if (a.size() != b.size() || a.empty()) return 0.0f;

float dot = 0.0f, ma = 0.0f, mb = 0.0f;

for (size_t i = 0; i < a.size(); ++i) {

dot += a[i] * b[i];

ma += a[i] * a[i];

mb += b[i] * b[i];

}

float denom = std::sqrt(ma) * std::sqrt(mb);

return (denom > 0.0f) ? dot / denom : 0.0f;

const EpisodeBoundaryParams& p) {

std::vector<size_t> boundary_indices;

if (candidates.empty()) return boundary_indices;

boundary_indices.push_back(0);

for (size_t i = 1; i < candidates.size(); ++i) {

const auto& prev = candidates[i - 1];

const auto& curr = candidates[i];

float turn_sim = cosine_similarity(curr.turn_embedding, prev.turn_embedding);

float summ_sim = cosine_similarity(curr.summary_embedding, prev.summary_embedding);

float avg_sim = (turn_sim + summ_sim) / 2.0f;

// Compute time-scaled threshold.

float gap_minutes = static_cast<float>(curr.epoch - prev.epoch) / 60.0f;

float threshold = p.base;

if (p.step_minutes > 0.0f)

threshold += p.step * static_cast<float>(

static_cast<int>(gap_minutes / p.step_minutes));

threshold = std::min(threshold, p.cap);

if (avg_sim <= threshold)

boundary_indices.push_back(i);

}

return boundary_indices;