URB #495: The Refutation Extension

URB #494 derived the confirmation ceiling +2 = (√2)² from the generators {√2, i} alone. The natural question follows immediately: does the refutation floor −3 have an equally rigorous derivation? **Answer: yes.** Brandon's intuition was precisely correct. The −3 threshold is derived from *both* primary generators: **−3 = −((√2)² + ln(e)) = −(2 + 1)**. The first term (√2)² = 2 is the confirmation ceiling already derived — the algebraic floor. The second term ln(e) = 1 is the contribution of e — the natural unit of analytical extension. The full PD scale is now generator-derived at both extremes: