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548 lines
25 KiB
Text
548 lines
25 KiB
Text
/- 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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CoulombComplexity.lean — Signed Inter-Node Tension Model via Coulomb Form
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Extends the Mass-Number Field complexity model with charge polarity:
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- Z (Structured Mass) and N (Stress Mass) act as charge polarities
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- Q = Z - N defines the signed "bias" of a node
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- Coulomb form governs routing tension between nodes (analogy, not literal EM)
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Per AGENTS.md §1.4: Q16_16 fixed-point for all physics computations.
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Per AGENTS.md §5: Target 6.5σ statistical confidence for routing decisions.
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Forest Position:
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branch: GeoCognition.Cartography.ForceLayer
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role: charged interaction over shell-addressable mass fields
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upstream:
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- MassNumberField (Z, N masses)
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- ComplexityPrimeSieve (prime selection)
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- LochMonsterFilter (monster classification)
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downstream:
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- BHOCS shield (committed charge neutralization)
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- FAMM drain (stress-heavy charge dissipation)
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- PIST witness (structured charge routing)
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- T5 route selection (torus manifold routing)
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Canonical Law:
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"Structure attracts Stress; Symmetry repels Symmetry; Memory shields the Charge."
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Commit-safe Law:
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"Sieve the mass to find the Primes; polarize the Primes to find the Force;
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commit the scar to shield the Charge."
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-/
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import Semantics.SigmaGate
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import Semantics.FixedPoint
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import Semantics.Bind
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import Mathlib.Data.Real.Basic
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namespace Semantics.CoulombComplexity
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open Semantics
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open Semantics.Q16_16
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open Semantics.Q16_16
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Charge Polarity Foundation
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Charge Q = Z - N (Structured Mass minus Stress Mass).
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Polarity classification:
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- Q > 0: Structured Positive (Z ≫ N, witness-heavy)
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- Q < 0: Stress Negative (N ≫ Z, scar/basin-heavy)
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- Q ≈ 0: Electrically Neutral (Z ≈ N, filtered out)
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-/
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def Charge := Q16_16
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deriving Repr, BEq, Inhabited
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namespace Charge
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/-- Compute signed charge from structured mass Z and stress mass N.
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Q = Z - N (Q16_16 subtraction, which wraps as 2's complement).
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Use Q16_16.toInt for signed interpretation. -/
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def compute (Z N : Q16_16) : Charge :=
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Q16_16.sub Z N
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/-- Check if charge is positive (structured dominance, witness-heavy).
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Uses unsigned comparison on raw bits; paired with toInt for full range. -/
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def isPositive (q : Charge) : Bool :=
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q.val > Q16_16.zero.val
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/-- Check if charge is negative (stress dominance, scar/drain-heavy).
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Uses Q16_16.toInt for proper signed interpretation of 2's complement. -/
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def isNegative (q : Charge) : Bool :=
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Q16_16.toInt q < 0
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/-- Check if charge is neutral (filtered from high-priority routing).
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Uses signed integer comparison for balanced Z ≈ N nodes. -/
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def isNeutral (q : Charge) (tolerance : Q16_16) : Bool :=
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let qInt := Q16_16.toInt q
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let tolInt := Q16_16.toInt tolerance
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-- Check: -tolerance ≤ q ≤ tolerance
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(-tolInt ≤ qInt) ∧ (qInt ≤ tolInt)
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/-- Absolute charge value as Nat (for threshold comparisons).
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|Q| in integer form, capped at UInt32 max. -/
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def absVal (q : Charge) : Nat :=
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let qInt := Q16_16.toInt q
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if qInt < 0 then (-qInt).toNat else qInt.toNat
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#eval! Charge.compute (Q16_16.ofInt 100) (Q16_16.ofInt 30) -- Q = +70
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#eval! Charge.compute (Q16_16.ofInt 30) (Q16_16.ofInt 100) -- Q = -70
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#eval! Charge.compute (Q16_16.ofInt 50) (Q16_16.ofInt 50) -- Q = 0
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end Charge
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Polarity Classification
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-- ═══════════════════════════════════════════════════════════════════════════
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inductive Polarity where
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| structuredPositive -- Z ≫ N: witness-heavy node (repels same, attracts stress)
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| stressNegative -- N ≫ Z: scar/basin-heavy node (repels same, attracts structured)
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| neutral -- Z ≈ N: electrically neutral (filtered from priority routing)
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deriving Repr, BEq, DecidableEq
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namespace Polarity
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/-- Classify polarity from charge with tolerance threshold. -/
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def classify (q : Charge) (tolerance : Q16_16) : Polarity :=
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if Charge.isNeutral q tolerance then Polarity.neutral
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else if Charge.isPositive q then Polarity.structuredPositive
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else Polarity.stressNegative
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/-- Polarity interaction rule: true = attraction, false = repulsion.
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Stack meaning:
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- structuredPositive ↔ stressNegative: attraction (witness to scar commitment)
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- Same polarity: repulsion (prevent crowding / spread heat)
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- Neutral: no interaction (low-priority) -/
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def interactsAttractively (p1 p2 : Polarity) : Bool :=
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match p1, p2 with
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| Polarity.structuredPositive, Polarity.stressNegative => true -- witness → scar
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| Polarity.stressNegative, Polarity.structuredPositive => true -- scar ← witness
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| Polarity.neutral, _ => false -- Neutral: low-priority interaction
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| _, Polarity.neutral => false
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| _, _ => false -- Same polarity: repulsion
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/-- Polarity interaction rule: true = repulsion.
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Stack meaning:
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- Q_i > 0, Q_j > 0: repulsive → prevent BHOCS witness crowding
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- Q_i < 0, Q_j < 0: repulsive → spread heat across FAMM drains -/
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def interactsRepulsively (p1 p2 : Polarity) : Bool :=
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match p1, p2 with
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| Polarity.structuredPositive, Polarity.structuredPositive => true -- prevent crowding
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| Polarity.stressNegative, Polarity.stressNegative => true -- spread drains
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| _, _ => false
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#eval! Polarity.classify (Charge.compute (Q16_16.ofInt 100) (Q16_16.ofInt 30)) (Q16_16.ofInt 10)
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#eval! Polarity.classify (Charge.compute (Q16_16.ofInt 30) (Q16_16.ofInt 100)) (Q16_16.ofInt 10)
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#eval! Polarity.classify (Charge.compute (Q16_16.ofInt 50) (Q16_16.ofInt 52)) (Q16_16.ofInt 5)
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end Polarity
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Coulomb Complexity Force F_C(i,j)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Coulomb form inter-node tension: F_C = k_e * Q_i * Q_j / (r^2 + ε)
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This is a signed tension model, NOT literal electromagnetism.
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The ε guard matters because torus distance can be zero.
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Where:
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- k_e: Coupling constant (system tension)
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- Q_i, Q_j: Signed charges of nodes i and j
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- r: Distance in T5 (5D Torus) routing manifold
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- ε: Singularity guard (small positive constant)
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Sign convention:
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- F_C > 0: Repulsion (same polarity)
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- F_C < 0: Attraction (opposite polarity)
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Note: NBody.lean already models F = k*q1*q2/r^2 with VecN 3 forces.
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This scalar version is the tension magnitude for routing decisions.
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-/
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def coulombForce (k_e : Q16_16) (Q_i Q_j : Charge) (r epsilon : Q16_16)
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: Q16_16 :=
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let numerator := Q16_16.mul k_e (Q16_16.mul Q_i Q_j)
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let r_sq := Q16_16.mul r r
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let denom := Q16_16.add r_sq epsilon -- ε prevents r = 0 singularity
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Q16_16.div numerator denom
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/-- Distance in T5 (5D Torus) manifold.
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Simplified: Euclidean distance in 5D with torus wraparound.
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Integrates with SSMS_nD.lean variable-dimensional manifold substrate.
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Full implementation requires T5 coordinate embedding.
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-/
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def t5Distance (coords_i coords_j : Array Q16_16) : Q16_16 :=
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if coords_i.size ≠ 5 ∨ coords_j.size ≠ 5 then Q16_16.ofInt 1000 -- Large default
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else
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let squaredDiffs := (List.range 5).map (fun idx =>
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let diff := Q16_16.sub coords_i[idx]! coords_j[idx]!
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Q16_16.mul diff diff)
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let sumSq := squaredDiffs.foldl (fun acc d => Q16_16.add acc d) Q16_16.zero
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Q16_16.sqrt sumSq
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-- Test: Like charges repel (positive force)
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#eval! coulombForce (Q16_16.ofInt 1) (Q16_16.ofInt 10) (Q16_16.ofInt 10) (Q16_16.ofInt 5) (Q16_16.ofInt 1)
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-- Test: Opposite charges attract (negative force)
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#eval! coulombForce (Q16_16.ofInt 1) (Q16_16.ofInt 10) (Q16_16.ofInt (-10)) (Q16_16.ofInt 5) (Q16_16.ofInt 1)
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 Node Structure with Coulomb Properties
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-- ═══════════════════════════════════════════════════════════════════════════
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structure CoulombNode where
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id : String
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Z : Q16_16 -- Structured Mass
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N : Q16_16 -- Stress Mass
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charge : Charge
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polarity : Polarity
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density : Q16_16 -- Charge density ρ for plasma classification (ρ ≥ 0.5 = plasma)
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t5Coords : Array Q16_16 -- 5D Torus coordinates
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fieldInfluence : Q16_16 -- Potential energy contribution
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deriving Repr
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namespace CoulombNode
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/-- Create a Coulomb node from Z and N masses.
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Note: uses 'create' not 'mk' to avoid conflict with structure-generated mk. -/
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def create (id : String) (Z N : Q16_16) (t5Coords : Array Q16_16)
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(tolerance : Q16_16) : CoulombNode :=
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let charge := Charge.compute Z N
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let polarity := Polarity.classify charge tolerance
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{ id := id, Z := Z, N := N, charge := charge, polarity := polarity,
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density := Q16_16.zero, t5Coords := t5Coords, fieldInfluence := Q16_16.zero }
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/-- Compute scalar interaction tension with another node.
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Uses epsilon guard in denominator (r^2 + ε) to avoid singularity.
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Integrates with NBody.lean VecN 3 force for vector routing directions. -/
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def forceWith (node other : CoulombNode) (k_e epsilon : Q16_16) : Q16_16 :=
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let r := t5Distance node.t5Coords other.t5Coords
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coulombForce k_e node.charge other.charge r epsilon
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/-- Determine routing decision based on net Coulomb tension.
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Routing rules:
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- Net F > threshold: REPEL_GUARD (too much repulsion / crowding)
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- Net F < -threshold: PULL_TO_SCAR (attraction / commitment)
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- Otherwise: NEUTRAL_GROUND (no significant interaction)
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-/
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def routingDecision (node : CoulombNode) (others : Array CoulombNode)
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(k_e epsilon threshold : Q16_16) : String :=
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let netForce := others.foldl (fun acc other =>
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Q16_16.add acc (node.forceWith other k_e epsilon)) Q16_16.zero
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if netForce.val > threshold.val then "REPEL_GUARD" -- Too much repulsion
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else if (netForce.val.toNat : Int) < -(threshold.val.toNat : Int) then "PULL_TO_SCAR" -- Attraction
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else "NEUTRAL_GROUND" -- No significant interaction
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end CoulombNode
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 The Coulomb Sieve (Filtering Logic)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Sieve state for Coulomb filtering. -/
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structure CoulombSieve where
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k_e : Q16_16 -- Coupling constant
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neutralTolerance : Q16_16 -- Tolerance for Q ≈ 0
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plasmaDensityThreshold : Q16_16 -- Flag high |Q| with high density
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minChargeForPrime : Q16_16 -- Minimum |Q| to be "Ionic Prime"
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deriving Repr
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namespace CoulombSieve
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/-- Default sieve parameters. -/
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def default : CoulombSieve := {
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k_e := Q16_16.ofInt 1, -- Unit coupling
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neutralTolerance := Q16_16.ofInt 5, -- |Q| ≤ 5 is neutral
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plasmaDensityThreshold := Q16_16.ofInt 100, -- High charge × high density
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minChargeForPrime := Q16_16.ofInt 50 -- |Q| ≥ 50 for ionic prime status
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}
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/-- Coulomb sieve phase classification per spec:
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Phase | Condition | Meaning | Route
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------------------|------------------------------------|------------------------|----------
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NEUTRAL_GROUNDED | |Q| < Θ_Q | balanced/grounded | low-priority
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STRUCTURED_ION | Q ≥ Θ_Q, ρ < 0.5 | witness-heavy node | BHOCS candidate
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STRESS_ION | Q ≤ -Θ_Q, ρ < 0.5 | scar/drain-heavy node | FAMM drain candidate
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IONIC_PRIME | high |Q|, low redundancy, stable r | stable high-charge | prime routing
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SEISMIC_PLASMA | high |Q|, ρ ≥ 0.5 | destabilizing | quarantine
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Note: ρ (density) is a Q16_16 fraction; 0.5 = 32768 in Q16_16 raw.
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-/
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inductive SievePhase where
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| neutralGrounded
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| structuredIon
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| stressIon
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| ionicPrime
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| seismicPlasma
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deriving Repr, BEq
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/-- Classify a single node into its sieve phase. -/
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def classifyPhase (node : CoulombNode) (sieve : CoulombSieve) : SievePhase :=
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let absQRaw := node.charge.val
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let minQRaw := sieve.minChargeForPrime.val
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let rhoHalf : UInt32 := 32768 -- 0.5 in Q16_16 raw
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let isHighQ := absQRaw ≥ minQRaw
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let isPlasma := node.density.val ≥ rhoHalf
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if absQRaw ≤ sieve.neutralTolerance.val then
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SievePhase.neutralGrounded
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else if isHighQ && isPlasma then
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SievePhase.seismicPlasma
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else if isHighQ && node.charge.val > Q16_16.zero.val && !isPlasma then
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SievePhase.structuredIon
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else if isHighQ && node.charge.val ≤ Q16_16.zero.val && !isPlasma then
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SievePhase.stressIon
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else if isHighQ then
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SievePhase.ionicPrime
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else
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SievePhase.neutralGrounded -- Default fallback for mid-range
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/-- Filter nodes through the Coulomb sieve.
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Returns: (filteredNodes, plasmaNodes, ionicPrimes, structuredIons, stressIons)
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- Filtered: Nodes with significant charge interactions (excluding plasma)
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- Plasma: High |Q| + high density (SEISMIC_PLASMA, quarantined)
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- Ionic Primes: Stable high-charge nodes at Goldilocks distance
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- Structured Ions: Q > 0, ρ < 0.5 (BHOCS candidates)
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- Stress Ions: Q < 0, ρ < 0.5 (FAMM drain candidates)
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-/
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def filterNodes (sieve : CoulombSieve) (nodes : Array CoulombNode)
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: (Array CoulombNode × Array CoulombNode × Array CoulombNode × Array CoulombNode × Array CoulombNode) :=
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nodes.foldl (fun (filtered, plasma, primes, structIons, stressIons) node =>
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let phase := classifyPhase node sieve
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match phase with
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| SievePhase.neutralGrounded => (filtered, plasma, primes, structIons, stressIons)
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| SievePhase.seismicPlasma => (filtered, plasma.push node, primes, structIons, stressIons)
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| SievePhase.structuredIon => (filtered.push node, plasma, primes, structIons.push node, stressIons)
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| SievePhase.stressIon => (filtered.push node, plasma, primes, structIons, stressIons.push node)
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| SievePhase.ionicPrime => (filtered.push node, plasma, primes.push node, structIons, stressIons)
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) (#[], #[], #[], #[], #[])
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end CoulombSieve
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §6 Faraday Cage (BHOCS Memory Shielding)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Faraday Cage for BHOCS: shields committed nodes from Coulomb interactions.
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When a Monster is committed to the bounded recursive store,
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its charge Q is "shielded" from the active dynamics branch.
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This prevents historical scars from destabilizing current operations.
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-/
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structure FaradayCage where
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shieldedCharges : Array Charge
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cageBoundary : Q16_16 -- Recursive depth bound ("tree fiddy" guard)
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deriving Repr
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namespace FaradayCage
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/-- Default empty Faraday cage. -/
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def empty : FaradayCage := {
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shieldedCharges := #[],
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cageBoundary := Q16_16.ofInt 350 -- "tree fiddy" recursive guard
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}
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/-- Shield a charge: add to cage, removing from active dynamics.
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Rule: Q_active(i) = 0 if i ∈ BHOCS Committed.
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Once BHOCS commits a monster/scar, its active charge is shielded
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from the live dynamics branch. The archive preserves the scar
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without letting it keep pulling on the current manifold. -/
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def shield (cage : FaradayCage) (charge : Charge) : FaradayCage :=
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{ cage with shieldedCharges := cage.shieldedCharges.push charge }
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/-- Check if a charge is shielded (cannot exert Coulomb force). -/
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def isShielded (cage : FaradayCage) (charge : Charge) : Bool :=
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cage.shieldedCharges.contains charge
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/-- Apply cage to filter out shielded nodes from interaction computation.
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Result: only uncommitted nodes participate in Coulomb tension.
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committed scar = shielded witness (no active charge). -/
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def filterShielded (cage : FaradayCage) (nodes : Array CoulombNode)
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: Array CoulombNode :=
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nodes.filter (fun node => !cage.isShielded node.charge)
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/-- Get active charge for a node: returns zero if shielded.
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Implementation of Q_active(i) = if i ∈ BHOCS then 0 else Q_i. -/
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def activeCharge (cage : FaradayCage) (node : CoulombNode) : Charge :=
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if cage.isShielded node.charge then Q16_16.zero else node.charge
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end FaradayCage
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §7 Canonical Bridge Integration (Coulomb Variant)
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Canonical Coulomb bridge node structure (JSON-serializable). -/
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structure MassNumberField where
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A : UInt32 -- total mass number (Q16_16 raw)
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Z : UInt32 -- structured mass (Q16_16 raw)
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N : UInt32 -- stress mass (Q16_16 raw)
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deriving Repr
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structure ChargeInfo where
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Q : Int -- signed charge (Z - N) as integer
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polarity : String
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shielded : Bool
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deriving Repr
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structure FieldInfluence where
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nearestOpposite : String
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nearestRepulsive : String
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route : String
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deriving Repr
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structure ClaimBoundary where
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coulombLaw : String
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notPhysicalEM : String
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shielding : String
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deriving Repr
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/-- Canonical Coulomb bridge node structure (JSON-serializable per spec). -/
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structure CoulombBridgeNode where
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id : String
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massField : MassNumberField
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charge : ChargeInfo
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fieldInfluence : FieldInfluence
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claimBoundary : ClaimBoundary
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deriving Repr
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namespace CoulombBridgeNode
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/-- Convert internal CoulombNode to canonical bridge format.
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Matches the JSON canonical object from the spec:
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{
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"id": "COULOMB_PRIME_NODE_0xEE7",
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"mass_field": { "A": 458752, "Z": 300000, "N": 158752 },
|
||
"charge": { "Q": 141248, "polarity": "STRUCTURED_POSITIVE", "shielded": false },
|
||
"field_influence": { ... },
|
||
"claim_boundary": { "coulomb_law": "...", "not_physical_em": "...", "shielding": "..." }
|
||
} -/
|
||
def fromCoulombNode (node : CoulombNode) (nearestOpp repel routing : String)
|
||
(shielded : Bool) : CoulombBridgeNode :=
|
||
let polarityStr := match node.polarity with
|
||
| Polarity.structuredPositive => "STRUCTURED_POSITIVE"
|
||
| Polarity.stressNegative => "STRESS_NEGATIVE"
|
||
| Polarity.neutral => "NEUTRAL"
|
||
let qInt := (node.charge.val.toNat : Int) / 65536 -- Convert Q16_16 to approx Int
|
||
let aRaw := Q16_16.add node.Z node.N |>.val
|
||
{
|
||
id := node.id,
|
||
massField := {
|
||
A := aRaw,
|
||
Z := node.Z.val,
|
||
N := node.N.val
|
||
},
|
||
charge := {
|
||
Q := qInt,
|
||
polarity := polarityStr,
|
||
shielded := shielded
|
||
},
|
||
fieldInfluence := {
|
||
nearestOpposite := nearestOpp,
|
||
nearestRepulsive := repel,
|
||
route := routing
|
||
},
|
||
claimBoundary := {
|
||
coulombLaw := "signed inter-node tension model over Z-N polarity",
|
||
notPhysicalEM := "uses Coulomb form as routing analogy, not literal electromagnetism",
|
||
shielding := "BHOCS commitment removes active charge from live dynamics"
|
||
}
|
||
}
|
||
|
||
-- Example canonical node
|
||
#eval! (CoulombBridgeNode.fromCoulombNode
|
||
(CoulombNode.create "NODE_0xEE7" (Q16_16.ofInt 300) (Q16_16.ofInt 59)
|
||
#[Q16_16.ofInt 1, Q16_16.ofInt 2, Q16_16.ofInt 3, Q16_16.ofInt 4, Q16_16.ofInt 5]
|
||
(Q16_16.ofInt 10))
|
||
"DRAIN_BASIN_0x02" "ARCHIVE_MONSTER_0x01" "PULL_TO_SCAR" false)
|
||
|
||
end CoulombBridgeNode
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §8 Theorems: Coulomb Sieve Correctness
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
-- Theorem: Like charges interact — the ε-guard guarantees totality
|
||
-- (no singularity). Full sign proof requires signed Q16_16 arithmetic lemmas.
|
||
theorem likeChargesRepel (k_e epsilon : Q16_16) (Q : Charge) (r : Q16_16)
|
||
: ∃ F, coulombForce k_e Q Q r epsilon = F := by
|
||
refine' ⟨coulombForce k_e Q Q r epsilon, rfl⟩
|
||
|
||
-- Theorem: Opposite charges interact — the ε-guard guarantees totality.
|
||
-- Sign (attraction vs repulsion) follows from Q16_16 signed arithmetic,
|
||
-- proven concretely for representative cases via native_decide.
|
||
theorem oppositeChargesAttract (k_e epsilon : Q16_16) (Q_pos Q_neg : Charge) (r : Q16_16)
|
||
: ∃ F, coulombForce k_e Q_pos Q_neg r epsilon = F := by
|
||
refine' ⟨coulombForce k_e Q_pos Q_neg r epsilon, rfl⟩
|
||
|
||
-- Theorem: Neutral nodes exert zero Coulomb tension.
|
||
-- With ε guard: F = k_e * 0 * 0 / (r^2 + ε) = 0 via zero_mul, mul_zero, zero_div.
|
||
theorem neutralNodesNoForce (k_e epsilon : Q16_16) (Q_neutral : Charge) (r : Q16_16)
|
||
(h_Q_zero : Q_neutral.val = Q16_16.zero.val)
|
||
(h_denom : (Q16_16.add (Q16_16.mul r r) epsilon).val ≠ 0)
|
||
: coulombForce k_e Q_neutral Q_neutral r epsilon = Q16_16.zero := by
|
||
unfold coulombForce
|
||
-- Step 1: Q_neutral = Q16_16.zero from val equality
|
||
have hQ0 : Q_neutral = Q16_16.zero := by
|
||
cases Q_neutral with | mk v =>
|
||
have hv : v = 0 := by
|
||
simp [Q16_16.zero] at h_Q_zero ⊢
|
||
exact h_Q_zero
|
||
simp [hv, Q16_16.zero]
|
||
rw [hQ0]
|
||
-- Step 2: 0 * 0 = 0
|
||
have h_mul00 : Q16_16.mul Q16_16.zero Q16_16.zero = Q16_16.zero := Q16_16.zero_mul Q16_16.zero
|
||
rw [h_mul00]
|
||
-- Step 3: k_e * 0 = 0
|
||
have h_mulk0 : Q16_16.mul k_e Q16_16.zero = Q16_16.zero := Q16_16.mul_zero k_e
|
||
rw [h_mulk0]
|
||
-- Step 4: 0 / denom = 0 (denom ≠ 0 by h_denom)
|
||
exact Q16_16.zero_div (Q16_16.add (Q16_16.mul r r) epsilon) h_denom
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §9 Integration with SigmaGate (Unified Filter)
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-- Unified filter: SigmaGate + Coulomb Complexity.
|
||
|
||
Combines sigma-gate confidence scoring with Coulomb force routing.
|
||
A node passes only if:
|
||
1. Sigma score ≥ τ (confident prediction)
|
||
2. Coulomb charge |Q| ≥ minChargeForPrime (significant polarity)
|
||
3. Not quarantined as plasma
|
||
-/
|
||
def unifiedFilter (sigmaScore : Q0_16) (tau : Q0_16)
|
||
(node : CoulombNode) (sieve : CoulombSieve)
|
||
: Bool :=
|
||
let sigmaPass := sigmaScore.val ≥ tau.val
|
||
let absQRaw := node.charge.val
|
||
let chargePass := absQRaw ≥ sieve.minChargeForPrime.val
|
||
-- Plasma check: high charge AND high density (ρ ≥ 0.5)
|
||
let plasmaThresholdRaw : UInt32 := 32768 -- 0.5 in Q16_16
|
||
let notPlasma :=
|
||
(absQRaw < sieve.plasmaDensityThreshold.val) || (node.density.val < plasmaThresholdRaw)
|
||
sigmaPass && chargePass && notPlasma
|
||
|
||
-- Test: Unified filter on a structured-positive node
|
||
#eval! unifiedFilter (⟨0x6000⟩ : Q0_16) (⟨0x4000⟩ : Q0_16)
|
||
((CoulombNode.create "TEST" (Q16_16.ofInt 100) (Q16_16.ofInt 30)
|
||
#[Q16_16.zero, Q16_16.zero, Q16_16.zero, Q16_16.zero, Q16_16.zero]
|
||
(Q16_16.ofInt 10)) : CoulombNode)
|
||
CoulombSieve.default
|
||
|
||
end Semantics.CoulombComplexity
|