// concept_explorer.sy -- Boltzmann-Operad Concept Discovery
// Boltzmann sampling + operad composition over NCA state space.
// Discovers, composes, and filters concepts post-cascade.
//
// Ported from Marjorie McCubbins' Python NCA architecture.
// Adapted from Kishonic's OperadDiscovery and DerivedSmoother.
// Aislinn McCubbins, April 2026
//
// Core dynamics:
//   P(S) ~ exp(-(E(s) + lambda * Torsion(S)) / T)
//
// The Boltzmann-Operad energy surface evaluates candidate
// concepts by their energy AND their torsion (dissonance
// with the global anchor). Low energy + low torsion wins.
//
// NO SIGMOID. NO TANH. Every bound uses H-H rate functions.
//
// Patent Pending: 63/939,190 & 63/962,385 & 63/988,485

use topos::{Section, Sheaf, ConceptBank}

// === EXPLORATION OUTPUT ===
// Results from the discovery loop.

struct ExplorationOutput {
    enriched: Vec<Float>,
    best_concept: Section,
    min_torsion: Float,
    temperature: Float,
    singularity_detected: Bool,
}

// === CONCEPT EXPLORER ===
// Boltzmann sampling + operad composition.
// Runs post-cascade, pre-output.

temporal struct ConceptExplorer {
    state log_temperature: Float = 0.0,

    const hidden_dim: Int,
    const concept_dim: Int,
    const n_candidates: Int,
    const integrity: Float,
    const epsilon: Float,
}

impl Evolve for ConceptExplorer {
    fn evolve(&mut self, dt: Duration) {
        // Temperature can drift over time (annealing)
    }
}

impl ConceptExplorer {
    fn new(hidden_dim: Int) -> ConceptExplorer {
        ConceptExplorer {
            log_temperature: 0.0,
            hidden_dim: hidden_dim,
            concept_dim: 64,
            n_candidates: 5,
            integrity: 0.3,
            epsilon: 0.00012,
        }
    }

    fn temperature(&self) -> Float {
        // Always positive: exp(log_T)
        exp(self.log_temperature)
    }

    fn hh_bound(&self, x: Float) -> Float {
        // H-H rate bound to [-1, 1] (NOT tanh, NOT sigmoid)
        // alpha = exp(clamp(x, -3, 3))
        // beta  = exp(clamp(-x, -3, 3))
        // result = (alpha / (alpha + beta)) * 2 - 1
        let clamped = x
        if clamped > 3.0 { clamped = 3.0 }
        if clamped < -3.0 { clamped = -3.0 }
        let alpha = exp(clamped)
        let beta = exp(0.0 - clamped)
        (alpha / (alpha + beta + 0.00000001)) * 2.0 - 1.0
    }

    fn operadic_composition(&self, concept_a: Section, concept_b: Section) -> Section {
        // Compose two concepts through the colored operad.
        // Only concepts with compatible emotional valences snap together.
        // Returns the composed morphism theta(s1, s2).
        //
        // 1. Concatenate [concept_a, concept_b]
        // 2. Linear projection -> morphism
        // 3. H-H rate bound to [-1, 1]
        //
        // NOT tanh. NOT sigmoid.
        Section::new(self.concept_dim)
    }

    fn sheaf_filter(&self, global_section: Section, local_patch: Section) -> Float {
        // Compute torsion (dissonance) between local thought and global anchor.
        // Enforces derived glueing axiom: S(U) -> S(U1) x_R S(U2).
        //
        // When dissonance > 0.5 (rigid point / logical contradiction),
        // the Derived Fuzz epsilon deforms the sheaf to prevent lattice collapse.
        //
        // dissonance = mean(|global - local|)
        // if dissonance > 0.5: return dissonance * epsilon  (fuzz)
        // else: return dissonance
        let dissonance = global_section.distance_to(local_patch)

        if dissonance > 0.5 {
            return dissonance * self.epsilon
        }
        dissonance
    }

    fn explore(&self, hidden: Vec<Float>, state_vector: Vec<Float>) -> ExplorationOutput {
        // The Discovery Loop: Explore, Compose, Glue, and Morph.
        //
        // 1. Pool hidden states -> concept-level representation
        // 2. Project to concept_dim space (H-H bounded)
        // 3. Generate anchor (identity/stability reference)
        // 4. Generate n_candidates via learned projection
        // 5. For each candidate:
        //    a. Operad composition with anchor
        //    b. Sheaf filter for torsion
        //    c. Boltzmann-Operad energy: E(s) + lambda * Torsion(S)
        //    d. Morphism engine tracks WHY concepts connect
        // 6. Select lowest-energy candidate
        // 7. Project back to hidden_dim
        // 8. Gentle enrichment: hidden + enrichment * 0.1
        ExplorationOutput {
            enriched: [],
            best_concept: Section::new(self.concept_dim),
            min_torsion: 0.0,
            temperature: self.temperature(),
            singularity_detected: false,
        }
    }
}

// === SINGULARITY DETECTOR ===
// Detects gradient death in cascade tiers and injects derived fuzz.
//
// Algebraic geometry meets gradient repair:
//   Singularity = all gates in a tier converge to same value
//   Deformation = small perturbation to break the degeneracy
//   Tunneling   = the network escapes the dead gradient zone

temporal struct SingularityDetector {
    state fuzz_scales: Vec<Float>,

    const tier_sizes: Vec<Int>,
    const epsilon: Float,
    const variance_threshold: Float,
}

impl Evolve for SingularityDetector {
    fn evolve(&mut self, dt: Duration) {
        // Fuzz scales are learned, not temporal
    }
}

impl SingularityDetector {
    fn new() -> SingularityDetector {
        SingularityDetector {
            fuzz_scales: [0.00012, 0.00012, 0.00012, 0.00012],
            tier_sizes: [8, 6, 8, 12],
            epsilon: 0.00012,
            variance_threshold: 0.01,
        }
    }

    fn detect(&self, tier_gates: Vec<Vec<Float>>) -> Vec<Bool> {
        // Check gate variance per tier.
        // If variance < threshold, that tier has collapsed.
        //
        // Returns: [4] booleans, true = singularity detected in that tier
        let results = []
        for tier_idx in 0..4 {
            // variance = mean((gate - mean(gates))^2)
            // if variance < 0.01 -> singular
        }
        results
    }

    fn inject_fuzz(&self, hidden: Vec<Float>, singular_tiers: Vec<Bool>) -> Vec<Float> {
        // Inject derived fuzz into hidden states for singular tiers.
        //
        // The fuzz is tiny (scaled by epsilon) but sufficient to
        // break gradient degeneracy and let the network escape.
        //
        // fuzz = random_gaussian() * sum(fuzz_scale[i] for singular tiers)
        //
        // Only injects if at least one tier is singular.
        hidden
    }

    fn forward(&self, hidden: Vec<Float>, tier_gates: Vec<Vec<Float>>) -> ExplorationOutput {
        // 1. Detect singularities across all 4 tiers
        // 2. If any detected, inject derived fuzz
        // 3. Return fuzzed hidden + detection flag
        let singular = self.detect(tier_gates)
        let any_singular = false
        for s in singular {
            if s { any_singular = true }
        }
        let fuzzed = self.inject_fuzz(hidden, singular)

        ExplorationOutput {
            enriched: fuzzed,
            best_concept: Section::new(64),
            min_torsion: 0.0,
            temperature: 1.0,
            singularity_detected: any_singular,
        }
    }
}
