Manuscript VII-J@1 · VII-J.tex · section · d8c01b04

Conclusion

Release, boundaries, and successor obligations › Conclusion · lines 2112–2139

complete localized network + explicit clocks + independent causal edge certificates ⟹ Inf_{Φ}^{-} (B) \subseteq Sch_{full}^{-} (B) \subseteq Phys^{-} (B), ∥ Φ_{B} - Ψ_{B} ∥_{⋄} \leq ϵ_{B} ⟹ Sig_{Φ} (A \to B) \leq Sig_{Ψ} (A \to B) + ϵ_{B}, s^{'} - s \geq (1 + \frac{2 2}{3}) d_{C} (x, y) ⟹ (F_{s} (x), x) ⪯ (F_{s^{'}} (y), y) .

The first line is causal safety. A separate comparison with $Ψ$ is simulation accuracy. The last line is the explicit bridge to VII-F's event, not an assertion that its cell adjacency graph is a physical light cone.

Displayed formulas in this passage

unlabeled · line 2114
$complete localized network + explicit clocks + independent causal edge certificates ⟹ Inf_{Φ}^{-} (B) \subseteq Sch_{full}^{-} (B) \subseteq Phys^{-} (B), ∥ Φ_{B} - Ψ_{B} ∥_{⋄} \leq ϵ_{B} ⟹ Sig_{Φ} (A \to B) \leq Sig_{Ψ} (A \to B) + ϵ_{B}, s^{'} - s \geq (1 + \frac{2 2}{3}) d_{C} (x, y) ⟹ (F_{s} (x), x) ⪯ (F_{s^{'}} (y), y) .$