futureCount
The theorem shows that the inductive type of future paradigm shifts contains exactly one element, the recognition science shift. Researchers formalizing the history of science in the Recognition framework cite it to fix the reserved sixth slot. The proof is a one-line decision procedure that uses the derived Fintype instance on the single-constructor inductive type.
claimLet $S$ be the inductive type whose sole constructor represents the reserved recognition-science paradigm shift. Then the cardinality of $S$ equals 1.
background
The Paradigm Shift Lattice module encodes the structural claim that five completed shifts (Copernican, Newtonian, Einsteinian, Quantum, Biological) plus one reserved future shift total six, matching the faces of the recognition cube $Q_3$. FutureShift is the inductive type with constructor recognitionScience, equipped with DecidableEq, Repr, BEq and Fintype instances. The upstream inductive definition supplies the finite enumeration used here.
proof idea
The proof is a one-line wrapper that applies the decide tactic to the Fintype.card expression. The tactic uses the automatically derived Fintype instance on the inductive type FutureShift, whose single constructor yields cardinality 1.
why it matters in Recognition Science
This result supplies the future_count field to the ParadigmShiftLatticeCert definition and is invoked inside allShifts_count to obtain the total cardinality 6. It thereby completes the lattice certification that five historical shifts plus the recognition-science shift equal the six faces of $Q_3$, directly supporting the module's claim that six is the cube-face count.
scope and limits
- Does not enumerate or describe the five historical shifts.
- Does not assert physical realization or timing of the future shift.
- Does not derive any Recognition Science constants or mass formulas.
- Does not prove that the total of six shifts is exhaustive beyond the cube-face analogy.
Lean usage
theorem total_six : Fintype.card AllParadigmShifts = 6 := by simp only [AllParadigmShifts, Fintype.card_sum, historicalCount, futureCount]formal statement (Lean)
27theorem futureCount : Fintype.card FutureShift = 1 := by decide
proof body
28