BZE Algorithm — Blending Zone Exit: A Universal Signal Discrimination

BZE Algorithm — Blending Zone Exit: A Universal Signal Discrimination Every measurement system encounters a moment when two genuinely different states become operationally indistinguishable. Not because they are actually the same — but because the surface through which we observe them has placed them in the same region of the measurement space. We call this region the Blending Zone. The standard response to a Blending Zone is amplification: increase the signal, reduce the noise, tighten the threshold. This response fails structurally. It operates on the same projection surface that caused the problem. The BZE Algorithm proposes a different response: change the projection surface itself. BZE is grounded in Digits Principle (DOI: 10.5281/zenodo.20737718): π(Q) = v, v ≠ Q. Any observation is a projection of a full state. A Blending Zone occurs not because two states are identical, but because the current projection maps them to indistinguishable values under noise. The solution is projection exchange: π₁ → Δπ → π₂. The algorithm operates in seven steps: (1) Blending Zone Detection, (2) Projection Exchange, (3) Recognition, (4) Polycube Geometry Assignment in {-1,0,+1}³, (5) Recognition Point establishment, (6) Euler Trajectory computation, (7) Triadic Consistency check and Bounded Closure. The algorithm terminates at SPACT — the first completed minimal transition with closure, trace, memory, and continuation. Three constituents — Projection, Recognition, Euler Dynamics — are each necessary. None is sufficient alone. Full closure requires their admissible consistency: BOUNDED CLOSURE = admissible_consistency(π, R, E) → SPACT. BZE is not a replacement for Needleman-Wunsch or Smith-Waterman. Those algorithms assume the projection surface is adequate. BZE operates at the prior level — it determines whether the current projection can discriminate states at all, before any alignment or scoring is attempted. Primary motivation domain: weak signal discrimination in biological and biotech data analysis, motivated by the published work of Daria Chudova, PhD (VP, Guardian Life Sciences). The algorithm is universal: it applies wherever distinguishable states become indistinguishable due to projection geometry and environmental noise. Theoretical foundations — SNT (10.5281/zenodo.19250332), DP (10.5281/zenodo.20737718), RPT (10.5281/zenodo.20590021), VCT (10.5281/zenodo.19045483), FFL (10.5281/zenodo.20600352), CLR (10.5281/zenodo.20619685). Corpus Root DOI: 10.5281/zenodo.19108892. keelcore.org. CC BY 4.0. Part I — Теоретическое основание: SNT как среда, Blending Zone с формальным определением, три составляющие (π, R, E), Digits Principle как механизм обмена проекций, Polycube геометрия, Euler динамика. Part II — Алгоритм: полная блок-схема в ASCII + семь шагов с условиями и действиями, включая ветвление на Step 2a/2b. Part III — Инварианты и запрещённые операции: 6 жёстких инвариантов, 6 запрещённых операций. Part IV — Биологическое применение: таблица BZE → биологический эквивалент, сравнение с Needleman-Wunsch и Smith-Waterman (BZE стоит до них, не конкурирует). Part V — Корпусные связи: SNT, DP, RPT, VCT, FFL, SPACT, CLR.