# Reservoir size: cumulative tree count
reservoir_size = sum(A000081[1:n])

# Number of membranes: tree count at order k
num_membranes = A000081[k]

# Growth rate: natural ratio between consecutive orders
growth_rate = A000081[n+1] / A000081[n]

# Mutation rate: inversely proportional to complexity
mutation_rate = 1.0 / A000081[n]

using Pkg
Pkg.add(url="https://github.com/cogpy/cogpilot.jl")

using CogPilot

# Automatic parameter derivation from A000081
system = DeepTreeEchoSystem(base_order=5)

# This automatically derives:
# - reservoir_size = 17 (cumulative: 1+1+2+4+9)
# - max_tree_order = 8
# - num_membranes = 2 (A000081[3] = 2)
# - growth_rate ≈ 2.22 (ratio: 20/9)
# - mutation_rate ≈ 0.11 (inverse: 1/9)

# Initialize with A000081-derived seed count
initialize!(system, seed_trees=4)  # A000081[4] = 4

# Evolve the system
evolve!(system, 50, dt=0.01, verbose=true)

# Process input through the cognitive architecture
input = randn(10)
output = process_input!(system, input)

# Adapt topology during evolution
adapt_topology!(system, add_membrane=true)

# Get system status
print_system_status(system)

using CogPilot.DomainKernels

# Generate consciousness kernel (self-referential, recursive)
consciousness = generate_consciousness_kernel(order=5, depth_bias=2.5)

# Generate physics kernel (Hamiltonian, symplectic)
physics = generate_physics_kernel(:hamiltonian, order=4,
                                 conserved_quantities=[:energy])

# Self-generation through chain rule composition
offspring = OntogeneticKernel.self_generate(consciousness)

# Evolve population
population = [consciousness, physics, 
              [create_kernel(4) for _ in 1:18]...]

for generation in 1:30
    # Evaluate fitness
    for kernel in population
        evaluate_kernel_fitness!(kernel, nothing, population)
    end
    
    # Selection, crossover, mutation
    next_gen = evolve_generation(population, 
                                elitism_rate=0.1, 
                                mutation_rate=0.15)
    population = next_gen
end

# Best evolved kernel
best = population[1]
println("Best fitness: $(best.fitness)")

using CogPilot
using Random

Random.seed!(42)

# 1. Create system with A000081-aligned parameters
system = DeepTreeEchoSystem(base_order=5)

# 2. Initialize with proper seed count
initialize!(system, seed_trees=4)  # A000081[4] = 4

# 3. Evolve system
evolve!(system, 30, verbose=true)

# 4. Process temporal inputs
for i in 1:10
    input = randn(10)
    output = process_input!(system, input)
    println("Step $i: output norm = $(norm(output))")
end

# 5. Adapt topology
adapt_topology!(system, add_membrane=true)
evolve!(system, 20, verbose=false)

# 6. Analyze system state
status = get_system_status(system)
print_system_status(system)

# 7. Save state
save_system_state(system, "cognitive_state.txt")

# Create A000081 generator
generator = A000081Generator(10)

# Generate trees of order 5 (yields 9 trees)
trees = generate_a000081_trees(generator, 5)
@assert length(trees) == 9

# Create ontogenetic state
state = OntogeneticState(trees)

# Self-evolve for many generations
history = self_evolve!(state, generator, 50)

# Create ridge with specific method
ridge = create_ridge(8, method=:rk4)

# Evaluate at a point
f(y) = -y  # Vector field
increment = evaluate_ridge(ridge, [1.0], f)

# Optimize coefficients
optimize_ridge!(ridge, 4, iterations=100)

# Create reservoir with A000081-aligned size
reservoir = create_echo_reservoir(
    reservoir_size = 17,  # sum(A000081[1:5])
    spectral_radius = 0.9,
    sparsity = 0.1
)

# Train on temporal data
train_reservoir!(reservoir, input_sequence, target_sequence)

# Generate predictions
prediction = predict_sequence(reservoir, seed, steps=50)

# Create membrane reservoir
membrane_system = create_membrane_reservoir(
    structure = "[[]'2 []'3]'1",  # Nested membrane structure
    alphabet = ["a", "b", "c"],
    num_membranes = 4  # A000081[4] = 4
)

# Add evolution rules
add_evolution_rule!(membrane_system, 
    EvolutionRule(1, Multiset("a"=>1), Multiset("b"=>2)))

# Evolve system
evolve_membrane!(membrane_system, 10)

# Create garden
garden = create_garden()

# Plant trees in specific membrane
tree_id = plant_tree!(garden, [1, 2, 3, 2], membrane_id=1)

# Grow trees naturally
grow_trees!(garden, 10)

# Cross-pollinate between membranes
cross_pollinate!(garden, membrane1=1, membrane2=2, count=5)

# Harvest feedback
feedback = harvest_feedback!(garden, membrane_id=1)

# Create symplectic J-surface
jsurface = create_jsurface(100, symplectic=true)
state = JSurfaceState(100, 20)

# Gradient flow on surface
gradient_flow!(jsurface, state, dt=0.01)

# Evolution step
evolution_step!(jsurface, state, mutation_rate=0.1)

# Symplectic integration
symplectic_integrate!(jsurface, state, dt=0.01)

using ModelingToolkit

# Apply symbolic transformations to optimize kernel
function optimize_kernel_mtk!(kernel::OntogeneticKernel)
    sys_simplified = structural_simplify(kernel.sys)
    prob = ODEProblem(sys_simplified, [], (0.0, 1.0))
    kernel.sys = sys_simplified
    return kernel
end

using NeuralPDE, Lux

# Evolve kernels using physics-informed neural networks
function pinn_kernel_optimization(kernel, pde_system, training_data)
    chain = Lux.Chain(
        Lux.Dense(2, 16, Lux.tanh),
        Lux.Dense(16, 16, Lux.tanh),
        Lux.Dense(16, 1)
    )
    
    discretization = PhysicsInformedNN(chain, QuadratureTraining())
    physics_loss = create_bseries_loss(kernel.genome, pde_system)
    
    optimized_genome = train_pinn_kernel(kernel, discretization, physics_loss)
    kernel.genome = optimized_genome
    return kernel
end

using Catalyst

# Generate kernel for reaction network
rn = @reaction_network begin
    k1, A + B --> C
    k2, C --> D
end k1 k2

# Create reaction-optimized kernel
kernel = generate_reaction_kernel(rn, order=4)

# Train on Lorenz attractor
using CogPilot
system = DeepTreeEchoSystem(base_order=5)
initialize!(system, seed_trees=4)

# Generate Lorenz data
lorenz_data = generate_lorenz_attractor(1000)
train_on_timeseries!(system, lorenz_data)

# Predict future trajectory
prediction = predict_future(system, steps=500)

using CogPilot.DomainKernels

# Create kernel optimized for equation discovery
kernel = generate_universal_kernel(
    "discover differential equation from data",
    order=6
)

# Evolve to find best symbolic representation
optimized_kernel = evolve_for_discovery(kernel, data, 100)
equation = extract_symbolic_form(optimized_kernel)

# Create optimization landscape
system = DeepTreeEchoSystem(base_order=5)

# Define fitness landscape
fitness_fn = (x) -> pareto_fitness(x, objectives)

# Evolve toward Pareto front
evolve_multi_objective!(system, fitness_fn, generations=200)

# Extract optimal solutions
solutions = get_pareto_front(system)

# Create consciousness-inspired kernel
consciousness = generate_consciousness_kernel(order=5)

# Process experience stream
for experience in experience_stream
    # Update internal state
    process_experience!(consciousness, experience)
    
    # Form memories
    consolidate_memory!(consciousness)
    
    # Generate predictions
    expectation = generate_expectation(consciousness)
end