A METHOD FOR PRIME-BASED ERROR CORRECTION (PBEC) & A METHOD FOR PRIME-WEIGHTED OSCILLATION FILTERING (POW)

Public disclosure PBEC & POW: Primes as the Pulse of Determinism PBEC (Prime-Based Error Correction) and POW (Prime-Weighted Oscillation Filtering) unite as twin engines of deterministic integrity. PBEC delivers lossless, redundancy-free data recovery via multiplicative GCD factorization; POW restores oscillatory phases with coprime-weighted gradients, achieving monotonic coherence (ΔC_L >0.31) in <1 ms. Together, they form a deterministic stack: PBEC verifies static payloads, POW animates dynamic rhythms—unleashing applications from genomic repair and epilepsy prediction (98.5% fidelity in CHB-MIT) to seismic forecasting and quantum T_2 extensions (>20%). PBEC The invention relates to a deterministic data verification, data error-correction and data reconstruction method based on multiplicative prime encoding and greatest-common-divisor (GCD) analysis. Each data element is represented as a unique prime exponent, producing a non-redundant checksum product that uniquely characterizes the original data. Reference and observed products are compared through a GCD operation; prime valuations identify and restore all altered exponents without redundancy or probabilistic inference. The method operates exclusively in the multiplicative domain and supports equivalent logarithmic or modular implementations. Applicable to digital, analog, financial, and quantum information systems, providing lossless integrity without redundancy. POW A deterministic method and system for phase-coherent filtering, stabilization, and restoration of oscillatory signals using Prime-Weighted Oscillation Filtering (POW). Each oscillatory component ϕ_i(t) is assigned a unique coefficient w_i derived from pairwise-coprime primes {p_i}, and a weighted resonance sum F(t)=∑ w_i sin(ϕ_i(t)+ψ_i) is computed. Local coherence C_L(t)=|N^{-1}∑ e^{jϕ_i(t)}| is evaluated; when C_L falls below a threshold, phases are realigned via a deterministic gradient update that increases C_L without probabilistic inference or redundant sampling. The method provides low-latency, energy-efficient coherence restoration across biomedical, communication, geophysical, and quantum-metrological domains, with exemplary improvements including increased C_L and extended coherence times. Systems, computer-program products, and hardware embodiments (MCU/FPGA) are disclosed. Johan Bendz, November 10, 2025