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:

Stratifies (layers structure hierarchically)
Fabricates (composes components into wholes)
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

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

fabricate(components...) = colimit(Diagram(components))

Rule F2: Operad Algebra Evaluation

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:

bisimulation-game verifies layer separation (PASSIVE vs ACTIVE)
acsets-algebraic-databases provides the structural schema
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:

polyglot-spi validates cross-language parallelism invariance
oapply-colimit evaluates operad algebra via colimits
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:

spi-parallel-verify checks stream conservation
autopoiesis maintains self-modifying closure
triad-interleave schedules balanced triplet execution

Seed Approach List

Seeds discovered during kinetic block formation:

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

# 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

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

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

# 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)

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

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

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

# 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 (>>):

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 (⊗):

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

# 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.

kinetic-block

Kinetic Block Skill

Overview

Rules for Stratificating

Rule S1: Passive/Active Layer Separation

Rule S2: NFU Enrichment

Rule S3: Dendroidal Stratification

Rule S4: Trit Assignment

Rules for Fabricating

Rule F1: Colimit Composition

Rule F2: Operad Algebra Evaluation

Rule F3: Bisimulation Invariance

Rule F4: Golden Thread Traversal

Enumeration: 3 Skills × 3 MCPs × 3 Tools

STRATIFICATION Interaction

FABRICATION Interaction

CONSERVATION Interaction

Seed Approach List

Usage

Python Interface

Julia Interface

Integration Points

Complete 3×3×3 Interaction Matrix

STRATIFICATION (Layer Formation)

FABRICATION (Component Assembly)

CONSERVATION (Invariant Verification)

XY Model Phase Semantics

References

GF(3) Conservation Proof

Information Energy Framework

Kinetic Information Energy (KIE)

Potential Information Energy (PIE)

Free Energy Principle

Energy Conservation

Markov Blanket as Energy Boundary

PCT Energy Dynamics

Valence as Energy Gradient

Seed Approaches (Energy-Extended)

Open Games Integration

Games as Energy Exchange

Lens Structure

Tripartite Game = Kinetic Block

Selection Functions as Energy Policies

Nash Equilibrium = Energy Minimum

Compositional Energy Transfer

GF(3) Triads for Open Games

Commands

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