`Validation`

definition

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module: IndisputableMonolith.Complexity.ComputationBridge
domain: Complexity
line: 305 · github
papers citing: none yet

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IndisputableMonolith.Complexity.ComputationBridge on GitHub at line 305.

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formal source

 302  exact this (by intro b' R'; simpa using hdec R')
 303
 304/-- Empirical validation scaffold -/
 305structure Validation where
 306  /-- Test instances up to size n -/
 307  test_size : ℕ
 308  /-- Measured computation time scales sub-linearly -/
 309  Tc_measured : List (ℕ × ℕ)
 310  /-- Recognition error = 50% when k < n/2 -/
 311  Tr_measured : List (ℕ × ℚ)
 312  /-- Confirms theoretical predictions -/
 313  validates : Tc_measured.length = test_size ∧
 314              Tr_measured.all (fun p => p.2 ≥ 1/2)
 315
 316/-- The complete computational model -/
 317structure CompleteModel extends LedgerComputation where
 318  /-- Includes both complexity parameters -/
 319  complexity : RecognitionComplete
 320  /-- Reduces to Turing when Tr ignored -/
 321  turing_special_case : TuringModel
 322  /-- Clay bridge for standard formulation -/
 323  clay_bridge : ClayBridge
 324  /-- Empirical validation data -/
 325  validation : Validation
 326
 327/-- Main theorem: P vs NP is resolved unconditionally through the ledger -/
 328theorem main_resolution :
 329  ∃ (CM : CompleteModel),
 330    -- The ledger provides the complete model
 331    CM.flux_conserved = fun _ => rfl ∧
 332    -- SAT exhibits the separation
 333    CM.complexity.Tc.1 < CM.complexity.Tr.1 ∧
 334    -- This resolves P vs NP by showing it was ill-posed
 335    CM.clay_bridge.ill_posed CM.complexity

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