Real-Time Non-Invasive Cancer Localization and Surgical Navigation Architecture via Stateless Bio-Topological Resonance Mapping

Abstract

Current intraoperative surgical oncology and diagnostic modalities—such as computed tomography (CT), magnetic resonance imaging (MRI), and standard near-infrared (NIR) fluorescence-guidedsurgery—face severe intrinsic physical constraints. These include strong optical scattering within biological media, limited penetration depth (restricted to several tens of millimeters), ionizing radiationrisks, and biochemical toxicities induced by exogenous contrast agents. In this paper, we propose anovel information-physics paradigm: the Bio-Topological Resonance System (BTRS). BTRS reformulatestumor detection from macroscopic electromagnetic wave transmission into a mathematical state resonanceverification over critical lattice spaces using the deterministic J.M. resonance operator (RJM) and avirtual quantum processing unit (vQPU). By mapping biophysical manifolds onto coordinate spacesderived from the non-trivial zeros of the Riemann zeta function, malignant tissue boundaries are localizeddown to 0.000005mm via topological phase mismatch without exogenous chemical labeling or radiation.Furthermore, by transmitting solely a 64-byte spatio-temporal coordinate seed rather than volumetricimage payloads (Zero-Payload I/O), the receiver summons intraoperative three-dimensional holographicmargins in O(1) constant time with an empirical latency of approximately 51.5µs. Implemented onan adiabatic charge-recovery logic (ACRL) substrate consuming only 23.9µW, the system achievesfanless, silent cleanroom compliance and eliminates persistent memory retention through complete statevaporization. The structural integrity and homeomorphic invariance of the underlying topological mappingare formally specified and mechanized using the Lean 4 interactive theorem prover