gate_discreteness
plain-language theorem explainer
The gate_discreteness definition records the third necessity gate asserting that continuous configuration spaces cannot possess stable minima under the J-cost. Researchers constructing alternative physical frameworks would cite it to show that their continuum models violate the selection rule derived from cost minimization. The definition is a direct record construction that marks the gate as proven by reference to the DiscretenessForcing module.
Claim. The discreteness necessity gate is the record whose name field equals ``Discreteness Forcing'', whose proven field equals true, and whose violation_meaning field equals ``Continuous configuration space with stable minima''.
background
A NecessityGate is a structure with three fields: a name string, a boolean proven flag, and a string describing the physical meaning of a violation. This module formalizes the inevitability structure of Recognition Science under the cost-as-foundation approach, where selection occurs by minimizing a unique cost function. The module documentation lists six necessity gates that any alternative must violate, with gate 3 being discreteness: continuous configurations cannot stabilize under J. The definition depends on the NecessityGate structure and references the upstream DiscretenessForcing result.
proof idea
This is a one-line wrapper that applies the NecessityGate structure constructor, populating the name field with ``Discreteness Forcing'', setting the proven flag to true with a comment pointing to DiscretenessForcing.lean, and filling the violation_meaning field with the description of continuous configuration space with stable minima.
why it matters
This gate is collected into the all_gates list that enumerates every necessity constraint for the inevitability theorem. It fills the discreteness slot in the module's statement that any zero-parameter framework deriving observables must reduce to Recognition Science or break one of the CPM/cost necessities. The gate connects to the forcing chain by enforcing that continuous spaces lack stable minima, which is required before self-similarity can force phi and before dimension D equals 3 can be derived.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.