← Moser's Worm Problem / Rounds / Round 14
Round 13 allowed only a single tanh curvature peak. This round adds two new degrees of freedom: splitting the same wing into two peaks, and an antisymmetric (chirality) offset of the left/right wing centers or widths — testing whether the single-peak mirror-symmetric candidate is merely a spurious isolated point produced by a restricted parametrization. Result: the best solution from an eight-parameter two-peak search collapses back to near-single-peak (peak separation only about 3.3×10⁻⁶), and under the same evaluator the two-peak version actually scores slightly worse; one-dimensional scans of both center chirality and width chirality attain their maximum at zero offset, with negative second-order coefficients in both cases; in an 80-point two-dimensional chirality survey, the best nonzero candidate is still worse than zero offset by about 2.8×10⁻⁵. Conclusion: within the directions tested, the single-peak mirror-symmetric candidate is locally stable, with no identifiable ascent direction. The round also honestly records a coordinate error in an early version (the right-wing local center was mistakenly set to c instead of the correct 1-c, which had produced a spurious improvement on a coarse grid); this has been completely excluded and was not carried into the conclusions.
Relationship to other packages, stated as far as possible in the document's own words, not my interpretation.
“The first version mistakenly set the right-wing local center equal to c again, instead of 1-c. This does not generate a mirror-symmetric baseline, and produced a spurious coarse-grid improvement, a narrow weak-phase branch, and a contradiction between coarse and fine resolution. This batch of values has been completely excluded and did not enter this round's conclusions.” — from Section 9, “Coordinate-Error Audit,” of this package's main document.
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