METRIC
3-PLATE
6-EVEN
6-ASYM
∑ SAGE MATH FRAMEWORK · GEOMETRIC SCORES · STATIC (COMPUTED FROM LAYOUT)
H₃ · Resonant Harmonic
|Σaᵢe^(i·3φᵢ)| / Σaᵢ
1=perfect · 0=cancelled
Cᵥᵥ · Weighted Coverage
Σ(aᵢ·wᵢ) / 2π
coupling opportunity
D · Drag Index
Σ(dᵢ·wᵢ) / 2π
mechanical cost
S = H₃·Cᵥᵥ · Geometric Score
resonance × coverage
before drag penalty
U = S − λD · Net Utility
λ=0.30 drag penalty
maximize H₃Cᵥᵥ − λD
δ* · Optimal Offset
(wₚ+wₛ)/2 = 0.45 rad
min non-overlap spacing
0.48–0.55r
δ*=0.45r · ✓ valid
⊞ SAGE DESIGN RULE:
Maximize H₃·Cᵥᵥ − λD
· Do not maximise plate count
· Preserve the m=3 resonant harmonic
·
6-ASYM achieves S ≈ baseline while adding 35% more coupling coverage
·
6-EVEN cancels H₃ entirely → S=0 regardless of coverage
Sage Verdict
BASELINE
MORE OUTPUT
LESS ASYM
BEST BALANCE
ASYM PRESERVED