feat(python): implement python bindings for all components and solvers

_bmad-output/planning-artifacts/epics.md

@@ -120,6 +120,8 @@ This document provides the complete epic and story breakdown for Entropyk, decom
 
 **FR51:** Swappable Calibration Variables - swap calibration factors (f_m, f_ua, f_power, etc.) into solver unknowns and measured values (Tsat, capacity, power) into constraints for one-shot inverse calibration
 
+**FR52:** Bounded Variable Step Clipping - during Newton-Raphson iterations, bounded control variables are clipped to [min, max] at EVERY iteration, preventing physically impossible values (e.g., valve > 100%) and improving convergence stability
+
 ### NonFunctional Requirements
 
 **NFR1:** Steady State convergence time < **1 second** for standard cycle in Cold Start
@@ -1009,6 +1011,37 @@ This document provides the complete epic and story breakdown for Entropyk, decom
 
 ---
 
+### Story 5.6: Control Variable Step Clipping in Solver
+
+**As a** control engineer,
+**I want** bounded control variables to be clipped at each Newton iteration,
+**So that** the solver never proposes physically impossible values (e.g., valve > 100%, frequency < min).
+
+**Context:** Story 5.2 implemented `BoundedVariable` and `clip_step()`, but the Newton-Raphson solver in Story 4.2 doesn't use them. The solver applies `x += delta` without checking bounds, allowing impossible values.
+
+**Acceptance Criteria:**
+
+**Given** a bounded variable with bounds [min, max]
+**When** the solver computes a Newton step Δx
+**Then** the new value is clipped: `x_new = clamp(x + Δx, min, max)`
+**And** the variable never goes outside bounds during ANY iteration
+
+**Given** control variables in the state vector at indices [2*edge_count, ...]
+**When** the solver updates the state vector
+**Then** bounded variables are clipped
+**And** regular edge states (P, h) are NOT clipped
+
+**Given** a converged solution with one or more bounded variables at bounds
+**When** checking convergence status
+**Then** `ConvergenceStatus::ControlSaturation` is returned
+**And** `saturated_variables()` returns the list of saturated variables
+
+**Given** existing code that doesn't use bounded variables
+**When** solving
+**Then** behavior is unchanged (no clipping applied)
+
+---
+
 ## Epic 6: Multi-Platform APIs
 
 ### Story 6.1: Rust Native API