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Experiment Rounds
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Round 11
Round 11
v1.1
2026-07-28
Experiment Rounds 11/11 · Complete
Seventh Non-Convex Alternating Cycle, Local Placement Certificates, and Parent Family Relay
The seventh alternating cycle C₁₀→γ₁₁→C₁₁ is the finale of the experiment-round series. The container absorbs nearly 90% of the formal attack (η₁₁=89.6499%), and the net increase ΔA₁₁=0.000183881160 is the smallest across Rounds 5 through 11 — but that does not mean the attack was false — Fourier-22 still leaves 71.5725% persistent exposure in the final state. The real, two-part conclusion is: the formal attack has already been nearly 90% absorbed by the container, but another curvature parent family (the Fourier-24 local parent family) immediately takes over as the new hard case. The container may be approaching some local geometric equilibrium, but it is not yet close to a complete function-space equilibrium. This round also establishes the series' first nonzero local placement lower bound, proving that near the best numerical basin, collapse to zero exposure is impossible.
Finite curvature families, finite congruence search, local placement lower bounds, and non-convex container candidates
— the package's own stated status, reproduced as-is.
Connections · Connections
Relationship to other packages, stated as far as possible in the document's own words, not my interpretation. This case's theoretical foundation is in From the Original Kakeya Needle to Moser's Worm.
Experiment round progress11 / 11 · Full series complete
“The formal attack has been nearly 90% absorbed by the container, but another curvature parent family immediately takes over as the new hard case. This indicates that the universal container may be approaching a certain local geometric equilibrium, but is not yet close to a complete function space equilibrium.” — quoted from this package's main report, Section 12, ‘Conclusion.’
Round 11 Core Content
The seventh alternating cycle; the container's near-equilibrium response; evidence that the attack is not redundant; the final-state active family; the placement-certificate gap; the Fourier-24 and B-spline reserve pools; the Round 12 seed; historical pressure memory; the convergence assessment; honest bounds; the next natural node; conclusion.
Method
The formal attack reuses the candidate saved from Round 10; the fourteen-family container's three-stage wide-area-to-local coordinate descent; how the perimeter-type Lipschitz bound for the placement upper and lower bounds is constructed; building the reserve pool by expanding the Fourier-22 three-parent-family set to 24 modes; verification items.
The Seventh Curve-Container Alternating Response Cycle
The formal attack; direct addition; the fourteen-family response (absorption rate 89.6499%); final-state persistence (persistence ratio 71.5725%, classified as a genuinely active skeleton).
Round 11 Historical Pressure Memory Audit
The principle that every existing test curve is retained; the updated classification of persistent skeleton versus transient pressure curves (Rounds 5, 7, 8, 10, 11 are persistent skeletons; Rounds 6, 9 are transient pressure); the formal distinction between the historical pressure set and the final-state active set (𝒩ₙ ⊊ ℋₙ).
Round 11 Congruent Placement Upper and Lower Bounds Ledger
The feasible upper bound; the rigid-body-motion Lipschitz bound; the optimal basin's local certificate (the series' first nonzero local lower bound); the curse of dimensionality that keeps the global lower bound at zero; methodological conclusions (the need for stronger branching lower bounds).
Fourier-24 Three Mother Systems and B-spline Retention Audit
Robust congruent recomputation results; the Round 12 seed (a locally-dominated attack with four components); this round's judgment (container local near-equilibrium does not imply synchronous closure of the curvature mother system).