Sum-of-Zeros at Infinity, Readout in Hardware: A Plateau Protocol via R ≈ 1

This work proposes an operational, cross-platform protocol for reading quantized plateaus in driven (Floquet) systems and related platforms. The core idea is to separate (1) the value set “at infinity” from (2) the act of holding and reading it in hardware. On the theory side, a symmetric/averaged Sum-of-Zeros (SoZ) prescription isolates a boundary-at-infinity integer W (consistent with Floquet–Streda results via Cesaro summation). On the operations side, a three-part stack—K (unit bridge), M (meter/map), and R (the containment lock with R = D/O ~ 1)—centers a finite window so the measured response holds S = K * W whenever the gap is open and time-reversal symmetry is broken. The paper turns this into falsifiable lab practice: An acceptance cut list (flatness ≤ 2%, odd-channel null, gap proxy open, dual-channel co-lock, sign flip under chirality or B-flip, protocol invariance). Additional tests (TRS-on null, injected gap closure giving an integer step, mobility-gap robustness, temperature/noise scaling of the band, hysteresis invariance, meter cross-check). A “gap cycle” timeline showing how Z-tension rises as the operating gap collapses, breaking the M ↔ R linkage until a new plateau reopens. A containment ladder with precise annulus conditions (stay gapped, fixed chirality, no spectral flow) to guarantee monotonicity of W across containments. “Directional infinity” (admissible rays): distinguishes edge-of-U approaches (no centering as the interior vanishes) from range-of-infinity paths where K can grow without losing the R ~ 1 lock. Platform mapping examples (density-slope/Hall style, photonics, cold atoms) and practical guardrails for servo/ADC headroom. The result is a portable recipe: value fixed at infinity by SoZ; value held and read in hardware by K–M–R; failure modes and falsifiers specified so experiments can confirm or refute claims quickly. What’s included Acceptance and falsifier checklists, operational notes (K, M, R), optional interpretive framing section Intended audienceExperimentalists and theorists working on Floquet phases, quantized transport/response, and robust readout protocols who want concrete, falsifiable tests.