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Free boundary critical-dimension research benchmark
Family 367: The critical dimension for the one-phase Bernoulli problem. First source-informed review, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Free boundary researchers can organize expected singularity behavior by dimension and examine whether a proposed solver test problem models a true one-phase energy minimizer.
Applicability and commercial boundary
Critical dimension seven and the dimension n−7 singular-set bound concern minimizers. They do not certify a finite mesh output or apply to every free boundary equilibrium, higher-order model or local stationary point.
Initial business decision
Research infrastructure. Commercial demand and profitability remain hypotheses. Research usefulness is not evidence of a buyer budget.
Next verification action
Extract a concrete cone and identify a separately justified discretization or minimization procedure before a benchmark implementation.
Evidence scope
The catalog statement and main-paper abstract or introductory theorem passages were individually reviewed. Available family-level scope documents were inspected, with attention to version differences and exclusions. This is a first application triage, not a full proof audit or independent Lean verification. Family 376 has nine paper abstracts inspected; selected scopes are not assumed to cover all nine papers in full. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.