pith. machine review for the scientific record. sign in
theorem

semanticGate_implies_gap_ready

proved
show as:
view math explainer →
module
IndisputableMonolith.Unification.CriticalRecognitionLoading
domain
Unification
line
161 · github
papers citing
none yet

open explainer

Generate a durable explainer page for this declaration.

open lean source

IndisputableMonolith.Unification.CriticalRecognitionLoading on GitHub at line 161.

browse module

All declarations in this module, on Recognition.

explainer page

Tracked in the explainer inventory; generation is lazy so crawlers do not trigger LLM jobs.

open explainer

depends on

used by

formal source

 158    attention ≤ phi ^ (3 : ℕ) :=
 159  h.2.2.2.1
 160
 161theorem semanticGate_implies_gap_ready
 162    {entropy entropyFloor attention signature signatureMin signatureMax z : ℝ}
 163    (h : SemanticCondensationGate entropy entropyFloor attention
 164      signature signatureMin signatureMax z) :
 165    phi ^ (45 : ℕ) ≤ z :=
 166  h.2.2.2.2
 167
 168/-! ## §4. Controller state and certificate -/
 169
 170/-- Minimal runtime state needed by the governor. -/
 171structure ControllerState where
 172  area : ℝ
 173  demand : ℝ
 174  entropy : ℝ
 175  entropyFloor : ℝ
 176  attention : ℝ
 177  signature : ℝ
 178  signatureMin : ℝ
 179  signatureMax : ℝ
 180  z : ℝ
 181  hArea : 0 < area
 182  hDemand : 0 < demand
 183
 184/-- The full critical-loading condition. -/
 185def IsCriticalRecognitionLoading (rhoMin : ℝ) (s : ControllerState) : Prop :=
 186  InCriticalBand rhoMin s.area s.demand ∧
 187    SemanticCondensationGate
 188      s.entropy s.entropyFloor s.attention
 189      s.signature s.signatureMin s.signatureMax s.z
 190
 191/-- The non-parameterized critical-loading condition. -/