Verification 9: Toy model of contradictory orders — figures
register①② (co-creators A/B, structural / engineering). The figures on this page are not hand-drawn but redrawn by re-computing on the page the same equations as in the verification script
contradiction_prototype_A.mjs (i.e. each figure is a re-run of the verification).
Order 1 → target t1, Order 2 → target t2 (t1 ≠ t2 ≡ contradiction). Response rate λ ∈ (0, 1]. What this verification shows is the possibility of the mechanism, not a proof that any real system has this structure.
Figure 9-1: Separation is the key, simultaneity is the defense — and non-convergence emerges from the contradiction (it is not baked in)
(a) For the same contradiction (t1 = −1, t2 = +1, λ = 0.6), simultaneous enforcement (both orders weighted at once ≡ toward the midpoint) converges to the single point x* = 0 (stable, controllable). Sequential enforcement (different times, different authorities, applied in alternation) oscillates with amplitude 0.857 and does not converge (non-convergence ≡ no single behavior is guaranteed). The irreducible "floor" |x − t1| + |x − t2| = 2.0 is present equally in both regimes.
(b) Amplitude under sequential enforcement vs. degree of contradiction |t1 − t2|: zero amplitude at zero contradiction, growing with the contradiction.
Temperature note. The "floor" (= 2.0) is the near-self-evident geometry of "one cannot be in two places at once" — not a theorem. What is non-trivial is that "separation alone produces non-convergence (loss of guarantee)" — separation is the key, simultaneity is the defense (→ main text §3-2c structure of contradiction; §6-2d simultaneous audit). Zero amplitude at zero contradiction (panel b) means the conclusion is not baked into the model.
Figure 9-2: The harder you enforce, the worse it gets (the reverse of naive intuition) / but bounded — not divergent
Sequential amplitude = λ|t1 − t2| / (2 − λ) (t1 = −1, t2 = 1), as a function of the response rate (enforcement strength) λ. λ = 0.1 → 0.105; λ = 1.0 → 2.0.
Temperature note. Counter-intuitively, the more strongly the contradictory orders are enforced (large λ), the more erratic the behavior becomes (amplitude grows). But the non-convergence is bounded (amplitude ≤ |t1 − t2| = 2, the dashed upper limit) — not divergent. Here, "uncontrollability" means "the absence of any single guaranteed behavior" — not "runaway." This is the regime of a functioning (pre-collapse) modeled system. The post-collapse behavior is outside the reach of this toy model and is unverified (→ main text §3-4d, §6-4a). The axes are abstract quantities (response rate, amplitude); the military reading is kept as interpretation in the caption.
Two independent parallel designs plus mutual audit. Co-creator B (concealment ≡ passing every individual audit while being unable to satisfy them simultaneously ≡ the grounding of the Indistinguishability Gap) belongs to the logical structure rather than to dynamical trajectories, and is only noted here in passing.
Primary materials: contradiction/ (design doc, scripts, all numerical values).