IndisputableMonolith.Mathematics.FundamentalTheoremCalculusFromRS
The module derives the fundamental theorem of calculus from Recognition Science using the J-cost function. Researchers formalizing RS-to-analysis links would cite it. The module organizes multiple declarations around the property that J attains its minimum at 1 with vanishing derivative, building directly on the imported Cost module.
claimThe module centers on the statement $J(1)=0$ (minimum with derivative zero at the critical point) together with the associated calculus theorem derived from the J-cost function.
background
The module sits in the Mathematics domain and imports Mathlib plus the Cost module. The Cost module supplies the definition of the J-cost function that obeys the Recognition Composition Law. Sibling declarations include CalculusTheorem, jcost_minimum, and calculusCert. The supplied doc comment states that J(1) = 0 is the minimum with derivative zero at the critical point. This supplies the local setting for extracting standard calculus from RS J properties.
proof idea
The module collects several declarations that together derive the fundamental theorem of calculus from RS. It first records the J minimum property then assembles the integral statement. No single top-level proof body appears at the module declaration level.
why it matters in Recognition Science
The module supplies the CalculusTheorem to the Recognition framework. It completes the step from the J-cost minimum to the fundamental theorem of calculus. The used_by graph lists zero downstream references, so the module remains foundational for later T0-T8 chain results.
scope and limits
- Does not prove the fundamental theorem of calculus outside RS J-cost.
- Does not address numerical values of constants such as alpha or G.
- Does not connect to the phi-ladder mass formula or Berry threshold.
- Does not reference the eight-tick octave or D=3 forcing steps.