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Allen–Cahn classification and phase-field research reference
Family 375: De Giorgi's conjecture in dimension eight. First source-informed review, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Phase-field researchers can compare entire monotone dimension-eight Allen–Cahn solutions and stable dimension-seven solutions with the planar heteroclinic classification.
Applicability and commercial boundary
These are exact entire-space, monotonicity or stability statements. They do not classify arbitrary transient simulations, finite domains, noisy interfaces, nonstandard potentials or higher-dimensional models.
Initial business decision
Research infrastructure. Commercial demand and profitability remain hypotheses. Research usefulness is not evidence of a buyer budget.
Next verification action
Use the explicit planar heteroclinic as a reference and inspect whether a numerical test genuinely meets the entire-solution or stability assumptions.
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.