Sub-Threshold Stochastic Micro-Burst Resonance: Extraction of Coherent Physiological Micro-Tremors Below the Thermal Noise Floor via Non-Markovian Kramers Dynamics and Bistable Potential Well Amplification

This theoretical monograph formulates the Stochastic Micro-Burst Resonator (SMBR) invariant (Falcon Impossibility F06). By transcending classical linear signal processing bounds (SNR <= -32 dB), we harness non-Markovian Stochastic Resonance (SR) within a dynamically tunable symmetric bistable quartic potential manifold V(x) = - (a/2) x^2 + (b/4) x^4. We prove that ambient biological and environmental noise acts as a constructive kinetic catalyst, driving synchronized Kramers transitions across the potential barrier in phase with sub-threshold physiological micro-tremors (8-12 Hz) and ocular micro-tremors (40-100 Hz). Derived via the Mori-Zwanzig projection operator, the Spectral Amplification Factor yields an effective SNR gain Delta SNR >= +24.6 dB. Furthermore, higher-order non-Gaussian kurtosis (kappa >= 6.8) and bispectral cross-frequency phase coupling (b^2 >= 0.74) establish an absolute mathematical barrier against physical electromechanical spoofing, enabling deterministic sub-noise bio-telemetry and sovereign hardware zeroization.