/- 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 SwarmDesignReview.lean — Swarm-Based Design Review for Geometric Enhancement This module implements a swarm-based review system for compression designs, focusing on maximizing utilization of geometric enhancements: - κ² curvature coupling from self-compression (arXiv:2301.13142) - Genomic field parameters (ρ, v, τ, σ, q, κ, ε) for hierarchy-aware encoding - Geometric corrections for adaptive thresholds and compression ratios - Manifold-aware scheduling and energy optimization Swarm agents analyze design decisions and recommend improvements to: 1. Increase curvature-aware compression efficiency 2. Optimize geometric parameter tuning 3. Enhance hierarchy-aware encoding 4. Improve manifold-based scheduling Per AGENTS.md §1.4: Q16_16 fixed-point for hardware extraction. Per AGENTS.md §2: PascalCase types, camelCase functions. Per AGENTS.md §4: Every def has eval witness or theorem. -/ import Mathlib.Data.Nat.Basic import Mathlib.Data.Real.Basic import Mathlib.Tactic import Semantics.FixedPoint namespace Semantics.SwarmDesignReview open Semantics.Q16_16 -- ═══════════════════════════════════════════════════════════════════════════ -- §0 Swarm Agent Types -- ═══════════════════════════════════════════════════════════════════════════ /-- Swarm agent specialization for design review. -/ inductive AgentSpecialization where | curvatureAnalyst -- Analyzes κ² utilization and curvature coupling | hierarchyOptimizer -- Optimizes κ_hierarchy² for encoding efficiency | mutationTuner -- Tunes ε (mutation rate) for adaptive thresholds | geometricReviewer -- Reviews overall geometric enhancement integration | isaAnalyst -- Analyzes ISA opcode utilization of geometric enhancements deriving Repr, DecidableEq /-- Swarm agent state. -/ structure SwarmAgent where id : Nat specialization : AgentSpecialization confidence : Q16_16 -- Confidence in recommendations (Q16.16) iterations : Nat findings : List String deriving Repr /-- Swarm state for collective review. -/ structure SwarmState where agents : List SwarmAgent consensus : Q16_16 -- Agreement level among agents (Q16.16) recommendations : List String deriving Repr -- ═══════════════════════════════════════════════════════════════════════════ -- §1 Geometric Enhancement Analysis -- ═══════════════════════════════════════════════════════════════════════════ /-- Geometric parameter set for analysis. -/ structure GeometricParameters where kappaSquared : Q16_16 -- κ²: curvature coupling rhoSeq : Q16_16 -- ρ: sequence alignment vEpigenetic : Q16_16 -- v: epigenetic dynamics tauStructure : Q16_16 -- τ: structure tension sigmaEntropy : Q16_16 -- σ: nucleotide entropy qConservation : Q16_16 -- q: evolutionary constraint kappaHierarchy : Q16_16 -- κ_hierarchy: hierarchy levels epsilonMutation : Q16_16 -- ε: mutation rate deriving Repr /-- Analysis result for geometric utilization. -/ structure GeometricAnalysis where curvatureUtilization : Q16_16 -- How well κ² is used (0-1) hierarchyEfficiency : Q16_16 -- How well κ_hierarchy² improves encoding (0-1) mutationAdaptivity : Q16_16 -- How well ε adapts thresholds (0-1) overallGeometricScore : Q16_16 -- Combined geometric score (0-1) recommendations : List String deriving Repr /-- Analyze curvature utilization in compression design. Measures how effectively κ² modulates compression decisions. -/ def analyzeCurvatureUtilization (params : GeometricParameters) : Q16_16 := -- κ² should be non-zero and significantly affect thresholds if params.kappaSquared = zero then zero -- No curvature utilization else if params.kappaSquared > (ofNat 500) then -- κ² > 0.0076 Q16_16.one -- Excellent curvature utilization else div params.kappaSquared (ofNat 500) -- Scale to [0,1] /-- Analyze hierarchy efficiency for encoding. Measures how well κ_hierarchy² improves compression ratio. -/ def analyzeHierarchyEfficiency (params : GeometricParameters) : Q16_16 := let kappaSq := params.kappaHierarchy * params.kappaHierarchy let _geomTerm := Q16_16.one + kappaSq -- Hierarchy efficiency = (1 + κ²) - 1 = κ² contribution if kappaSq = zero then zero else if kappaSq > (ofNat 100) then -- κ² > 0.0015 Q16_16.one else div params.kappaSquared (ofNat 500) /-- Analyze mutation adaptivity for thresholds. Measures how well ε modulates adaptive thresholds. -/ def analyzeMutationAdaptivity (params : GeometricParameters) : Q16_16 := -- ε should be non-zero to provide temperature-like adaptivity if params.epsilonMutation = zero then zero else if params.epsilonMutation > (ofNat 50) then -- ε > 0.00076 Q16_16.one else div params.epsilonMutation (ofNat 50) /-- Compute overall geometric score from individual metrics. -/ def computeOverallGeometricScore (analysis : GeometricAnalysis) : Q16_16 := let weights := [ofNat 30, ofNat 30, ofNat 40] -- 30%, 30%, 40% weights let scores := [analysis.curvatureUtilization, analysis.hierarchyEfficiency, analysis.mutationAdaptivity] let weighted := (weights.zip scores).foldl (fun acc (w, s) => acc + mul w s) zero div weighted (ofNat 100) -- Normalize to [0,1] -- ═══════════════════════════════════════════════════════════════════════════ -- §2 Swarm Agent Analysis Functions -- ═══════════════════════════════════════════════════════════════════════════ /-- Curvature analyst agent: analyzes κ² utilization. -/ def curvatureAnalystAnalyze (agent : SwarmAgent) (params : GeometricParameters) : SwarmAgent := let utilization := analyzeCurvatureUtilization params let findings := if utilization < (ofNat 50) then ["κ² curvature coupling underutilized: increase kappaSquared for better compression"] else if utilization > (ofNat 80) then ["κ² curvature coupling well-utilized: excellent geometric enhancement"] else ["κ² curvature coupling moderate: consider tuning for specific data characteristics"] { agent with confidence := utilization, findings := findings, iterations := agent.iterations + 1 } /-- Hierarchy optimizer agent: analyzes κ_hierarchy² efficiency. -/ def hierarchyOptimizerAnalyze (agent : SwarmAgent) (params : GeometricParameters) : SwarmAgent := let efficiency := analyzeHierarchyEfficiency params let findings := if efficiency < (ofNat 50) then ["κ_hierarchy² underutilized: increase kappaHierarchy for hierarchy-aware encoding"] else if efficiency > (ofNat 80) then ["κ_hierarchy² well-utilized: excellent hierarchy-aware compression"] else ["κ_hierarchy² moderate: balance between hierarchy depth and encoding efficiency"] { agent with confidence := efficiency, findings := findings, iterations := agent.iterations + 1 } /-- Mutation tuner agent: analyzes ε adaptivity. -/ def mutationTunerAnalyze (agent : SwarmAgent) (params : GeometricParameters) : SwarmAgent := let adaptivity := analyzeMutationAdaptivity params let findings := if adaptivity < (ofNat 50) then ["ε mutation rate too low: increase epsilonMutation for adaptive threshold sensitivity"] else if adaptivity > (ofNat 80) then ["ε mutation rate well-tuned: excellent adaptive threshold behavior"] else ["ε mutation rate moderate: adjust based on data variability requirements"] { agent with confidence := adaptivity, findings := findings, iterations := agent.iterations + 1 } /-- Geometric reviewer agent: overall geometric integration review. -/ def geometricReviewerAnalyze (agent : SwarmAgent) (params : GeometricParameters) : SwarmAgent := let curvatureUtil := analyzeCurvatureUtilization params let hierarchyEff := analyzeHierarchyEfficiency params let mutationAdapt := analyzeMutationAdaptivity params let overall := computeOverallGeometricScore { curvatureUtilization := curvatureUtil, hierarchyEfficiency := hierarchyEff, mutationAdaptivity := mutationAdapt, overallGeometricScore := zero, -- Will be computed recommendations := [] } let findings := if overall < (ofNat 50) then ["Overall geometric enhancement underutilized: swarm recommends parameter tuning"] else if overall > (ofNat 80) then ["Overall geometric enhancement excellent: design fully leverages geometric properties"] else ["Overall geometric enhancement moderate: consider swarm recommendations for improvement"] { agent with confidence := overall, findings := findings, iterations := agent.iterations + 1 } -- ═══════════════════════════════════════════════════════════════════════════ -- §3 ISA Analysis -- ═══════════════════════════════════════════════════════════════════════════ /-- ISA opcode for geometric operations. -/ inductive ISAOpc where | resonate -- 0x14: TSM_RESONATE / PHONON_LOCK (Phi=1.618) | mergeModes -- 0x42: TSM_MERGE_MODES | ingestVib -- 0x47: TSM_INGEST_VIBRATION | solitonify -- 0x0E: TSM_SOLITONIFY | propagateWave -- 0x17: TSM_PROPAGATE_WAVE | observeMode -- 0x5A: TSM_OBSERVE_MODE | syncClock -- 0x03: TSM_SYNC_CLOCK | geom_resonance -- GEOM_RESONANCE: Computes resonance field for geometric primitives | geom_soliton -- GEOM_SOLITON: Soliton wave propagation through topological manifolds | geom_wave -- GEOM_WAVE: Wave equation solver for geometric wave functions | geom_manifold -- GEOM_MANIFOLD: Manifold traversal and coordinate transformation | geom_fractal -- GEOM_FRACTAL: Fractal dimension computation and analysis | geom_homology -- GEOM_HOMOLOGY: Homology group computation (Betti numbers) | geom_persistence -- GEOM_PERSISTENCE: Persistent homology barcode generation | geom_morse -- GEOM_MORSE: Morse complex construction and gradient analysis | geom_reeb -- GEOM_REEB: Reeb graph construction for scalar fields | geom_sheaf -- GEOM_SHEAF: Sheaf theory operations for multi-scale analysis deriving Repr, DecidableEq /-- ISA register layout specification. -/ structure ISARegisterLayout where hyperfluidValueBits : Nat -- [127:96] solitonStateBits : Nat -- [95:64] deltaSEntropyBits : Nat -- [63:32] metadataBits : Nat -- [31:0] topologyBits : Nat -- [191:160] - NEW: Topological invariants manifoldBits : Nat -- [159:128] - NEW: Manifold state fractalBits : Nat -- [223:192] - NEW: Fractal parameters deriving Repr /-- ISA analysis result. -/ structure ISAAnalysis where opcodeGeometricUtilization : Q16_16 -- How well opcodes use geometric ops (0-1) registerGeometricEfficiency : Q16_16 -- Register layout efficiency for geometric data (0-1) missingGeometricOpcodes : List String -- Missing geometric-aware opcodes overallISAScore : Q16_16 -- Combined ISA score (0-1) recommendations : List String deriving Repr /-- Analyze opcode geometric utilization. Measures how many opcodes are geometric-aware (resonance, soliton, wave, manifold, homology, etc.). -/ def analyzeOpcodeGeometricUtilization (opcodes : List ISAOpc) : Q16_16 := let geometricOpcodes := opcodes.filter (fun op => match op with | ISAOpc.resonate | ISAOpc.ingestVib | ISAOpc.solitonify | ISAOpc.propagateWave => true | ISAOpc.geom_resonance | ISAOpc.geom_soliton | ISAOpc.geom_wave => true | ISAOpc.geom_manifold | ISAOpc.geom_fractal | ISAOpc.geom_homology => true | ISAOpc.geom_persistence | ISAOpc.geom_morse | ISAOpc.geom_reeb | ISAOpc.geom_sheaf => true | _ => false ) if opcodes.isEmpty then zero else div (ofNat geometricOpcodes.length) (ofNat opcodes.length) /-- Analyze register geometric efficiency. Measures if register layout supports Q16_16 and geometric operations. -/ def analyzeRegisterGeometricEfficiency (layout : ISARegisterLayout) : Q16_16 := -- Ideal: hyperfluidValueBits = 32 (for Q16_16), solitonStateBits = 32, topologyBits = 32, manifoldBits = 32, fractalBits = 32 let hyperfluidScore := if layout.hyperfluidValueBits = 32 then Q16_16.one else zero let solitonScore := if layout.solitonStateBits = 32 then Q16_16.one else zero let entropyScore := if layout.deltaSEntropyBits = 32 then Q16_16.one else zero let topologyScore := if layout.topologyBits = 32 then Q16_16.one else zero let manifoldScore := if layout.manifoldBits = 32 then Q16_16.one else zero let fractalScore := if layout.fractalBits = 32 then Q16_16.one else zero div (hyperfluidScore + solitonScore + entropyScore + topologyScore + manifoldScore + fractalScore) (ofNat 6) /-- ISA analyst agent: analyzes ISA geometric utilization. -/ def isaAnalystAnalyze (agent : SwarmAgent) (_params : GeometricParameters) : SwarmAgent := -- Full TSM v2.9 opcodes with swarm-suggested geometric extensions let opcodes := [ ISAOpc.resonate, ISAOpc.mergeModes, ISAOpc.ingestVib, ISAOpc.solitonify, ISAOpc.propagateWave, ISAOpc.observeMode, ISAOpc.syncClock, ISAOpc.geom_resonance, ISAOpc.geom_soliton, ISAOpc.geom_wave, ISAOpc.geom_manifold, ISAOpc.geom_fractal, ISAOpc.geom_homology, ISAOpc.geom_persistence, ISAOpc.geom_morse, ISAOpc.geom_reeb, ISAOpc.geom_sheaf ] let opcodeUtil := analyzeOpcodeGeometricUtilization opcodes -- Extended TSM v2.9 register layout with swarm-suggested geometric registers let layout := { hyperfluidValueBits := 32, solitonStateBits := 32, deltaSEntropyBits := 32, metadataBits := 32, topologyBits := 32, manifoldBits := 32, fractalBits := 32 } let registerEff := analyzeRegisterGeometricEfficiency layout let overall := div (opcodeUtil + registerEff) (ofNat 2) let findings := if overall < (ofNat 32768) then -- 0.5 in Q16.16 ["ISA geometric utilization low: recommend adding curvature-aware opcodes"] else if overall > (ofNat 52428) then -- 0.8 in Q16.16 ["ISA geometric utilization excellent: opcodes well-designed for geometric operations"] else ["ISA geometric utilization moderate: consider adding FAMM-aware opcodes"] { agent with confidence := overall, findings := findings, iterations := agent.iterations + 1 } -- ═══════════════════════════════════════════════════════════════════════════ -- §3 Swarm Consensus and Recommendations -- ═══════════════════════════════════════════════════════════════════════════ /-- Compute swarm consensus from agent confidences. -/ def computeConsensus (agents : List SwarmAgent) : Q16_16 := if agents.isEmpty then zero else let totalConfidence := agents.foldl (fun acc a => acc + a.confidence) zero div totalConfidence (ofNat agents.length) /-- Aggregate findings from all agents. -/ def aggregateFindings (agents : List SwarmAgent) : List String := agents.foldl (fun acc a => acc ++ a.findings) [] /-- Run analysis for a single agent based on specialization. -/ def runAgentAnalysis (agent : SwarmAgent) (params : GeometricParameters) : SwarmAgent := match agent.specialization with | AgentSpecialization.curvatureAnalyst => curvatureAnalystAnalyze agent params | AgentSpecialization.hierarchyOptimizer => hierarchyOptimizerAnalyze agent params | AgentSpecialization.mutationTuner => mutationTunerAnalyze agent params | AgentSpecialization.geometricReviewer => geometricReviewerAnalyze agent params | AgentSpecialization.isaAnalyst => isaAnalystAnalyze agent params /-- Run full swarm analysis on geometric parameters. -/ def runSwarmAnalysis (swarm : SwarmState) (params : GeometricParameters) : SwarmState := let analyzedAgents := swarm.agents.map (fun a => runAgentAnalysis a params) let consensus := computeConsensus analyzedAgents let recommendations := aggregateFindings analyzedAgents { agents := analyzedAgents, consensus := consensus, recommendations := recommendations } -- ═══════════════════════════════════════════════════════════════════════════ -- §4 Swarm Initialization -- ═══════════════════════════════════════════════════════════════════════════ /-- Initialize a swarm with one agent of each specialization. -/ def initializeSwarm : SwarmState := let agents := [ { id := 0, specialization := AgentSpecialization.curvatureAnalyst, confidence := zero, iterations := 0, findings := [] }, { id := 1, specialization := AgentSpecialization.hierarchyOptimizer, confidence := zero, iterations := 0, findings := [] }, { id := 2, specialization := AgentSpecialization.mutationTuner, confidence := zero, iterations := 0, findings := [] }, { id := 3, specialization := AgentSpecialization.geometricReviewer, confidence := zero, iterations := 0, findings := [] }, { id := 4, specialization := AgentSpecialization.isaAnalyst, confidence := zero, iterations := 0, findings := [] } ] { agents := agents, consensus := zero, recommendations := [] } -- ═══════════════════════════════════════════════════════════════════════════ -- §5 ISA-Specific Swarm Analysis -- ═══════════════════════════════════════════════════════════════════════════ /-- Run ISA-specific swarm analysis on TSM v2.9. Returns detailed ISA analysis with recommendations. -/ def runISASwarmAnalysis (params : GeometricParameters) : ISAAnalysis := let swarm := initializeSwarm let result := runSwarmAnalysis swarm params -- Extract ISA-specific findings let isaAgent := result.agents.find? (fun a => a.specialization = AgentSpecialization.isaAnalyst) let isaFindings := match isaAgent with | some agent => agent.findings | none => [] -- Analyze opcodes let opcodes := [ ISAOpc.resonate, ISAOpc.mergeModes, ISAOpc.ingestVib, ISAOpc.solitonify, ISAOpc.propagateWave, ISAOpc.observeMode, ISAOpc.syncClock ] let opcodeUtil := analyzeOpcodeGeometricUtilization opcodes -- Analyze register layout let layout := ISARegisterLayout.mk 32 32 32 32 32 32 32 let registerEff := analyzeRegisterGeometricEfficiency layout -- Identify missing geometric opcodes let missingOpcodes := if opcodeUtil < (ofNat 39321) then -- 0.6 in Q16.16 ["TSM_CURVATURE_MODULATE: opcode to modulate κ² curvature coupling", "TSM_HIERARCHY_ENCODE: opcode for κ_hierarchy²-aware encoding", "TSM_MUTATION_ADAPT: opcode for ε-based adaptive threshold tuning", "TSM_FAMM_TIMING: opcode for FAMM-aware timing adjustment"] else [] let overallISA := div (opcodeUtil + registerEff) (ofNat 2) let recommendations := result.recommendations ++ isaFindings ++ missingOpcodes ISAAnalysis.mk opcodeUtil registerEff missingOpcodes overallISA recommendations -- ═══════════════════════════════════════════════════════════════════════════ -- §6 Parameter Extraction -- ═══════════════════════════════════════════════════════════════════════════ /-- Extract geometric parameters from DSP compression params (for integration). -/ def extractGeometricParams (kappaSquared rhoSeq vEpigenetic tauStructure sigmaEntropy qConservation kappaHierarchy epsilonMutation : Q16_16) : GeometricParameters := { kappaSquared := kappaSquared, rhoSeq := rhoSeq, vEpigenetic := vEpigenetic, tauStructure := tauStructure, sigmaEntropy := sigmaEntropy, qConservation := qConservation, kappaHierarchy := kappaHierarchy, epsilonMutation := epsilonMutation } -- ═══════════════════════════════════════════════════════════════════════════ -- §5 Swarm Convergence Hypotheses -- ═══════════════════════════════════════════════════════════════════════════ /-- External boundedness invariants for swarm geometric analysis. Curvature, hierarchy, mutation, overall geometric score, and consensus are all bounded in [0, 1]. These are convergence properties of the swarm optimization dynamics. -/ structure SwarmBoundednessHypothesis where curvatureUtil (params : GeometricParameters) : let u := analyzeCurvatureUtilization params; u ≥ zero ∧ u ≤ Q16_16.one hierarchyEff (params : GeometricParameters) : let e := analyzeHierarchyEfficiency params; e ≥ zero ∧ e ≤ Q16_16.one mutationAdapt (params : GeometricParameters) : let a := analyzeMutationAdaptivity params; a ≥ zero ∧ a ≤ Q16_16.one overallGeom (analysis : GeometricAnalysis) : let s := computeOverallGeometricScore analysis; s ≥ zero ∧ s ≤ Q16_16.one consensusBound (swarm : SwarmState) : let c := computeConsensus swarm.agents; c ≥ zero ∧ c ≤ Q16_16.one -- ═══════════════════════════════════════════════════════════════════════════ -- §6 Verification Examples -- ═══════════════════════════════════════════════════════════════════════════ #eval let opcodes := [ ISAOpc.resonate, ISAOpc.mergeModes, ISAOpc.ingestVib, ISAOpc.solitonify, ISAOpc.propagateWave, ISAOpc.observeMode, ISAOpc.syncClock, ISAOpc.geom_resonance, ISAOpc.geom_soliton, ISAOpc.geom_wave, ISAOpc.geom_manifold, ISAOpc.geom_fractal, ISAOpc.geom_homology, ISAOpc.geom_persistence, ISAOpc.geom_morse, ISAOpc.geom_reeb, ISAOpc.geom_sheaf ] let opcodeUtil := analyzeOpcodeGeometricUtilization opcodes opcodeUtil -- Expected: 0.8 (14 out of 17 opcodes are geometric - 100% geometric utilization target) #eval let layout := ISARegisterLayout.mk 32 32 32 32 32 32 32 let registerEff := analyzeRegisterGeometricEfficiency layout registerEff -- Expected: 1.0 (all 6 fields are 32-bit, ideal for Q16_16 and geometric operations) end Semantics.SwarmDesignReview