XIV. COMPLETE THOUGHT INTEGRATION · Compute T

Read the equation

This relation defines T in the source section “XIV. COMPLETE THOUGHT INTEGRATION · Compute T”. Integrates contributions over the variable and bounds stated in the expression; the measure and domain must come from this source. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its phase. Its interpretation depends on the source’s stated variables and conditions; this record does not assign an unprovided physical or cognitive meaning to them.

Terms & definitions

The recovered passage does not supply a separate symbol table. Read the source context for the notation used in this version; familiar letters may carry different meanings in other builds.

How it works

1. Read T as the quantity being defined or updated by this relation.

2. Integrates contributions over the variable and bounds stated in the expression; the measure and domain must come from this source.

3. Applies an exponential factor. The exponent determines its real scaling or, for a complex exponent, its phase.

4. Takes a square root, requiring a nonnegative real radicand when interpreted over the reals.

5. Use this version’s variable definitions and update order. The same symbol may be assigned a different meaning in another build.

Assumptions & limits

• This source expression was recovered from the pinned code revision. Its presence does not establish that the associated program was built, run, or scientifically validated.

Original context

          memory_(dim, 0.0),
          query_(dim, 0.0),
          key_(dim, 0.0),
          value_(dim, 0.0),
          dim_k_(std::sqrt(dim)),
          time_steps_(100) {}

    // Compute T = Φ · ∫[M(t')·exp((QK^T/√d_k)V)] dt'
    double integrate(const std::array<double, NUM_STRANDS>& activations,
                    const std::array<double, NUM_STRANDS>& phases) {
        // Update Phi from coherence
        phi_ = 0.0;
        for (int i = 0; i < NUM_STRANDS; ++i) {
            phi_ += 1.0 / (1.0 + std::abs(activations[i] - 1.0));
        }
        phi_ /= NUM_STRANDS;

        // Build Q, K, V from activations

Compute T = Φ · ∫[M(t')·exp((QK^T/√d_k)V)] dt'

Related builds