← Moser's Worm Problem / Rounds / Round 13
The five parameters p=(w,β,δ,c,ε) handed off from Round 12 are formally written as a 12-unknown event–KKT system: equal height across the four controlling branches (two low-phase stationary points, 120°, 270°), dual stationarity conditions, branch-pressure-weighted gradient balance, and multipliers summing to one. Solving it gives s₁₃=0.998914343297485, only about 4.2×10⁻⁹ higher than Round 8 — a fine correction to the peak's location, not a new geometric-scale breakthrough. The full 12×12 Jacobian is numerically full rank, but its condition number is as high as about 3.77×10⁷, highly ill-conditioned: this supports numerical isolation but not a robust conclusion of interval invertibility. The 120° branch carries about 73.6% of the branch pressure, the 270° branch about 20.7%. All 20 random perturbations converge back to the same scale basin.
Relationship to other packages, stated as far as possible in the document's own words, not my interpretation.
“The most accurate description at present is: a finite-width tanh curvature layer forms a numerically isolated, but highly ill-conditioned, minimax candidate within the five-parameter family.” — from Section 15, “Conclusion,” of this package's main document.
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sha256 35ea4218bb7396137f226d4b3b8d9ae34b6581306b2df84f28f7defea2f880e4