IndisputableMonolith.CrossDomain.ParadigmShiftLattice
The module CrossDomain.ParadigmShiftLattice models paradigm shifts as lattice elements whose total count is six, matching the faces of the 3-cube Q₃. It separates HistoricalShift and FutureShift collections, defines their cardinalities, and certifies the correspondence through matching lemmas. Researchers applying lattice models to historical transitions in foundational physics would cite it. The module builds via successive set definitions and direct equality checks on counts.
claimThe module introduces sets $HistoricalShift$ and $FutureShift$ with $|HistoricalShift| + |FutureShift| = 6$ and a bijection to the six faces of the cube $Q_3$.
background
This module operates in the cross-domain extension of Recognition Science. It defines HistoricalShift as the collection of realized past paradigm changes and FutureShift as the set of anticipated ones. AllParadigmShifts forms their union, with cardinality functions historicalCount and futureCount. The cubeFaces definition lists the six faces of Q₃ while shifts_match_cube_faces asserts the exact correspondence. The module imports only Mathlib for basic set and finiteness operations.
proof idea
This is a definition module with supporting lemmas. The structure proceeds by defining the two shift sets, computing their separate counts, proving the sum equals six via five_plus_one_equals_six, and establishing the lattice match to cube faces through shifts_match_cube_faces together with future_slot_realised.
why it matters in Recognition Science
The module supplies the lattice model for paradigm shifts that aligns with the three spatial dimensions D=3 from the forcing chain. It feeds the certification object ParadigmShiftLatticeCert and the associated theorem paradigmShiftLatticeCert. It addresses how discrete historical and future shifts fit the overall Recognition structure without reference to specific constants.
scope and limits
- Does not derive the shift sets from the J-cost equation or Recognition Composition Law.
- Does not assign explicit content or timing to individual shifts beyond cardinality.
- Does not prove uniqueness or invariance properties of the lattice.
- Does not connect the six faces to the phi-ladder or mass formulas.
declarations in this module (12)
-
inductive
HistoricalShift -
inductive
FutureShift -
theorem
historicalCount -
theorem
futureCount -
abbrev
AllParadigmShifts -
theorem
allShifts_count -
def
cubeFaces -
theorem
shifts_match_cube_faces -
theorem
future_slot_realised -
theorem
five_plus_one_equals_six -
structure
ParadigmShiftLatticeCert -
def
paradigmShiftLatticeCert