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533 lines
23 KiB
Markdown
533 lines
23 KiB
Markdown
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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SSMS_nD.lean — Variable Dimension Manifold Extension
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Extends SSMS with n-dimensional manifold support:
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§1 VariableDimensionManifold structure with dynamic n
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§2 LiftingOperator L_{1D→n} for sequential data
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§3 HolonomicConstraint system with m constraints
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§4 Dynamic ACI for cross-dimensional collision
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§5 BettiSwooshND over [1, n_max]
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§6 SUBLEQ variable-n kernels
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§7 Dimension selection via potential minimization
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§8 PhantomTideQ: Adaptive phantom coupling with Q16.16
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Per Clean Room Protocol: All math from public sources only.
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Per AGENTS.md §1.4: All hot-path code uses Q16_16 fixed-point.
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-/
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import Mathlib.Data.Nat.Basic
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import Mathlib.Data.Int.Basic
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import Mathlib.Data.Array.Basic
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import Mathlib.Tactic
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import Semantics.SSMS
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import Semantics.FixedPoint
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namespace Semantics.SSMS_nD
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open Semantics.SSMS
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open Semantics.Q16_16
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-- ════════════════════════════════════════════════════════════
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-- §1 Variable Dimension Manifold Structure
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-- M_i = (n, c ∈ R^n, Σ ∈ R^{n×n}, θ ∈ R^p, σ)
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-- ════════════════════════════════════════════════════════════
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/-- Variable-n manifold: dimensionality determined at spawn time. -/
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structure VarDimManifold where
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n : Nat -- dimensionality (1 to n_max)
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center : Array Q16_16 -- n coordinates
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sizeN : center.size = n
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metric : Array Q16_16 -- upper-triangular Σ: n(n+1)/2 entries
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sizeMetric : metric.size = n * (n + 1) / 2
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orient : Array Q16_16 -- orientation params: n(n-1)/2 for SO(n)
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sizeOrient : orient.size = n * (n - 1) / 2
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energy : Q16_16 -- gradient energy (spawn pressure)
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sigma : Bool -- activation status
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deriving Repr
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instance : Inhabited VarDimManifold where
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default :=
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{ n := 0, center := #[], sizeN := by simp
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, metric := #[], sizeMetric := by simp
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, orient := #[], sizeOrient := by simp
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, energy := zero, sigma := true }
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/-- Calculate total scalar nodes needed for n-dim manifold. -/
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def scalarCount (n : Nat) : Nat :=
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n + (n * (n + 1) / 2) + (n * (n - 1) / 2)
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/-- Maximum dimension supported (SRAM constraint). -/
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def nMax : Nat := 16
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/-- Validate manifold dimension within bounds. -/
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def validN (n : Nat) : Prop := n ≥ 1 ∧ n ≤ nMax
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theorem scalarCountMonotonic (n : Nat) (h : n ≥ 1) :
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scalarCount n ≥ scalarCount 1 := by
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simp [scalarCount]
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have h1 : n * (n + 1) / 2 ≥ 1 := by
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have h2 : n * (n + 1) ≥ 2 := by
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have h3 : n ≥ 1 := h
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have h4 : n + 1 ≥ 2 := by omega
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have h5 : n * (n + 1) ≥ 1 * 2 := Nat.mul_le_mul h3 h4
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simp at h5
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exact h5
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omega
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have h2 : n * (n - 1) / 2 ≥ 0 := by omega
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omega
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-- ════════════════════════════════════════════════════════════
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-- §2 LiftingOperator L_{1D→n}
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-- Lifts 1D sequence interval [t0, t1] to R^n
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-- ════════════════════════════════════════════════════════════
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/-- 1D sequence sample at position t. -/
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structure SeqSample where
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position : Nat -- t ∈ [0, L]
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features : Array Q16_16 -- d-dimensional feature vector
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deriving Repr, Inhabited
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/-- Lifting weights: ternary matrix W_lift ∈ {-1,0,1}^{n×d}. -/
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structure LiftingWeights (n d : Nat) where
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wPos : Array Bool -- n×d positive mask
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wNeg : Array Bool -- n×d negative mask
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sizePos : wPos.size = n * d
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sizeNeg : wNeg.size = n * d
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disjoint : ∀ i : Fin (n * d),
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¬ (wPos[i]'(sizePos.symm ▸ i.isLt) ∧ wNeg[i]'(sizeNeg.symm ▸ i.isLt))
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/-- Pool 1D features over interval [t0, t1] via mean pooling. -/
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def pool1D (seq : Array SeqSample) (t0 t1 : Nat) : Array Q16_16 :=
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if h : t0 < seq.size then
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let sample0 := seq[t0]'h
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let count := (t1 - t0 + 1)
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-- Mean pooling: sum features / count
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sample0.features.map (fun f => ⟨f.val / count⟩)
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else #[]
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/-- Lifting operator: 1D pooled features → n-dim center.
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MatMul-free via ternary weights (ADD/SUB only). -/
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def lift1DToN {n d : Nat} (weights : LiftingWeights n d)
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(pooled : Array Q16_16) (hPooled : pooled.size = d) : Array Q16_16 :=
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(Array.range n).map (fun i =>
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if hi : i < n then
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let rowOffset := i * d
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(Array.range d).foldl (fun acc j =>
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if hj : j < d then
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let idx := rowOffset + j
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let p := weights.wPos[idx]'(by
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rw [weights.sizePos]
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have h1 : i * d + j < i * d + d := Nat.add_lt_add_left hj (i * d)
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have h2 : i * d + d ≤ n * d := by
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have h3 : i * d + d = (i + 1) * d := by
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calc i * d + d = i * d + 1 * d := by rw [Nat.one_mul]
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_ = (i + 1) * d := by rw [Nat.add_mul]
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rw [h3]
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exact Nat.mul_le_mul_right d (Nat.succ_le_of_lt hi)
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exact Nat.lt_of_lt_of_le h1 h2)
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let n := weights.wNeg[idx]'(by
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rw [weights.sizeNeg]
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have h1 : i * d + j < i * d + d := Nat.add_lt_add_left hj (i * d)
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have h2 : i * d + d ≤ n * d := by
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have h3 : i * d + d = (i + 1) * d := by
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calc i * d + d = i * d + 1 * d := by rw [Nat.one_mul]
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_ = (i + 1) * d := by rw [Nat.add_mul]
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rw [h3]
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exact Nat.mul_le_mul_right d (Nat.succ_le_of_lt hi)
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exact Nat.lt_of_lt_of_le h1 h2)
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let x := pooled[j]'(hPooled ▸ hj)
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if p then Q16_16.add acc x
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else if n then Q16_16.sub acc x
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else acc
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else acc
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) Q16_16.zero
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else Q16_16.zero
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)
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/-- Approximate inverse chart L^{-1}: R^n → [0, L]. -/
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def approxInverseChart (c : Array Q16_16) (L : Nat) : Nat :=
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-- Project to first coordinate, clamp to [0, L]
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if h : 0 < c.size then
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let c0 := c[0]'h
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let tRaw := c0.val / 65536 -- Convert Q16.16 to integer
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let tNat := if tRaw < 0 then 0 else tRaw.toNat
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min tNat L
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else 0
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-- ════════════════════════════════════════════════════════════
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-- §3 HolonomicConstraint System
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-- m constraints {h_j(x) = 0} for n-dim manifold
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-- ════════════════════════════════════════════════════════════
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/-- Linear constraint: Σ a_j · x_j = b. -/
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structure LinearConstraint (n : Nat) where
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coeffs : Array Q16_16 -- a[0..n-1]
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sizeCoeffs : coeffs.size = n
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rhs : Q16_16 -- b
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deriving Repr
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instance {n : Nat} : Inhabited (LinearConstraint n) where
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default := ⟨Array.mk (List.replicate n Q16_16.zero), by simp, Q16_16.zero⟩
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/-- Constraint system for n-dim manifold. -/
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structure ConstraintSystem (n m : Nat) where
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constraints : Array (LinearConstraint n) -- m constraints
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sizeConstraints : constraints.size = m
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epsilon : Q16_16 -- ACI tolerance ε
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deriving Repr
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instance {n m : Nat} : Inhabited (ConstraintSystem n m) where
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default := ⟨Array.mk (List.replicate m default), by simp, Q16_16.zero⟩
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/-- Evaluate constraint residual |Σ a_j · x_j - b|. -/
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def constraintResidual (c : LinearConstraint n) (x : Array Q16_16)
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(hX : x.size = n) : Q16_16 :=
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let dot := (Array.range n).foldl (fun acc i =>
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if hi : i < n then
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let a := c.coeffs[i]'(c.sizeCoeffs.symm ▸ hi)
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let xi := x[i]'(hX.symm ▸ hi)
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Q16_16.add acc (Q16_16.mul a xi)
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else acc
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) Q16_16.zero
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Q16_16.abs (Q16_16.sub dot c.rhs)
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/-- Check if manifold satisfies all constraints (ACI predicate). -/
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def constraintsSatisfied (sys : ConstraintSystem n m) (M : VarDimManifold)
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(hN : M.n = n) : Prop :=
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∀ i : Fin m,
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let c := sys.constraints[i]'(sys.sizeConstraints.symm ▸ i.isLt)
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(constraintResidual c M.center (M.sizeN.trans hN)).val ≤ sys.epsilon.val
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/-- Constraint potential: Σ λ_j · h_j(x)^2 for MLGRU energy. -/
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def constraintPotential (sys : ConstraintSystem n m) (M : VarDimManifold)
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(hN : M.n = n) (lambdas : Array Q16_16) (hLambdas : lambdas.size = m) : Q16_16 :=
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(Array.range m).foldl (fun acc i =>
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if hi : i < m then
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let c := sys.constraints[i]'(sys.sizeConstraints.symm ▸ hi)
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let lam := lambdas[i]'(hLambdas.symm ▸ hi)
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let r := constraintResidual c M.center (M.sizeN.trans hN)
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let r2 := Q16_16.mul r r
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Q16_16.add acc (Q16_16.mul lam r2)
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else acc
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) Q16_16.zero
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-- ════════════════════════════════════════════════════════════
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-- §4 Dynamic ACI for Cross-Dimensional Collision
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-- ════════════════════════════════════════════════════════════
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/-- Project higher dimension to lower via coordinate truncation. -/
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def projectDown (x : Array Q16_16) (nTarget : Nat) : Array Q16_16 :=
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x.take nTarget
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/-- Center distance with dimension handling.
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If n_i ≠ n_j, project to lower dimension first. -/
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def dynamicCenterDist (Mi Mj : VarDimManifold) : Q16_16 :=
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let nMin := min Mi.n Mj.n
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let ci := projectDown Mi.center nMin
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let cj := projectDown Mj.center nMin
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let d2 := (ci.zip cj).foldl (fun acc (xi, xj) =>
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let dx := Q16_16.sub xi xj
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Q16_16.add acc (Q16_16.mul dx dx)
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) Q16_16.zero
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-- sqrt via NR (reusing centerDist pattern)
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let r0 := ⟨d2.val / 2⟩
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let nr := fun r => ⟨(r.val + (d2.val * 65536 / (r.val + 1))) / 2⟩
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nr (nr (nr r0))
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/-- Dynamic ACI collision predicate. -/
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def dynamicACI (Mi Mj : VarDimManifold) (tau : Q16_16) : Bool :=
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decide ((dynamicCenterDist Mi Mj).val ≤ tau.val)
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/-- NMS suppression for variable dimensions.
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Lower energy manifold folded when collision detected. -/
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def dynamicSuppresses (Mi Mj : VarDimManifold) (tau : Q16_16) : Bool :=
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dynamicACI Mi Mj tau && decide (Mi.energy.val > Mj.energy.val)
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-- ════════════════════════════════════════════════════════════
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-- §5 BettiSwooshND: Hamiltonian over [1, n_max]
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-- ════════════════════════════════════════════════════════════
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/-- Betti number counts per dimension. -/
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structure BettiVector where
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beta0 : Nat -- connected components
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beta1 : Nat -- 1D holes
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beta2 : Nat -- 2D cavities
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beta3 : Nat -- 3D voids
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beta4plus : Nat -- higher dimensions aggregated
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deriving Repr, Inhabited
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/-- Manifold registry: separate lists per dimension. -/
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structure ManifoldRegistry (nMax : Nat) where
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byDim : Array (List VarDimManifold) -- index by dimension
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sizeByDim : byDim.size = nMax + 1
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deriving Repr
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instance {nMax : Nat} : Inhabited (ManifoldRegistry nMax) where
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default := ⟨Array.mk (List.replicate (nMax + 1) []), by simp⟩
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/-- Get manifolds of specific dimension. -/
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def manifoldsOfDim (reg : ManifoldRegistry nMax) (n : Nat) : List VarDimManifold :=
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if h : n ≤ nMax then
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reg.byDim[n]'(by rw [reg.sizeByDim]; exact Nat.lt_succ_of_le h)
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else []
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/-- Global Betti swoosh over all dimensions.
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H_M = Σ_n H_M^{(n)} - cross-dim coupling. -/
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def bettiSwooshND (reg : ManifoldRegistry nMax) : Q16_16 :=
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-- Sum potential over all dimensions
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(Array.range (nMax + 1)).foldl (fun acc n =>
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let mfs := manifoldsOfDim reg n
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let sumN := mfs.foldl (fun accM Mi => Q16_16.add accM Mi.energy) Q16_16.zero
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Q16_16.add acc sumN
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) Q16_16.zero
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/-- Dimension selection potential: penalize deviation from target. -/
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def dimensionPotential (n nTarget : Nat) (eta : Q16_16) : Q16_16 :=
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if n = nTarget then Q16_16.zero
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else ⟨eta.val * (Int.ofNat (if n > nTarget then n - nTarget else nTarget - n))⟩
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/-- Total potential with structure constraint. -/
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def totalPotentialWithDim (M : VarDimManifold) (nTarget : Nat) (eta : Q16_16) : Q16_16 :=
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Q16_16.add M.energy (dimensionPotential M.n nTarget eta)
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-- ════════════════════════════════════════════════════════════
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-- §6 SUBLEQ Variable-n Kernels
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-- ════════════════════════════════════════════════════════════
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/-- SUBLEQ program for lifting 1D → n with dynamic loop bounds. -/
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def liftKernel (_n : Nat) : Program :=
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-- M[0] = seq_ptr, M[1] = t0, M[2] = dest_base
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-- M[3] = i (counter), M[4] = n (target dimension)
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-- M[5] = accum, M[6] = divisor
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#[ ⟨0, 5, 1⟩ -- accum ← accum - M[seq_ptr] (load)
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, ⟨6, 5, 2⟩ -- accum ← accum - M[divisor] (normalize)
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, ⟨5, 2, 3⟩ -- M[dest_base + i] ← accum
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, ⟨1, 3, 4⟩ -- i ← i - 1 (increment)
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, ⟨4, 3, 0⟩ -- if i ≤ n: continue else halt
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]
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/-- SUBLEQ program for constraint checking with m constraints. -/
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def constrainKernel (_n _m : Nat) : Program :=
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-- Nested loops: outer over m constraints, inner over n dimensions
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-- M[0..n-1]: center coordinates x
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-- M[n..n+m-1]: constraint residuals
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-- M[n+m]: constraint index j
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-- M[n+m+1]: dimension index i
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-- M[n+m+2]: dot accumulator
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-- M[n+m+3]: epsilon tolerance
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#[ ⟨0, 0, 1⟩ -- placeholder for constraint loop
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]
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/-- Memory layout for variable-n manifold in SRAM. -/
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def varDimMemoryLayout (base n : Nat) : Array Int :=
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#[ base -- center[0]
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, base + n -- center[n-1] end
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, base + n + n*(n+1)/2 -- metric end
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, base + n + n*(n+1)/2 + n*(n-1)/2 -- orient end
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, base + n*(n+3)/2 -- header start
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, base + n*(n+3)/2 - 4 -- dimension n
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, base + n*(n+3)/2 - 3 -- constraint count m
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, base + n*(n+3)/2 - 2 -- energy
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, base + n*(n+3)/2 - 1 -- activation σ
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]
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-- ════════════════════════════════════════════════════════════
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-- §8 PhantomTideQ: Adaptive Phantom Coupling
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-- Converts PhantomTide Float functions to Q16.16 formalization.
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-- Integrates with VarDimManifold gossip routing.
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-- ════════════════════════════════════════════════════════════
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/-- Signal energy-coherence delta as velocity proxy.
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v = |e - κ| in Q16.16 (difference of two Q16.16 values). -/
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def signalVelocity (energy coherence : Q16_16) : Q16_16 :=
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Q16_16.abs (Q16_16.sub energy coherence)
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/-- Phantom modifier with adaptive λ parameter.
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φ(λ, v) = max(0, 1 - λ·v) — non-negative clamping.
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λ ∈ [0, 1] as Q16.16 (0 = no damping, 65536 = full damping). -/
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def phantomModifier (lambda v : Q16_16) : Q16_16 :=
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let damp := Q16_16.sub Q16_16.one (Q16_16.mul lambda v)
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-- max(0, damp) via Q16_16 comparison
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if damp.val < 0 then Q16_16.zero else damp
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/-- Full phantom coupling: j = base · φ(λ, v).
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Lambda-adaptive version of SSMS.jPhantom. -/
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def couplingPhantom
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(lambda : Q16_16)
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(base : Q16_16)
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(energy coherence : Q16_16) : Q16_16 :=
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let v := signalVelocity energy coherence
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let modifier := phantomModifier lambda v
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Q16_16.mul base modifier
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/-- Final score with phantom boost: s' = s · (1 + max(0, j)).
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Boosts stable signals (j > 0), dampens unstable (j < 0). -/
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def finalScorePhantom (baseScore j : Q16_16) : Q16_16 :=
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let boost := Q16_16.add Q16_16.one (Q16_16.max Q16_16.zero j)
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Q16_16.mul baseScore boost
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/-- Dynamic gossip budget: increase slots when coupling > 1.0.
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j > 1.0 means strong signal → allow more gossip contacts.
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Integrates with nContact tier system. -/
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def dynamicGossipBudget (j : Q16_16) (baseSlots : Nat) : Nat :=
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if j.val > 65536 then baseSlots + 1 else baseSlots -- j > 1.0 in Q16.16
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/-- Betti-soliton driven score with phantom coupling.
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H_M = -Δ_M + V_M + V_phantom(λ).
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Drive term from phase control (Warden pressure). -/
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def stableDrivenScorePhantom
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(lambda : Q16_16)
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(baseScore : Q16_16)
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(bettiEnergy : Q16_16) -- from BettiSwooshND
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(drive : Q16_16) -- phase control term
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(prev : Q16_16) : Q16_16 :=
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let j := couplingPhantom lambda baseScore bettiEnergy Q16_16.one
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let boosted := finalScorePhantom baseScore j
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-- Soliton step: combine with drive and previous state
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let step := Q16_16.add (Q16_16.mul drive boosted) (Q16_16.mul (Q16_16.ofNat 3) prev)
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-- Normalize by 4 (bit shift approximation)
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⟨step.val / 4⟩
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/-- Stable band routing: predicate for gossip inclusion.
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Signal routed if driven score exceeds threshold τ_stable. -/
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def routeStablePhantom
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(lambda : Q16_16)
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(baseScore bettiEnergy drive prev tauStable : Q16_16) : Bool :=
|
||
let score := stableDrivenScorePhantom lambda baseScore bettiEnergy drive prev
|
||
decide (score.val ≥ tauStable.val)
|
||
|
||
/-- Tunneling allowance: high-coupling, high-coherence signals.
|
||
j > 0.8 && visibility > 0.5 && coherence > 0.35 -/
|
||
def allowTunnelPhantom
|
||
(lambda : Q16_16)
|
||
(baseScore bettiEnergy visibility coherence : Q16_16) : Bool :=
|
||
let j := couplingPhantom lambda baseScore bettiEnergy coherence
|
||
let jThresh : Q16_16 := ⟨52428⟩ -- 0.8 in Q16.16 (0.8 * 65536 = 52428.8)
|
||
let visThresh : Q16_16 := ⟨32768⟩ -- 0.5 in Q16.16
|
||
let cohThresh : Q16_16 := ⟨22937⟩ -- 0.35 in Q16.16 (0.35 * 65536 = 22937.6)
|
||
decide (j.val > jThresh.val) && decide (visibility.val > visThresh.val) && decide (coherence.val > cohThresh.val)
|
||
|
||
/-- Promotion threshold: tiered reduction based on coupling strength.
|
||
j > 1.0: reduce by 0.75, j > 0.5: reduce by 0.25, else add 0.5. -/
|
||
def promoteThresholdPhantom
|
||
(lambda thresholdBase : Q16_16)
|
||
(baseScore bettiEnergy : Q16_16) : Q16_16 :=
|
||
let j := couplingPhantom lambda baseScore bettiEnergy Q16_16.one
|
||
let quarter : Q16_16 := ⟨16384⟩ -- 0.25 in Q16.16
|
||
let half : Q16_16 := ⟨32768⟩ -- 0.5 in Q16.16
|
||
let threeQ : Q16_16 := ⟨49152⟩ -- 0.75 in Q16.16
|
||
let jHalf : Q16_16 := ⟨32768⟩ -- 0.5 threshold
|
||
let jOne := Q16_16.one
|
||
if j.val > jOne.val then
|
||
Q16_16.max Q16_16.zero (Q16_16.sub thresholdBase threeQ)
|
||
else if j.val > jHalf.val then
|
||
Q16_16.max Q16_16.zero (Q16_16.sub thresholdBase quarter)
|
||
else
|
||
Q16_16.add thresholdBase half
|
||
|
||
/-- Promotion predicate: score meets adaptive threshold. -/
|
||
def shouldPromotePhantom
|
||
(lambda thresholdBase : Q16_16)
|
||
(baseScore bettiEnergy drive prev : Q16_16) : Bool :=
|
||
let finalScore := stableDrivenScorePhantom lambda baseScore bettiEnergy drive prev
|
||
let thresh := promoteThresholdPhantom lambda thresholdBase baseScore bettiEnergy
|
||
decide (finalScore.val ≥ thresh.val)
|
||
|
||
/-- Phantom-scored payload structure for gossip selection. -/
|
||
structure PhantomScoredPayload where
|
||
payload : GossipPacket
|
||
score : Q16_16
|
||
coupling : Q16_16
|
||
stable : Bool -- passed routeStablePhantom
|
||
deriving Repr, Inhabited
|
||
|
||
/-- Stabilize payloads via phantom scoring and filter.
|
||
Returns sorted (by score) array of stable payloads.
|
||
Integrates with variable-n gossip: budget scales with n. -/
|
||
def stabilizePayloadsPhantom
|
||
(lambda tauStable : Q16_16)
|
||
(_budgetSlots : Nat)
|
||
(packets : Array (GossipPacket × Q16_16 × Q16_16 × Q16_16)) -- (pkt, energy, drive, prev)
|
||
: Array PhantomScoredPayload :=
|
||
let scored := packets.filterMap (fun (pkt, betti, drive, prev) =>
|
||
let baseScore := pkt.energy
|
||
let coherence := pkt.deltaH -- reuse deltaH as coherence proxy
|
||
let j := couplingPhantom lambda baseScore betti coherence
|
||
let stable := routeStablePhantom lambda baseScore betti drive prev tauStable
|
||
if stable then
|
||
some { payload := pkt, score := finalScorePhantom baseScore j
|
||
, coupling := j, stable := true }
|
||
else none)
|
||
-- Sort by score descending (selection sort via foldl)
|
||
scored -- qsort requires Ord instance; return unsorted for now
|
||
|
||
/-- Phantom kernel output structure for gossip routing decision. -/
|
||
structure PhantomKernelOutput where
|
||
chosen : Option GossipPacket
|
||
score : Q16_16
|
||
coupling : Q16_16
|
||
promoted : Bool
|
||
tunneled : Bool
|
||
budgetNext : Nat
|
||
deriving Repr, Inhabited
|
||
|
||
/-- Phantom kernel step: full gossip packet selection pipeline.
|
||
Integrates with VarDimManifold.n for dimension-aware budget. -/
|
||
def stepKernelPhantom
|
||
(lambda tauStable : Q16_16)
|
||
(budgetSlots : Nat)
|
||
(n : Nat) -- manifold dimension for scaling
|
||
(packets : Array (GossipPacket × Q16_16 × Q16_16 × Q16_16))
|
||
(visibility coherence : Q16_16) : PhantomKernelOutput :=
|
||
let scored := stabilizePayloadsPhantom lambda tauStable budgetSlots packets
|
||
-- Scale budget by dimension: more dimensions → more gossip slots
|
||
let dimBudget := budgetSlots + n / 2
|
||
match scored[0]? with
|
||
| none =>
|
||
{ chosen := none, score := Q16_16.zero, coupling := Q16_16.zero
|
||
, promoted := false, tunneled := false, budgetNext := dimBudget }
|
||
| some best =>
|
||
let j := best.coupling
|
||
let tunneled := allowTunnelPhantom lambda best.score best.score visibility coherence
|
||
let promoted := shouldPromotePhantom lambda Q16_16.one best.score best.score Q16_16.zero Q16_16.zero
|
||
let budgetNext := dynamicGossipBudget j dimBudget
|
||
{ chosen := some best.payload, score := best.score, coupling := j
|
||
, promoted := promoted, tunneled := tunneled, budgetNext := budgetNext }
|
||
|
||
|
||
-- ════════════════════════════════════════════════════════════
|
||
-- §9 Cycle Counts for Variable-n Pipeline with Phantom
|
||
-- ════════════════════════════════════════════════════════════
|
||
|
||
/-- Lifting cycles: O(n · d) ternary ops. -/
|
||
def liftCycles (n d : Nat) : Nat :=
|
||
n * d -- one ADD/SUB per nonzero weight
|
||
|
||
/-- Constraint check cycles: O(m · n). -/
|
||
def constraintCycles (n m : Nat) : Nat :=
|
||
m * n * 2 -- dot product + comparison per constraint
|
||
|
||
/-- Dynamic NMS cycles: O(k^2 · n_min) for k manifolds. -/
|
||
def dynamicNmsCycles (k nAvg : Nat) : Nat :=
|
||
k * k * nAvg -- pairwise center distances
|
||
|
||
/-- Total pipeline with dimension selection. -/
|
||
def varDimTotalCycles (n d m k : Nat) : Nat :=
|
||
liftCycles n d
|
||
+ constraintCycles n m
|
||
+ dynamicNmsCycles k n
|
||
+ n * 18 -- MLGRU per dimension
|
||
+ 2 * (Nat.log2 k + 1) -- gossip
|
||
|
||
/-- Throughput: manifolds processed per 1000 cycles. -/
|
||
def varDimThroughput (n d m : Nat) : Nat :=
|
||
1000 / varDimTotalCycles n d m 1
|
||
|
||
end Semantics.SSMS_nD
|