On this page
Localized homotopy finite-generation contract
Family 313: Finite generation for the $K(n)$-local sphere. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Record degreewise finite generation over p-adic integers for the specified localized sphere and finite-complex homotopy groups.
Applicability and commercial boundary
Degreewise finiteness gives neither a uniform rank bound nor a terminating general computation procedure.
Initial business decision
Research reference or conditional symbolic/verification engineering. No recurring buyer need, practical implementation or profitability has been demonstrated. Defer a standalone commercial product until a constructive example and a measurable workflow improvement exist. These records also identify unsupported inferences that an evidence platform could flag.
Next verification action
Inspect effective bounds at one prime, height and degree.
Evidence scope
The repository catalog statement was individually read. Main-paper construction, effectiveness and selected formal-scope comparison remain queued for this record. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.