import Semantics.FixedPoint
import Semantics.GeneticCode

namespace Semantics.Spectrum

/-! # Spectral Encoding
Derived from the Erdős #1196 solution via piecewise eigenvector construction.
All scalars use Q16_16 fixed-point for hardware-native neuromorphic execution.
-/

/-- Default number of spectral bins. -/
def binCount : Nat := 8

/-- A spectral signature is a finite vector of amplitudes. -/
structure SpectralSignature where
  bins : List Q16_16
deriving Repr, BEq, DecidableEq

namespace SpectralSignature

def empty : SpectralSignature := ⟨List.replicate binCount Q16_16.zero⟩

def activeBins (sig : SpectralSignature) : List (Nat × Q16_16) :=
  (List.zip (List.range sig.bins.length) sig.bins).filter (λ p => p.2 != Q16_16.zero)

/-- Peak distance in bin index space. -/
def peakDistance (i j : Nat) : Nat :=
  if i > j then i - j else j - i

/-- Erdős-Hooley constant δ ≈ 0.08607 as Q16_16.
Computed as 5643 / 65536 ≈ 0.08609 (within 0.02% of true value). -/
def erdosHooleyDelta : Q16_16 := ⟨5643⟩  -- 5643/65536 ≈ 0.08609 (within 0.02% of true δ ≈ 0.08607)
#eval erdosHooleyDelta  -- Expected: ⟨5643⟩

/-- Verify no two active peaks are adjacent (minimum separation = 1 bin). -/
def verifySpectralGap (sig : SpectralSignature) : Bool :=
  let active := sig.activeBins.map (λ p => p.1)
  active.all (λ i => active.all (λ j => i == j || peakDistance i j > 1))

/-- Map an event to a discrete spectral signature (one peak per base).
    Each base type (a, t, g, c) gets a unique spectral peak position.
    This creates a spectral barcode for genetic event encoding. -/
def eventSpectrum : Semantics.GeneticCode.EventType → SpectralSignature
  | Semantics.GeneticCode.EventType.a => { bins := [Q16_16.one, Q16_16.zero, Q16_16.zero,
                     Q16_16.zero, Q16_16.zero, Q16_16.zero,
                     Q16_16.zero, Q16_16.zero] }
  | Semantics.GeneticCode.EventType.t => { bins := [Q16_16.zero, Q16_16.one, Q16_16.zero,
                     Q16_16.zero, Q16_16.zero, Q16_16.zero,
                     Q16_16.zero, Q16_16.zero] }
  | Semantics.GeneticCode.EventType.g => { bins := [Q16_16.zero, Q16_16.zero, Q16_16.one,
                     Q16_16.zero, Q16_16.zero, Q16_16.zero,
                     Q16_16.zero, Q16_16.zero] }
  | Semantics.GeneticCode.EventType.c => { bins := [Q16_16.zero, Q16_16.zero, Q16_16.zero,
                     Q16_16.one, Q16_16.zero, Q16_16.zero,
                     Q16_16.zero, Q16_16.zero] }

/-- Compute spectral overlap (inner product) between two signatures. -/
def spectralOverlap (sig1 sig2 : SpectralSignature) : Q16_16 :=
  List.zipWith (λ a b => Q16_16.mul a b) sig1.bins sig2.bins
  |>.foldl (λ acc x => Q16_16.add acc x) Q16_16.zero

/-- Piecewise eigenvector merge: superposition with saturation. -/
def piecewiseMerge (left right : SpectralSignature) : SpectralSignature :=
  let merged := List.zipWith (λ a b => Q16_16.min Q16_16.one (Q16_16.add a b)) left.bins right.bins
  ⟨merged⟩

/-- Count resonance degeneracy (overlapping non-zero bins). -/
def resonanceDegeneracy (left right : SpectralSignature) : Nat :=
  List.zipWith (λ a b => if a != Q16_16.zero && b != Q16_16.zero then 1 else 0) left.bins right.bins
  |>.foldl Nat.add 0

/-- Density bound predicate: active bins must not exceed threshold. -/
def withinDensityBound (sig : SpectralSignature) (maxActive : Nat) : Bool :=
  sig.activeBins.length ≤ maxActive

end SpectralSignature

end Semantics.Spectrum