Microsecond Intraoperative Margin Sensing via Cycle-Space Bioimpedance Sifting and Sherman-Morrison Invariants: A Rigorous Benchmark on Clinical and Hardware Datasets

Between 15% and 35% of solid tumor surgeries leave positive microscopic margins, requiring secondary operations and increasing recurrence risk. Traditional frozen-section histology requires 30 to 45 minutes of processing time, while optical cameras are blinded by blood pooling and surgical cautery smoke. This repository deposits the scientific publication, high-resolution figures, and reproducible source code for a real-time intraoperative margin sensing framework based on electrical bioimpedance and dynamic low-rank algebraic updates. Key Milestones and Verified Technical Achievements: Microsecond Edge Execution (316x Speedup): By replacing brute-force matrix inversion with dynamic Sherman-Morrison rank-1 updates, the computational latency on commodity edge processors drops from 2.37 milliseconds to between 2.09 and 7.49 microseconds, delivering over 130,000 evaluations per second without GPUs, dedicated matrix hardware, or cloud connectivity. Clinical Validation on Excised Human Tissue: Evaluated on 106 clinical human breast tissue specimens, single-channel high-frequency phase dispersion achieves a diagnostic accuracy of 97.0% (ROC-AUC 0.970) and a 95.9% negative predictive value under rigorous nested cross-validation without threshold leakage. Hardware Multi-Electrode Tomography: Benchmarked on physical 16-electrode phantom tomography hardware across 73 independent physical orientations, weighted spectral invariants achieve 100% separation against baseline, while direct boundary voltage tracking localizes anomalies with an error of only 4.5 degrees. Organ-Specific Biophysical Dual: Resolves the physical contrast mechanisms distinguishing dielectric tumor signatures in fatty stroma (breast carcinoma) from ionic conductive flooding caused by blood-brain barrier disruption and vasogenic edema in brain white matter (glioblastoma).