Harmonic growth dimension comparison limitation

Family 361: Failure of integer-degree harmonic dimension comparison. First application triage, 9 October 2026 Australia/Brisbane.

Problem and potential new use

Geometry researchers can flag the proposed Euclidean dimension upper bound violated on specially constructed nonnegative-Ricci metrics.

Applicability and commercial boundary

The metric may depend on growth degree k, and exact integer growth classes differ from finite sampled basis dimensions. No new general numerical basis solver follows.

Initial business decision

Research or conditional engineering only. A practical implementation, recurring buyer problem and willingness to pay have not been established. Mathematical usefulness alone is insufficient evidence for a standalone lucrative product.

Next verification action

Extract a finite exact example and preserve the metric-dependence quantifier.

Evidence scope

The catalog statement was individually reviewed. The manuscript proof and formal-scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.

A counterexample to integer-degree harmonic dimension comparison.