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Round 5 v0.5 2026-07-26

Contact-Event Equations, a Non-Smooth KKT System, and an Isolated Five-Link Candidate

Shifts from black-box branch tracking to explicit contact events: exact analytic phase formulas for the four cusps, plus branch-pressure stationarity conditions, assembled into a combined event–KKT system of 9 equations in 9 unknowns. The numerical solution s=0.998903757132509, together with a full-rank 9×9 Jacobian and the convergence of all 40 randomly perturbed initial values back to the same root, strongly supports this being a numerically isolated stationary point.

Numerical structural reconstruction; not a formal proof; not an interval certificate — Stage status as self-declared by the in-package documents, reproduced verbatim. “The real achievement is not the improvement beyond the decimal point, but writing out in full the reason the candidate was generated.”

Connections · Connections

Relationship to other packages, stated as far as possible in the document's own words, not my interpretation.

“This improvement is only about 10⁻⁹; its significance lies not in substantively raising the Moser lower bound, but in projecting Round 4's black-box equalization point onto a stationary solution of the exact event equations… four cusp contact events in equalization + four-branch pressure stationarity = a numerically isolated five-link candidate.” — excerpted from Section 5 and the Conclusion of this package's main document.

Core Content of Round 5

Analytic phase formulas for the four exact contact events, the event scale function, the nine-equation event–KKT system, the solution of the event system, the branch-pressure ledger, the non-smooth local-minimum check, isolation diagnostics (Jacobian rank, perturb-and-return-to-root testing), a full phase audit, and Round 6's two paths (topology boundary-crossing search vs. a local topological-limit certificate).

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Files · Files

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