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Hilbert function and Betti bound research adapter
Family 200: Eisenbud–Green–Harris and lex-plus-powers. First application triage, 9 October 2026 Australia/Brisbane.
Problem and potential new use
Symbolic algebra teams can compare homogeneous ideals with lex-plus-powers models sharing Hilbert functions and bounding graded Betti numbers.
Applicability and commercial boundary
Characteristic zero and a contained regular sequence of degrees at least two matter. Existence is not a cheap ideal constructor or generic polynomial optimization improvement.
Initial business decision
Research reference or conditional symbolic/verification engineering. No practical implementation, recurring buyer need or profitability has been demonstrated; a weak business bridge is explicitly deferred.
Next verification action
Inspect constructive degree bounds and compare one existing Gröbner-basis workflow.
Evidence scope
The catalog statement was individually reviewed. Main-paper proof, construction effectiveness and selected formal scope comparison remain queued. No independent Lean verification was run. Source revision fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb. See source metadata.