# Adaptive 1-Bit CMYK Merged Architecture

**Source**: ChatGPT refinement on combining 1-bit noise-shaped encoding with CMYK/SLUQ routing
**Status**: Design integration ready
**Cross-ref**: LUT_AS_DSP_EQUATION.md, FPGA_WARDEN_NODE_SPEC.md

---

## Core Insight

The 1-bit pipeline provides **cheap signal encoding over time**.
CMYK/SLUQ provides **cheap routing based on signal trustworthiness**.

Combined: **Adaptive encoder** that triages effort based on stream stability.

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## The Merged Update Loop

### 1. φ-Accumulator (Threshold Generation)

$$
\boxed{
\Phi_{t+1} = \Phi_t + \Delta_\phi \quad (\text{mod } 2^{32})
}
$$

$$
\boxed{
i(t) = (\Phi_t \gg n) \oplus \text{mask}
}
$$

$$
\boxed{
\theta_t = \text{LUT}_{\text{void}}[i(t)]
}
$$

### 2. 1-Bit Noise-Shaped Encoder

$$
\boxed{
b_t = \begin{cases} 1 & \text{if } v_t + e_{t-1} > \theta_t \\ 0 & \text{otherwise} \end{cases}
}
$$

$$
\boxed{
e_t = v_t + e_{t-1} - b_t
}
$$

### 3. SLUQ Routing Accumulator

$$
\boxed{
a_{t+1} = a_t - (a_t \gg r) + \lambda_1 |e_t| + \lambda_2 \Delta_t + \lambda_3 m_t
}
$$

### 4. CMYK State Classification

$$
\boxed{
s_t = a_t \gg 14 \in \{0, 1, 2, 3\}}
$$

| State | Bits | Action |
|-------|------|--------|
| **K** | 00 | Fast path - normal 1-bit pipeline |
| **C** | 01 | Monitor - widen observation window |
| **M** | 10 | Verify - secondary check vs attestation |
| **Y** | 11 | Prune/Reset - swap shadow table |

---

## Stress Function

$$
\boxed{
\text{stress}_t = \alpha |e_t| + \beta |\hat{\mu}_t - \mu^*_t| + \gamma \cdot \text{popcount}(\text{LUT}_{\text{void}}[i] \land \text{deviation})
}
$$

---

## Summary

**A 1-bit noise-shaped transport encoder whose local residual stress is bucketed by a 2-bit SLUQ state machine into CMYK routing policies, allowing stable segments to flow cheaply and unstable segments to trigger verification or reset.**