--- name: kinetic-block description: Kinetic Block Skill version: 1.0.0 --- # Kinetic Block Skill > **Seed Approach List for Stratification × Fabrication via GF(3) Conservation** ## Overview The **kinetic block** is the atomic unit of ASI skill orchestration—a seed-determined triplet of operations that: 1. **Stratifies** (layers structure hierarchically) 2. **Fabricates** (composes components into wholes) 3. **Conserves** (maintains GF(3) = 0 invariant) ``` ┌─────────────────────────────────────────────────────────────────────┐ │ KINETIC BLOCK = Stratification ⊗ Fabrication ⊗ Conservation │ │ │ │ ┌──────────┐ ┌──────────┐ ┌──────────┐ │ │ │ STRATUM │───▶│ FABRIC │───▶│ CONSERVE │ │ │ │ (layer) │ │ (weave) │ │ (verify) │ │ │ └──────────┘ └──────────┘ └──────────┘ │ │ ⊖ ○ ⊕ │ │ (-1) (0) (+1) │ │ │ │ Σ trits = (-1) + 0 + 1 = 0 ≡ 0 (mod 3) ✓ │ └─────────────────────────────────────────────────────────────────────┘ ``` --- ## Rules for Stratificating **Stratification** = hierarchical layering via operadic category structure (Feferman, Batanin-Cisinski-Weber) ### Rule S1: Passive/Active Layer Separation ``` PASSIVE (compositional): Evidence → Entailment → Hypothesis ACTIVE (emergent): Goal → Attention → Focus ``` ### Rule S2: NFU Enrichment From Feferman's "Enriched Stratified Systems": - Stratified pairing allows category of all categories - Functors between unrestricted categories - Typical ambiguity resolution ### Rule S3: Dendroidal Stratification From Cisinski-Moerdijk: - Trees → Operads (single-sorted) - Graphs → Modular operads (cyclic) - Segal/Kan conditions for ∞-operads ### Rule S4: Trit Assignment ```julia layer_trit(layer::Int) = (layer % 3) - 1 # Maps to {-1, 0, +1} ``` --- ## Rules for Fabricating **Fabrication** = compositional assembly via operad algebras (Koszul duality, oapply colimits) ### Rule F1: Colimit Composition ```julia fabricate(components...) = colimit(Diagram(components)) ``` ### Rule F2: Operad Algebra Evaluation ```julia oapply(operad, algebra, args) = algebra.operation(args) ``` ### Rule F3: Bisimulation Invariance Fabricated systems must be observationally equivalent: ``` attacker_view(F) ∼ defender_view(F) ``` ### Rule F4: Golden Thread Traversal ``` γ = 2⁶⁴/φ → hue += 137.508° → spiral out forever → never repeat → always return ``` --- ## Enumeration: 3 Skills × 3 MCPs × 3 Tools ### STRATIFICATION Interaction | Trit | Skill | MCP Tool | Amp Tool | |------|-------|----------|----------| | ⊖ (-1) | `bisimulation-game` | `mcp__gay__hierarchical_control` | `mcp__tree_sitter__get_ast` | | ○ (0) | `acsets-algebraic-databases` | `mcp__gay__loopy_strange` | `finder` | | ⊕ (+1) | `segal-types` | `mcp__gay__golden_thread` | `skill` | **Interaction Flow:** 1. `bisimulation-game` verifies layer separation (PASSIVE vs ACTIVE) 2. `acsets-algebraic-databases` provides the structural schema 3. `segal-types` ensures composites exist uniquely up to homotopy ### FABRICATION Interaction | Trit | Skill | MCP Tool | Amp Tool | |------|-------|----------|----------| | ⊖ (-1) | `polyglot-spi` | `mcp__gay__comparator` | `Grep` | | ○ (0) | `oapply-colimit` | `mcp__gay__interleave` | `Task` | | ⊕ (+1) | `operad-compose` | `mcp__gay__palette` | `create_file` | **Interaction Flow:** 1. `polyglot-spi` validates cross-language parallelism invariance 2. `oapply-colimit` evaluates operad algebra via colimits 3. `operad-compose` generates new compositions from primitives ### CONSERVATION Interaction | Trit | Skill | MCP Tool | Amp Tool | |------|-------|----------|----------| | ⊖ (-1) | `spi-parallel-verify` | `mcp__gay__reafference` | `Bash` | | ○ (0) | `autopoiesis` | `mcp__gay__self_model` | `todo_write` | | ⊕ (+1) | `triad-interleave` | `mcp__gay__efference_copy` | `oracle` | **Interaction Flow:** 1. `spi-parallel-verify` checks stream conservation 2. `autopoiesis` maintains self-modifying closure 3. `triad-interleave` schedules balanced triplet execution --- ## Seed Approach List Seeds discovered during kinetic block formation: ```python SEED_APPROACHES = { # Stratification seeds "feferman_nfu": 0x42D, # NFU enriched stratification "dendroidal_nerve": 0x1066, # Cisinski-Moerdijk nerve "segal_kan": 0xBEEF, # ∞-operad Kan condition # Fabrication seeds "koszul_dual": 0xCAFE, # Batanin-Markl Koszul duality "colimit_oapply": 0xDEAD, # Operad algebra evaluation "golden_spiral": 0x9E37, # φ-derived golden angle # Conservation seeds "gf3_trivial": 0x0000, # χ₀ character (uniform) "gf3_cyclic": 0x0001, # χ₁ character (ω rotation) "gf3_anticyclic": 0x0002, # χ₂ character (ω² rotation) # Composite seeds "kinetic_block_alpha": 0x42D ^ 0xCAFE, # S ⊕ F "kinetic_block_beta": 0x1066 ^ 0xDEAD, # Nerve ⊕ Colimit "kinetic_block_gamma": 0xBEEF ^ 0x9E37, # Kan ⊕ Golden } ``` --- ## Usage ```bash # Generate kinetic block schedule just kinetic-block 0x42D 9 # Verify GF(3) conservation just kinetic-verify # Run stratification layer just kinetic-stratify # Run fabrication composition just kinetic-fabricate ``` ### Python Interface ```python from kinetic_block import KineticBlock, StratificationRules, FabricationRules block = KineticBlock(seed=0x42D) # Apply stratification layers = block.stratify( passive=["evidence", "entailment"], active=["goal", "attention"] ) # Apply fabrication composite = block.fabricate( operand="operad_compose", components=["skill_a", "skill_b", "skill_c"] ) # Verify conservation assert block.conserved() # Σ trits ≡ 0 (mod 3) ``` ### Julia Interface ```julia using KineticBlock block = KineticBlock(seed=0x42D) # Stratification via SCL foundation stratify!(block, SchHypothesis) # Fabrication via oapply fabricate!(block, :operad_compose, [skill_a, skill_b, skill_c]) # Conservation check @assert gf3_conserved(block) ``` --- ## Integration Points | Component | Location | Purpose | |-----------|----------|---------| | `scl_foundation.jl` | `plurigrid/asi/lib/` | Hypothesis ACSet | | `abduction_engine.jl` | `plurigrid/asi/lib/` | Skill discovery | | `pattern_types.py` | `plurigrid/asi/lib/` | Walk classification | | `gay-mcp` | MCP Server | Deterministic colors | | `tree-sitter-mcp` | MCP Server | AST stratification | --- ## Complete 3×3×3 Interaction Matrix ### STRATIFICATION (Layer Formation) | Trit | Skill | Gay MCP Tool | Amp Tool | |------|-------|--------------|----------| | ⊖ (-1) | `bisimulation-game` | `hierarchical_control` | `mcp__tree_sitter__get_ast` | | ○ (0) | `acsets-algebraic-databases` | `loopy_strange` | `finder` | | ⊕ (+1) | `segal-types` | `golden_thread` | `skill` | ### FABRICATION (Component Assembly) | Trit | Skill | Gay MCP Tool | Amp Tool | |------|-------|--------------|----------| | ⊖ (-1) | `polyglot-spi` | `comparator` | `Grep` | | ○ (0) | `oapply-colimit` | `interleave` | `Task` | | ⊕ (+1) | `operad-compose` | `palette` | `create_file` | ### CONSERVATION (Invariant Verification) | Trit | Skill | Gay MCP Tool | Amp Tool | |------|-------|--------------|----------| | ⊖ (-1) | `spi-parallel-verify` | `reafference` | `Bash` | | ○ (0) | `autopoiesis` | `self_model` | `todo_write` | | ⊕ (+1) | `triad-interleave` | `efference_copy` | `oracle` | --- ## XY Model Phase Semantics Kinetic blocks operate at BKT critical temperature τ* ≈ 0.5: ``` ┌─────────────────────────────────────────────────────────────────────┐ │ PHENOMENAL PHASES (from Gay.jl xy_model) │ ├─────────────────────────────────────────────────────────────────────┤ │ τ < τ* → ORDERED (smooth field, bound pairs, high valence) │ │ τ = τ* → CRITICAL (BKT transition, defects mobile, annealing) │ │ τ > τ* → DISORDERED (frustrated, strobing, high defect density) │ ├─────────────────────────────────────────────────────────────────────┤ │ Colors: │ │ Smooth: #AC2A5A (purple-red) │ │ Critical: #DDB562 (golden) │ │ Frustrated: #28C3BF (cyan) │ └─────────────────────────────────────────────────────────────────────┘ ``` --- ## References - Feferman, S. (1974). "Enriched Stratified Systems for Category Theory" - Batanin, Cisinski, Weber. "Multitensor Lifting and Strictly Unital Higher Category Theory" - Cisinski, Moerdijk. "Dendroidal Sets and Simplicial Operads" - Batanin, Markl. "Operadic Categories as Environment for Koszul Duality" - Powers, W. (1973). "Behavior: The Control of Perception" - Kosterlitz, Thouless. "BKT Phase Transition in XY Model" --- ## GF(3) Conservation Proof For any kinetic block K with components (s, f, c): ``` trit(s) + trit(f) + trit(c) = (-1) + 0 + 1 = 0 ≡ 0 (mod 3) ✓ ``` The kinetic block is **closed under composition**: composing two blocks preserves conservation. ``` K₁ ⊗ K₂ = (s₁⊗s₂, f₁⊗f₂, c₁⊗c₂) Σ trits = 2×((-1) + 0 + 1) = 0 ✓ ``` --- ## Information Energy Framework ### Kinetic Information Energy (KIE) **Definition**: Energy associated with *active* information flow—computation in progress. ``` KIE = ½ × m_info × v²_processing where: m_info = information mass (bits in transit) v_processing = processing velocity (bits/sec) ``` In the kinetic block: - **Stratification** → KIE increases (layer separation requires work) - **Fabrication** → KIE converts to structure (composition crystallizes) - **Conservation** → KIE verified (no energy leak) ### Potential Information Energy (PIE) **Definition**: Energy stored in *latent* structure—information ready to be activated. ``` PIE = m_info × g_entropy × h_depth where: m_info = information mass (bits stored) g_entropy = entropy gradient (bits/layer) h_depth = structural depth (layers) ``` Energy wells correspond to: - **H^0 generators**: Stable configurations (local minima) - **Cohomology obstructions**: Barriers between wells - **Spectral gap**: Minimum energy to transition between wells ### Free Energy Principle From Friston's active inference: ``` F = Prediction Error + Model Complexity F = D_KL[Q(s) || P(s|o)] + E_Q[log P(o,s)] ``` In kinetic blocks: - **Prediction**: Expected color from seed - **Observation**: Actual color generated - **Free Energy**: Hue difference / 180° (normalized) ### Energy Conservation ``` Total Energy = KIE + PIE = constant When KIE ↑ (active processing): - PIE ↓ (structure being consumed) - Free energy fluctuates When KIE ↓ (processing complete): - PIE ↑ (new structure formed) - Free energy minimized ``` ### Markov Blanket as Energy Boundary The Markov blanket separates: - **Internal states**: PIE reservoir (stored structure) - **External states**: Environment (potential KIE source) - **Blanket states**: Energy exchange interface ```julia # From Gay.jl markov_blanket tool blanket = MarkovBlanket(internal_seed=35271, external_seed=42069) # Permeability determines energy flow rate if blanket.permeable KIE_flow = gradient(PIE_internal, PIE_external) else KIE_flow = 0 # Insulated system end ``` ### PCT Energy Dynamics Powers' Perceptual Control Theory provides the control loop: ``` Reference (desired PIE state) ↓ Comparator: error = reference - perception ↓ Output: corrective action (KIE expenditure) ↓ Environment: action affects world ↓ Sensor: new perception (updated PIE) ↓ Loop continues until error ≈ 0 ``` **Gain** controls KIE/PIE conversion efficiency: - High gain (0.8-1.0): Rapid response, oscillation risk - Low gain (0.1-0.3): Slow response, stable convergence ### Valence as Energy Gradient From QRI's Symmetry Theory of Valence: ``` Valence = -∇(Defect Density) High valence: Smooth field, low defects, PIE minimum Low valence: Frustrated field, high defects, PIE maximum ``` Kinetic blocks operate optimally at **BKT critical temperature** τ* ≈ 0.5: - Defects mobile enough to annihilate (KIE available) - Not proliferating (PIE stable) ### Seed Approaches (Energy-Extended) ```python ENERGY_SEEDS = { # KIE-dominant (active processing) "kinetic_alpha": 0x88E7, # High KIE, stratification "fabrication_flow": 0xCAFE, # KIE → structure conversion # PIE-dominant (stored structure) "potential_well": 0x42D, # H^0 generator, stable "spectral_gap": 0x1066, # Barrier between wells # Energy balance "free_energy_min": 0x0000, # F = 0, equilibrium "critical_tau": 0x5555, # τ* ≈ 0.5, BKT transition # Markov blanket configurations "permeable_blanket": 0xAAAA, # Energy exchange enabled "insulated_blanket": 0xFFFF, # Closed system } ``` --- ## Open Games Integration ### Games as Energy Exchange Open games provide the **strategic structure** for kinetic block interactions: ``` ┌───────────────────┐ X ──→│ Kinetic Block │──→ Y (PIE) │ │ (KIE) R ←──│ play / coplay │←── S (KIE')│ │ (PIE') └───────────────────┘ Forward (play): PIE → KIE (activate potential) Backward (coplay): KIE' → PIE' (store results) ``` ### Lens Structure ```ruby class KineticLens < Lens def initialize(block_type, seed) super( name: "kinetic_#{block_type}", forward: ->(pie) { stratify(pie) }, # PIE → KIE backward: ->(kie, r) { conserve(kie, r) }, # (KIE, R) → PIE' trit: BLOCK_TRITS[block_type] ) end end BLOCK_TRITS = { stratify: -1, # MINUS: constrain structure fabricate: 0, # ERGODIC: transport composition conserve: +1 # PLUS: generate verification } ``` ### Tripartite Game = Kinetic Block ```ruby class KineticGame < TripartiteGame def initialize(seed) super(seed) @stratifier = create_kinetic_player(:stratify, -1) @fabricator = create_kinetic_player(:fabricate, 0) @conservator = create_kinetic_player(:conserve, +1) end def play_block(pie_input) # Phase 1: Stratification (PIE → KIE) strat_result = @stratifier.play(pie_input) kie = strat_result[:outcome] # Phase 2: Fabrication (KIE → structure) fab_result = @fabricator.play(kie) structure = fab_result[:outcome] # Phase 3: Conservation (verify → PIE') cons_result = @conservator.play(structure) pie_output = cons_result[:outcome] { phases: [strat_result, fab_result, cons_result], energy_flow: { kie_in: pie_input, pie_out: pie_output }, gf3_sum: (-1 + 0 + 1), # Always 0 equilibrium: nash_equilibrium? } end end ``` ### Selection Functions as Energy Policies ```ruby # Argmax: Maximize energy throughput (PLUS +1) ε_max = SelectionFunction.argmax(trit: +1) # Argmin: Minimize energy expenditure (MINUS -1) ε_min = SelectionFunction.argmin(trit: -1) # Random: Neutral exploration (ERGODIC 0) ε_rand = SelectionFunction.random(trit: 0) # Energy-weighted selection ε_energy = SelectionFunction.new( name: "energy_weighted", selector: ->(valuation, domain) { # Weight by free energy (prefer low F) domain.min_by { |x| free_energy(valuation.call(x)) } }, trit: 0 ) ``` ### Nash Equilibrium = Energy Minimum **Key insight**: Nash equilibrium in kinetic games corresponds to free energy minimum. ``` Nash equilibrium: No player can improve by unilateral deviation ⟺ Free energy min: F = Prediction Error + Complexity is minimized ⟺ GF(3) conserved: Σ trits ≡ 0 (mod 3) ``` ### Compositional Energy Transfer Sequential composition (`>>`): ```ruby block_1 >> block_2 = KineticGame where play = block_2.play ∘ block_1.play coplay = block_1.coplay ∘ (id × block_2.coplay) energy = block_1.kie + block_2.kie ``` Parallel composition (`⊗`): ```ruby block_1 ⊗ block_2 = KineticGame where play = block_1.play × block_2.play coplay = block_1.coplay × block_2.coplay energy = block_1.kie ⊗ block_2.kie # Tensor product ``` ### GF(3) Triads for Open Games ``` temporal-coalgebra (-1) ⊗ open-games (0) ⊗ operad-compose (+1) = 0 ✓ three-match (-1) ⊗ open-games (0) ⊗ gay-mcp (+1) = 0 ✓ bisimulation-game (-1) ⊗ kinetic-block (0) ⊗ triad-interleave (+1) = 0 ✓ ``` ### Commands ```bash # Run kinetic game just kinetic-game 0x42D 10 # Check Nash equilibrium just kinetic-nash game_id # Compose blocks just kinetic-compose block_1 block_2 # Verify energy conservation just kinetic-energy block_id ``` ``` ## Scientific Skill Interleaving This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem: ### Graph Theory - **networkx** [○] via bicomodule - Universal graph hub ### Bibliography References - `general`: 734 citations in bib.duckdb ## SDF Interleaving This skill connects to **Software Design for Flexibility** (Hanson & Sussman, 2021): ### Primary Chapter: 5. Evaluation **Concepts**: eval, apply, interpreter, environment ### GF(3) Balanced Triad ``` kinetic-block (+) + SDF.Ch5 (−) + [balancer] (○) = 0 ``` **Skill Trit**: 1 (PLUS - generation) ### Secondary Chapters - Ch3: Variations on an Arithmetic Theme - Ch1: Flexibility through Abstraction - Ch4: Pattern Matching - Ch6: Layering - Ch2: Domain-Specific Languages - Ch10: Adventure Game Example ### Connection Pattern Evaluation interprets expressions. This skill processes or generates evaluable forms. ## Cat# Integration This skill maps to **Cat# = Comod(P)** as a bicomodule in the equipment structure: ``` Trit: 0 (ERGODIC) Home: Prof Poly Op: ⊗ Kan Role: Adj Color: #26D826 ``` ### GF(3) Naturality The skill participates in triads satisfying: ``` (-1) + (0) + (+1) ≡ 0 (mod 3) ``` This ensures compositional coherence in the Cat# equipment structure.