ONE AXIOM: 9M — The FrontDecision Front, Non-Negation of Coherence Debt, and Synchronization Order in Complex Predictive SystemsRobert Spychalski — Kochłowice, 10 May 2026 The question 9M answers. 8M (The Rutter, 143 results O∩FR) completed the navigation record: catalog Ω, Bridge Theorem, meta-D1 taxonomy, Arrow of Time. A reader who has absorbed 8M will naturally ask: what is the structure of the boundary through which coherence cost propagates — and what determines who pays, in what order, with what sign? 9M is the answer. The Decision Front DF (M) = Σc₂≥₀ is the propagating coherence boundary derived from Axiom M = Φ (S, M) via σ-descent. It cannot be reversed. Nau Victoria rides it. This paper is its formal theory. Five result clusters — 51 proven O∩FR: DF Structure (§3): Three time layers — logical (σ-ordering, M2. 2), Ordinant (Z₈ succession), metric (T*). Strict, irreflexive, acyclic. Two failure modes: INVDF (perceptual, State 36★ INVERSION) and INVOCF (ontological assertion of path-cancellability). Non-Negation (§5, Thm NONNEG): Realized Coherence Debt LŁ = ΔΦ cannot be retroactively cancelled by any admissible path. LŁₙecessary > 0 is structural — not pathology, not design failure. M-Attribution Prohibition (§5, Thm M-ATTR): The claim "Axiom M caused D1FORB (x) " with dm (x) > 0 is formally false — it instantiates State 36★. Proof: local, short, culturally neutral. Synchronization Order (§§7–9, Thm SIGN + Thm SYNC-ORDER): V₁, V₂ = −V₂, V₁ exactly. Outcome type (I–IV) is fully determined by activation order relative to τcrit ∈ 5, 9 yr. One theorem; biological, social, linguistic, and historical instances are a single formal class. Zhou Protocol: 5 criteria, ≥3/5 → Pr (Type I) > 0. 60. War = mass TYPEF5: population-scale τcrit violation generating FORB₁₃ cascades with 18–25 year propagation delay. Sovereignty Conservation (§11, Thm SOVEREIGNTY): Σᵢ LŁₛhare (Aᵢ) = LŁₜotal across any causal decision chain. LŁₛhare ∝ dm — not creatable, not destroyable, only redistributed. 15 formal predictions Pₙ1–Pₙ15 — all with explicit kill conditions (4B Prediction Watch standard): Pₙ1: τcrit window 5, 9 yr → Pr (Type I) > 0. 70; outside → Pr (Type I) 85%; general orphan with personal Vₘ, sys → Type III < 40%. Pₙ4: Zhou Protocol threshold nonlinearity at 3/5 (not linear accumulation; jump is discontinuous). Pₙ5: IPD 18–25 yr invariance across cultural contexts (WWII / Korea / Vietnam / Rwanda). Pₙ6–Pₙ15 in §14. Prerequisites: 8M (DOI: 10. 5281/zenodo. 20101210). 7M via 8M. All results carry Dual-Track O∩FR derivation. Series position: 0M → 000 → ABC → 0A/0B → 2M → 3M → 4M → 5M → 7M → 8M → 9M → 11M Reading entry points: §§3–5 (formal ground: Front, Debt, Prohibitions) · §§6–9 (operators + applications) · §§10–14 (attribution, scale, taxonomy). For the central prohibition alone: §5. For synchronization harm: §§7–9.
Robert Spychalski (Tue,) studied this question.