🎛️ R4 — Escalating Complexity Resistance Synthesizer

🧠 Synthesis Methodology & Escalating Complexity Tiers

R4 analyzes four base resistors ($R_1, R_2, R_3, R_4$) mounted horizontally across rows 1–4 of a solderless breadboard center well. It stratifies the series-parallel domain into five complexity tiers:

• Level 1 (k = 4): Isolated Singlets. Each component is isolated and connected directly between Bus A and Bus B using two vertical rail taps ($R_A, R_B$). Zero cross-well routing.
• Level 2 (k = 16): 4-Stage Cauer Ladder. Evaluates the 16 binary switching states of the alternating series-shunt ladder network using local bypass shunts.
• Level 3 (k = 28): Planar Dual-Rail Matrix. Strictly uses vertical rail taps ($R_A, R_B$) and same-side horizontal jumpers ($J_1, J_2, J_3$). Zero jumpers cross the center well ($X = 0$). Series strings route alternately from left to right through the resistors themselves.
• Level 4 (k ≈ 59): Tolerance-Deduplicated 88. Evaluates all 88 topologies with cross-well jumpers, merging near-identical states within a physical resistor tolerance band (default $\pm 0.4\%$).
• Level 5 (k = 88): Full Combinatorial Ladder. The complete set of 88 series, parallel, and compound ladder configurations utilizing all 9 jumper shapes.