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New symbolic regression equation/README.md

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+# SAAQ 1.5 Delta-Q Adaptation Law
+
+Discovered via SymbolicRegression.jl, this equation is the first compact control law governing how quantization pressure adapts dynamically based on population firing activity and recurrent state memory.
+
+---
+
+## The Equation
+
+$$\Delta q_{\text{target}} \approx 0.0573 \cdot \sqrt{\bar{f}_{\text{pop}}} + 0.496 \cdot \Delta q_{\text{prev}}$$
+
+---
+
+## Variable Breakdown
+
+| Symbol | Full Name | Description |
+|--------|-----------|-------------|
+| $\Delta q_{\text{target}}$ | `saaq_delta_q_target` | The new quantization adjustment target for this tick |
+| $\bar{f}_{\text{pop}}$ | `avg_pop_firing_rate_hz` | Average population firing rate (Hz) across active walkers |
+| $\Delta q_{\text{prev}}$ | `saaq_delta_q_prev` | The quantization delta from the previous tick (recurrent memory) |
+| $0.0573$ | Firing drive coefficient | Scales the square-root firing pressure term |
+| $0.496$ | Memory carryover coefficient | Controls how much of the previous delta-q survives into the next update |
+
+---
+
+## Plain-Language Interpretation
+
+**Square-root firing drive:** Quantization pressure grows with population firing, but sublinearly. Doubling the firing rate does not double the drive — the square root compresses high activity and still responds to low-to-moderate activity. Runaway amplification is structurally suppressed.
+
+**Half-memory carryover:** Approximately 49.6% of the previous `delta_q` carries forward into the next update. The system does not fully forget the last quantization state every tick.
+
+**Stable leaky recurrence:** Because the carryover coefficient is `0.496 < 1.0`, this recurrence is not explosive. It behaves as a controlled temporal process — inertia without instability.
+
+In plain terms:
+
+> **new quantization target = current activity pressure + residual memory of the previous state**
+
+---
+
+## Why This Equation Matters
+
+The square-root term is the most significant structural feature:
+
+- High activity gets compressed rather than amplified
+- Low-to-moderate activity still drives the system
+- The response is compatible with biological fatigue mechanics — a strong stimulus does not cause runaway voltage
+
+This is directionally consistent with the **SAAQ 1.0 L2-normalized voltage foundation**: just as L2 normalization bounds raw voltage pressure by Euclidean length, the square-root term bounds firing-rate drive by its own nonlinear compression. Both mechanisms enforce the same core principle — energy cannot flow without constraint.
+
+The `0.496 · delta_q_prev` term gives the system **temporal inertia**: quantization state evolves smoothly across ticks rather than jumping on every new stimulus. This makes `delta_q` behave more like a controlled physical process than a feedthrough variable.
+
+---
+
+## Relationship to SAAQ 1.0 Foundation
+
+SAAQ 1.0 establishes the voltage bounding law:
+
+$$V_{\text{norm}} = \frac{V}{\sqrt{\sum V_i^2 + \epsilon}}$$
+
+SAAQ 1.5 operates one layer above this: it takes the activity that emerges *after* voltage normalization and determines how the quantization target should adapt in response. Together they form a two-layer control structure:
+
+1. **SAAQ 1.0** — bounds the raw voltage so no single walker collapses under unbounded pressure
+2. **SAAQ 1.5** — adapts the quantization target based on the bounded firing activity that results
+
+---
+
+## Scope and Caveat
+
+This equation is a **global baseline law** — not the final universal law.
+
+The routing telemetry already demonstrates piecewise semantic structure: abstract English, Rust syntax, and mathematical logic do not occupy identical route bands (2000-route vs. 600–800 band). A single global `delta_q` law may not capture the full per-route adaptation dynamics.
+
+Treat SAAQ 1.5 as:
+
+- A compact, stable, interpretable starting point
+- A hardware-friendly control law suitable for porting into Spikenaut
+- The baseline against which per-route variants should be tested
+
+---
+
+## Next Steps
+
+- Validate the equation against held-out routing sessions (English, Rust, Math inputs separately)
+- Test whether per-route variants of the coefficients improve fit within each semantic band
+- Feed this law into the `corinth-canal` pipeline as the `delta_q` update rule
+- Use SymbolicRegression.jl hall-of-fame deeper nestings as benchmarks if the global baseline underperforms on specific route bands