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The matrix first transforms the state. The stored state then moves by dt times the difference between that transformed, externally driven value and its current value. This is a forward Euler discretization of a linear relaxation with forcing; its stability depends on the matrix spectrum and dt.
Terms & definitions
| Term | Meaning in this source |
|---|---|
| Registry | Kernel matrix |
| state | Current vector |
| new_state | Matrix-transformed vector |
| dt | Time increment |
| core | Driving core value |
How it works
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Assumptions & limits
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Original context
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## 10.2 Strand State Update ``` new_state[i] = Σ_j Registry[k][i][j] · state[j] state[i] ← state[i] · (1 - dt) + (new_state[i] + 0.1 · core_state[i]) · dt ``` **Explanation**: Each strand's state evolves through kernel transformation blended with core state influence. ## 10.3 Strand Energy ``` energy = √(Σ_i state[i]²) ``` **Explanation**: L2 norm of the state vector represents the strand's energy level. ## 10.4 Local Coherence ``` φ_local = 1 / (1 + energy / φ) ``` **Explanation**: Each strand has local coherence inversely related to its energy, normalized by the golden ratio.
Exact original notation
new_state[i] = Σ_j Registry[k][i][j] · state[j] state[i] ← state[i] · (1 - dt) + (new_state[i] + 0.1 · core_state[i]) · dt