One Axiom : The Front

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) = {Σ_c}_{c≥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: INV_DF (perceptual, State 36★ INVERSION) and INV_OCF (ontological assertion of path-cancellability). Non-Negation (§5, Thm NONNEG): Realized Coherence Debt LŁ = ΔΦ cannot be retroactively cancelled by any admissible path. LŁ_necessary > 0 is structural — not pathology, not design failure. M-Attribution Prohibition (§5, Thm M-ATTR): The claim "Axiom M caused D1_FORB(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): [V_1,V_2] = −[V_2,V_1] exactly. Outcome type (I–IV) is fully determined by activation order relative to τ_crit ∈ [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 TYPE_F5: population-scale τ_crit violation generating FORB₁₃ cascades with 18–25 year propagation delay. Sovereignty Conservation (§11, Thm SOVEREIGNTY): Σ_i LŁ_share(A_i) = LŁ_total across any causal decision chain. LŁ_share ∝ dm — not creatable, not destroyable, only redistributed. 15 formal predictions P_n1–P_n15 — all with explicit kill conditions (4B Prediction Watch standard):P_n1: τ_crit window [5,9] yr → Pr(Type I) > 0.70; outside → Pr(Type I) < 0.30.P_n2 (★ new): Sign Order Invariance — reversing activation order reverses outcome type exactly.P_n3: Residential institutionalization → Type III rate > 85%; general orphan with personal V_m,sys → Type III < 40%.P_n4: Zhou Protocol threshold nonlinearity at 3/5 (not linear accumulation; jump is discontinuous).P_n5: IPD 18–25 yr invariance across cultural contexts (WWII / Korea / Vietnam / Rwanda).[P_n6–P_n15 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.