recognition /
Modal /
Modal.Actualization /
explainer
No prose has been written for this declaration yet. The Lean source and graph data below render
without it.
generate prose now
formal statement (Lean)
236 theorem collapse_automatic (c : Config) (_ : J c.value ≥ collapse_threshold) :
237 has_definite_pointer (Actualize c) ∨ J (Actualize c).value < collapse_threshold := by
proof body
Term-mode proof.
238 right
239 simp only [Actualize, identity_config, J_at_one, collapse_threshold]
240 norm_num
241
242 /-! ## The Actualization Operator -/
243
244 /-- **THE ACTUALIZATION OPERATOR A**: Maps current to actualized configuration.
245
246 A : Config → Config
247 A(c) = argmin_{y ∈ P(c)} J(y)
248
249 This is dual to the Possibility operator P:
250 - P gives what COULD happen
251 - A gives what DOES happen
252
253 Together, P and A completely characterize RS modal dynamics. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (20)
Lean names referenced from this declaration's body.
J_at_one
in IndisputableMonolith.Algebra.CostAlgebra
decl_use
A
in IndisputableMonolith.Foundation.IntegrationGap
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
Config
in IndisputableMonolith.Gravity.ILG
decl_use
A
in IndisputableMonolith.Masses.Anchor
decl_use
J_at_one
in IndisputableMonolith.Masses.BaselineDerivation
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
A
in IndisputableMonolith.Modal.Actualization
decl_use
collapse_threshold
in IndisputableMonolith.Modal.Actualization
decl_use
has_definite_pointer
in IndisputableMonolith.Modal.Actualization
decl_use
Actualize
in IndisputableMonolith.Modal.Possibility
decl_use
Config
in IndisputableMonolith.Modal.Possibility
decl_use
identity_config
in IndisputableMonolith.Modal.Possibility
decl_use
J_at_one
in IndisputableMonolith.Modal.Possibility
decl_use
Possibility
in IndisputableMonolith.Modal.Possibility
decl_use
and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
decl_use
J_at_one
in IndisputableMonolith.QFT.HiggsMechanism
decl_use
value
in IndisputableMonolith.QFT.SpinStatistics
decl_use