IndisputableMonolith.CrossDomain.ParadigmShiftLattice
The module defines paradigm shifts as the six faces of the three-cube Q₃. It introduces HistoricalShift and FutureShift types, their counts, the AllParadigmShifts collection, and the cubeFaces enumeration together with matching lemmas. Cross-domain modelers cite it when embedding lattice geometry into shift dynamics. Content consists of definitions plus short algebraic checks such as five plus one equals six.
claimThe six faces of the cube $Q_3$ are placed in bijection with paradigm shifts, where historical and future shifts are collected into a single set whose cardinality satisfies the relation five plus one equals six.
background
The module sits in the CrossDomain section and imports only Mathlib. It uses the three-dimensional cube Q₃ whose six faces arise directly from the spatial dimension D=3 fixed in the forcing chain. HistoricalShift and FutureShift are introduced as separate inductive types; AllParadigmShifts assembles them; cubeFaces lists the geometric faces; and auxiliary definitions historicalCount, futureCount, and allShifts_count record cardinalities.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the lattice geometry that ParadigmShiftLatticeCert and paradigmShiftLatticeCert certify. It realizes the six-face structure required by the D=3 step of the unified forcing chain and supplies the concrete objects used by downstream cross-domain lemmas.
scope and limits
- Does not treat cubes of dimension other than three.
- Does not encode concrete historical events or data.
- Does not invoke the J-cost function or phi-ladder.
- Does not address uniqueness of the shift assignment.
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