that closes the engineering application. It directly encodes the DOC_COMMENT claim that the carrier equals 5φ Hz, linking the forcing chain (T5–T7) to neuromodulation hardware.
scope and limits
- Does not derive the 5φ choice from a variational principle.
- Does not model neural tissue response or field propagation.
- Does not address fabrication tolerances or power budgets.
- Does not connect to clinical trial endpoints.
depends on (2)
declarations in this module (14)
-
def
carrier -
theorem
carrier_pos -
theorem
carrier_band -
def
pulseSpacing -
theorem
pulseSpacing_pos -
theorem
pulseSpacing_band -
def
entrainmentConfidence -
theorem
entrainmentConfidence_zero -
theorem
entrainmentConfidence_pos -
theorem
entrainmentConfidence_le_one -
theorem
entrainmentConfidence_strict_anti -
structure
CorticalNeuromodulationDeviceCert -
def
corticalNeuromodulationDeviceCert -
theorem
neuromod_one_statement