Two projections gave exact 45-degree phase limits for bounded real future voltage in 430 SEEG windows with fixed linear filtering

We derived an exact phase stability check for a fixed linear filter. The baseline uses only samples before a fixed cutoff. Two real projections give the least future voltage norm that can reach a phase sector edge or make phase undefined. We applied the check to 430 later pulse windows at 86 sites in eight public SEEG sessions. The source was OpenNeuro ds004696 v1.0.1. The fixed complex filter had 1 s support. Labels were 49.805 ms before pulses. Fifteen windows passed the conditional 45-degree check when allowed future RMS equaled baseline RMS. The equal-person mean was 4.07%, with a descriptive patient bootstrap interval from 1.15% to 7.52%. An operator-norm disc accepted 13 windows. A complex Cauchy disc accepted seven. All 15 recorded futures were above the assumed baseline-energy limit. This conditional check did not certify those native labels. With recorded future energy as the bound, two windows passed. The equal-person mean was 0.44%. The proof gives a sharp limit for real futures in an energy ball. Boundary voltage tests passed in all 10,320 supported data windows. A separate optimizer agreed in 160 test systems. A full analysis repeat matched all saved numerical results exactly. A complete public source rebuild for one person matched every saved input array. The package preserves the proof, source code, voltage windows, filter, provenance, results, figures, and retrieval instructions. The method can screen offline phase references for brain-computer interface research. It does not establish true neural phase or stimulation benefit.

phase estimation · signal processing · stereoelectroencephalography · SEEG · future-data dependence · robustness certificate · brain-computer interface