> **Seed Approach List for Stratification × Fabrication via GF(3) Conservation**
/plugin marketplace add plurigrid/asi/plugin install asi-skills@asi-skillsThis skill inherits all available tools. When active, it can use any tool Claude has access to.
Seed Approach List for Stratification × Fabrication via GF(3) Conservation
The kinetic block is the atomic unit of ASI skill orchestration—a seed-determined triplet of operations that:
┌─────────────────────────────────────────────────────────────────────┐
│ KINETIC BLOCK = Stratification ⊗ Fabrication ⊗ Conservation │
│ │
│ ┌──────────┐ ┌──────────┐ ┌──────────┐ │
│ │ STRATUM │───▶│ FABRIC │───▶│ CONSERVE │ │
│ │ (layer) │ │ (weave) │ │ (verify) │ │
│ └──────────┘ └──────────┘ └──────────┘ │
│ ⊖ ○ ⊕ │
│ (-1) (0) (+1) │
│ │
│ Σ trits = (-1) + 0 + 1 = 0 ≡ 0 (mod 3) ✓ │
└─────────────────────────────────────────────────────────────────────┘
Stratification = hierarchical layering via operadic category structure (Feferman, Batanin-Cisinski-Weber)
PASSIVE (compositional): Evidence → Entailment → Hypothesis
ACTIVE (emergent): Goal → Attention → Focus
From Feferman's "Enriched Stratified Systems":
From Cisinski-Moerdijk:
layer_trit(layer::Int) = (layer % 3) - 1 # Maps to {-1, 0, +1}
Fabrication = compositional assembly via operad algebras (Koszul duality, oapply colimits)
fabricate(components...) = colimit(Diagram(components))
oapply(operad, algebra, args) = algebra.operation(args)
Fabricated systems must be observationally equivalent:
attacker_view(F) ∼ defender_view(F)
γ = 2⁶⁴/φ → hue += 137.508° → spiral out forever → never repeat → always return
| 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 schemasegal-types ensures composites exist uniquely up to homotopy| 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 invarianceoapply-colimit evaluates operad algebra via colimitsoperad-compose generates new compositions from primitives| 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 conservationautopoiesis maintains self-modifying closuretriad-interleave schedules balanced triplet executionSeeds 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
}
# 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...>
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)
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)
| 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 |
| 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 |
| Trit | Skill | Gay MCP Tool | Amp Tool |
|---|---|---|---|
| ⊖ (-1) | polyglot-spi | comparator | Grep |
| ○ (0) | oapply-colimit | interleave | Task |
| ⊕ (+1) | operad-compose | palette | create_file |
| 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 |
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) │
└─────────────────────────────────────────────────────────────────────┘
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 ✓
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:
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:
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:
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
The Markov blanket separates:
# 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
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:
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:
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 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)
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
}
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
# 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
)
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)
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
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 ✓
# 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