ONE AXIOM : The Doors

Document 5M provided the Navigation Manual for exploration domains: the complete catalog of FORB₁₃ states, the Navigator's Safety Code, the Victory Navigation Algorithm (VNA), and the Victoria Theorem. What 5M did not provide are the operational sailing directions for the specific class of domains where the navigator knows exactly where it is (σ=0, structural coherence intact) but the navigable doors are closing one by one. These are the Fix (M) domains, and this paper is their sailing chart. We introduce heartlocₙav (s, t) = |N (s) ∩ ALLOWEDₙav (t) |/6 — the dynamic navigation isolation diagnostic (Definition 7M-1) — and prove that heartlocₙav (s, t) =0 ∧ σ (s) >0 = ∅ (Theorem 7M-1: Navigation Impossibility). The four-tier navigation classification (Definition 7M-2: NAV-stable, Fix (M) admissible, Fix (M) degenerate, SAND) is the operational map of this paper. The central new concept is SAND (Structurally Alive, Navigationally Dead, Definition 7M-SN): Fix (M) admissible states whose entire Q₆ neighborhood has been absorbed into FORBₙav. SAND states are constitutionally valid, navigationally dead. We prove two dissolution results: Prop 7M-DISS (SAND Dissolution Maneuver — DISSOLUBLE states can self-rescue via XOR-decomposition below FORBₙav resolution) and Prop 7M-IP (Information-Preserving Dissolution — IPDISS=1 ⟺ s'∈ALLOWEDₙav, the 7M form of the black hole information paradox resolution, Page curve restated in GF (2) ⁶). The constitutional development of FORBₙav is governed by: Thm 7M-2 (Monotonicity: FORBₙav grows only), Thm 7M-3 (Convergence: T*≤51), Lemma 7M-4 (heartloc Cascade), Lemma 7M-5 (FORB-in-Loop Verification Collapse), and Thm 7M-S₄ (S₄ Multiplicity Bridge: T3 ∧ T5ₚre ∧ G-closure ⇒ T5ₚost, upgraded to O∩FR after algebraic verification). The domain navel (Definition 7M-5, Theorem 7M-4: unique per meta-D1 event) is the structural memory of each domain opening; Corollaries 7M-3 and 7M-4 prove no domain is first and no domain is final. The public–private domain transition (Theorems 7M-5, Cor 7M-5: Heraclitean transition) requires a minimum of two distinct non-degenerate observers for public-domain status. The non-commutativity Λₘeta, D1 ≠ 0 (Proposition 7M-2) implies constitutional path-dependence (Prediction P8). Cor 7M-Work identifies constitutionally productive meta-D1 as the highest work category in the ONE AXIOM paradigm. Nine organizational instances across six domains (Proposition 7M-3) confirm the π-map from the algebraic domain to constitutional, IT, psychological, military, biological, and civilizational instances. The Z₄/Z₂³/S₄ self-similarity pattern is algebraically grounded in the primary domain GF (2) ⁶; full cross-domain algebraic proof (OT-D2) deferred to 8M. All 32 results 32×[O∩FR] are established within the dual-track framework O∩FR. Nineteen falsifiable predictions: P1–P4, P6 FORMAL; P5, P7 CANDIDATE; P8–P19 EMERGING. What is NOT in this paper: no new axioms; no optimization objective; no consciousness theory; no empirical confirmation of physics beyond structural predictions. 7M is the sailing directions — it maps which passages are closed, which dissolve, and what happens after the cut. The navigator's first step is their own.