kinetic-block

# 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 <layer_index>

# Run fabrication composition
just kinetic-fabricate <component_ids...>
```

### 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

## 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.