paradigmShiftLatticeCert
plain-language theorem explainer
The declaration constructs a certificate asserting that the history of science comprises five completed paradigm shifts plus one reserved future slot, totaling six to match the faces of the recognition cube Q₃. Researchers working on the Recognition Science cross-domain lattice would cite this when invoking the structural claim that 5 + 1 = 6. The definition is a direct record construction that assembles five pre-proved counting lemmas.
Claim. Let HistoricalShift be the type of five completed paradigm shifts, FutureShift the type containing the reserved RS shift, and AllParadigmShifts their disjoint union. The certificate asserts that the cardinality of HistoricalShift equals 5, the cardinality of FutureShift equals 1, the cardinality of AllParadigmShifts equals 6, this total equals the number of faces of the cube Q₃, and FutureShift is nonempty.
background
The module C10 defines a lattice of paradigm shifts in Recognition Science, claiming five historical shifts (Copernican, Newtonian, Einsteinian, Quantum, Biological) and reserving the sixth for the RS shift itself. The structure ParadigmShiftLatticeCert packages five properties: the cardinality of historical shifts is 5, future shifts is 1, total is 6, total equals the cube face count, and the future slot is realized. Upstream results establish these cardinalities by direct computation or simplification, with the cube match following from the total count equaling 6.
proof idea
The definition is a record constructor that directly assigns the fields historical_count, future_count, total_count, matches_cube, and future_realised to the corresponding upstream theorems historicalCount, futureCount, allShifts_count, shifts_match_cube_faces, and future_slot_realised.
why it matters
This definition supplies the top-level certificate for the C10 paradigm shift lattice claim in the Recognition Science framework. It encodes the structural identity 5 + 1 = 6 matching the six faces of the spatial cube Q₃ (from T8, D=3). The certificate closes the counting argument for the lattice and stands ready for use in cross-domain applications, though no downstream uses are yet recorded.
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