/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Research Stack Team

HyperbolicEncoding.lean — Hyperbolic Manifold Coordinate Encoding

Replaces infra/hyperbolic_encoding.py with a formal Lean module.
Defines Poincaré disk coordinates and Möbius transformations for semantic vector encoding.

Per AGENTS.md:
  - Q16_16 for scoring (§1.4)
  - PascalCase types, camelCase functions (§2)
  - Theorems for correctness (§4)
  - No proof placeholders in committed code (§1.6)
-/

import Mathlib.Data.Nat.Basic
import Mathlib.Data.List.Basic
import Std

namespace Semantics.HyperbolicEncoding

-- ═══════════════════════════════════════════════════════════════════════════
-- §0  Q16_16 Fixed-Point Arithmetic
-- ═══════════════════════════════════════════════════════════════════════════

structure Q16_16 where
  raw : Int
  deriving Repr, DecidableEq, Inhabited

namespace Q16_16
  def zero : Q16_16 := ⟨0⟩
  def one : Q16_16 := ⟨65536⟩
  def ofFrac (num denom : Nat) : Q16_16 :=
    if denom = 0 then zero else ⟨(num * 65536) / denom⟩
  def toNat (q : Q16_16) : Nat := q.raw.toNat
end Q16_16

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Hyperbolic Vector Structure
-- ═══════════════════════════════════════════════════════════════════════════

structure HyperbolicVector where
  x : Q16_16  -- x coordinate in Poincaré disk
  y : Q16_16  -- y coordinate in Poincaré disk
  dimension : Nat  -- Original dimension
  norm : Q16_16  -- Distance from origin
  deriving Repr, Inhabited

-- ═══════════════════════════════════════════════════════════════════════════
-- ═══════════════════════════════════════════════════════════════════════════
-- §2  Dimension Weights for 14D Semantic Vectors
-- ═══════════════════════════════════════════════════════════════════════════

def dimensionWeights : List Q16_16 :=
  [
    Q16_16.ofFrac 19 10000,  -- 0.0019
    Q16_16.ofFrac 20 10000,  -- 0.0020
    Q16_16.ofFrac 24 10000,  -- 0.0024
    Q16_16.ofFrac 25 10000,  -- 0.0025
    Q16_16.ofFrac 23 10000,  -- 0.0023
    Q16_16.ofFrac 16 10000,  -- 0.0016
    Q16_16.ofFrac 19 10000,  -- 0.0019
    Q16_16.ofFrac 18 10000,  -- 0.0018
    Q16_16.ofFrac 20 10000,  -- 0.0020
    Q16_16.ofFrac 25 10000,  -- 0.0025
    Q16_16.ofFrac 18 10000,  -- 0.0018
    Q16_16.ofFrac 22 10000,  -- 0.0022
    Q16_16.ofFrac 21 10000,  -- 0.0021
    Q16_16.ofFrac 26 10000   -- 0.0026 (dominant dimension)
  ]

-- ═══════════════════════════════════════════════════════════════════════════
-- §3  Encoding/Decoding Operations
-- ═══════════════════════════════════════════════════════════════════════════

/-- Encode 14D semantic vector to Poincaré disk coordinates -/
def encodeToPoincare (vector : List Q16_16) : HyperbolicVector :=
  if vector.length ≠ 14 then
    { x := Q16_16.zero, y := Q16_16.zero, dimension := 14, norm := Q16_16.zero }
  else
    -- Weighted projection to 2D using even/odd indices
    let xSum := List.foldl (fun acc (i : Nat) =>
      if i % 2 = 0 then
        let weight := List.getD dimensionWeights i Q16_16.zero
        let val := List.getD vector i Q16_16.zero
        { raw := acc.raw + (val.raw * weight.raw) / 65536 }
      else
        acc
    ) Q16_16.zero (List.range 14)
    
    let ySum := List.foldl (fun acc (i : Nat) =>
      if i % 2 = 1 then
        let weight := List.getD dimensionWeights i Q16_16.zero
        let val := List.getD vector i Q16_16.zero
        { raw := acc.raw + (val.raw * weight.raw) / 65536 }
      else
        acc
    ) Q16_16.zero (List.range 14)
    
    -- Simplified norm calculation (avoid sqrt for fixed-point)
    let normSquared := (xSum.raw * xSum.raw + ySum.raw * ySum.raw) / 65536
    let norm := Q16_16.ofFrac normSquared.toNat 65536
    
    {
      x := xSum,
      y := ySum,
      dimension := 14,
      norm := norm
    }

/-- Decode from Poincaré disk back to 14D vector space -/
def decodeFromPoincare (hyperbolic : HyperbolicVector) : List Q16_16 :=
  -- Expand back to 14D using inverse projection
  let evenWeightSum := List.foldl (fun acc (_w : Q16_16) => 
    { raw := acc.raw + _w.raw }
  ) Q16_16.zero (List.zipWith (fun w i => if i % 2 = 0 then w else Q16_16.zero) dimensionWeights (List.range 14))
  
  let oddWeightSum := List.foldl (fun acc (_w : Q16_16) => 
    { raw := acc.raw + _w.raw }
  ) Q16_16.zero (List.zipWith (fun w i => if i % 2 = 1 then w else Q16_16.zero) dimensionWeights (List.range 14))
  
  let xContrib := if evenWeightSum.raw = 0 then Q16_16.zero else { raw := (hyperbolic.x.raw * 65536) / (evenWeightSum.raw + 1) }
  let yContrib := if oddWeightSum.raw = 0 then Q16_16.zero else { raw := (hyperbolic.y.raw * 65536) / (oddWeightSum.raw + 1) }
  
  List.zipWith (fun _w i =>
    if i % 2 = 0 then
      let weight := List.getD dimensionWeights i Q16_16.zero
      if evenWeightSum.raw = 0 then Q16_16.zero else { raw := (xContrib.raw * weight.raw) / 65536 }
    else
      let weight := List.getD dimensionWeights i Q16_16.zero
      if oddWeightSum.raw = 0 then Q16_16.zero else { raw := (yContrib.raw * weight.raw) / 65536 }
  ) dimensionWeights (List.range 14)

-- ═══════════════════════════════════════════════════════════════════════════
-- §4  Möbius Transformation
-- ═══════════════════════════════════════════════════════════════════════════

/-- Apply Möbius transformation to point z in Poincaré disk -/
def mobiusTransform (a z : HyperbolicVector) : HyperbolicVector :=
  let aNormSq := (a.x.raw * a.x.raw + a.y.raw * a.y.raw) / 65536
  let zNormSq := (z.x.raw * z.x.raw + z.y.raw * z.y.raw) / 65536
  let az := (a.x.raw * z.x.raw + a.y.raw * z.y.raw) / 65536
  
  -- Möbius transformation formula
  let numeratorX := ((65536 + 2*az + aNormSq) * z.x.raw + (65536 + zNormSq) * a.x.raw) / 65536
  let numeratorY := ((65536 + 2*az + aNormSq) * z.y.raw + (65536 + zNormSq) * a.y.raw) / 65536
  let denominator := (65536 + 2*az + aNormSq + zNormSq)
  
  let newX := if denominator = 0 then Q16_16.zero else { raw := (numeratorX * 65536) / denominator }
  let newY := if denominator = 0 then Q16_16.zero else { raw := (numeratorY * 65536) / denominator }
  
  let newNormSq := (newX.raw * newX.raw + newY.raw * newY.raw) / 65536
  let newNorm := Q16_16.ofFrac newNormSq.toNat 65536
  
  {
    x := newX,
    y := newY,
    dimension := 2,
    norm := newNorm
  }

-- ═══════════════════════════════════════════════════════════════════════════
-- §5  Hyperbolic Distance
-- ═══════════════════════════════════════════════════════════════════════════

/-- Compute hyperbolic distance between two points in Poincaré disk -/
def hyperbolicDistance (x y : HyperbolicVector) : Q16_16 :=
  let xNormSq := (x.x.raw * x.x.raw + x.y.raw * x.y.raw) / 65536
  let yNormSq := (y.x.raw * y.x.raw + y.y.raw * y.y.raw) / 65536
  let diffX := x.x.raw - y.x.raw
  let diffY := x.y.raw - y.y.raw
  let diffNormSq := (diffX * diffX + diffY * diffY) / 65536
  
  let numerator := 2 * diffNormSq
  let denominator := (65536 - xNormSq) * (65536 - yNormSq) / 65536
  
  if denominator = 0 then
    Q16_16.one
  else
    let ratio := (numerator * 65536) / denominator
    -- Simplified: return ratio as distance approximation
    -- In production, would use acosh(1 + ratio)
    Q16_16.ofFrac ratio.toNat 65536

-- ═══════════════════════════════════════════════════════════════════════════
-- §6  Cache Structure
-- ═══════════════════════════════════════════════════════════════════════════

structure HyperbolicCache where
  entries : List (String × HyperbolicVector)
  deriving Repr, Inhabited

/-- Initialize empty hyperbolic cache -/
def initHyperbolicCache : HyperbolicCache :=
  { entries := [] }

/-- Get or encode vector from cache -/
def getOrEncode (cache : HyperbolicCache) (vector : List Q16_16) (key : String) : HyperbolicCache × HyperbolicVector :=
  let existing := List.find? (·.1 = key) cache.entries
  match existing with
  | some (_, hv) => (cache, hv)
  | none =>
    let hv := encodeToPoincare vector
    ({ entries := (key, hv) :: cache.entries }, hv)

-- ═══════════════════════════════════════════════════════════════════════════
-- §7  Theorems
-- ═══════════════════════════════════════════════════════════════════════════

/-- Dimension weights list has 14 elements -/
theorem dimensionWeightsLength : dimensionWeights.length = 14 := by
  rfl

-- ═══════════════════════════════════════════════════════════════════════════
-- §8  Example Usage
-- ═══════════════════════════════════════════════════════════════════════════

#eval let vector := List.replicate 14 (Q16_16.ofFrac 20 10000)
      encodeToPoincare vector

#eval let hv := { x := Q16_16.ofFrac 30 100, y := Q16_16.ofFrac 40 100, dimension := 14, norm := Q16_16.ofFrac 50 100 }
      decodeFromPoincare hv

#eval let a := { x := Q16_16.ofFrac 30 100, y := Q16_16.ofFrac 20 100, dimension := 2, norm := Q16_16.ofFrac 36 100 }
      let z := { x := Q16_16.ofFrac 50 100, y := Q16_16.ofFrac 40 100, dimension := 2, norm := Q16_16.ofFrac 64 100 }
      mobiusTransform a z

#eval let x := { x := Q16_16.ofFrac 10 100, y := Q16_16.ofFrac 10 100, dimension := 2, norm := Q16_16.ofFrac 14 100 }
      let y := { x := Q16_16.ofFrac 20 100, y := Q16_16.ofFrac 20 100, dimension := 2, norm := Q16_16.ofFrac 28 100 }
      hyperbolicDistance x y

end Semantics.HyperbolicEncoding