Discount: V_hyp=A/(1+kt); V_exp=A·e^{−kt}; t½_hyp/t½_exp=1/ln2; ∫V_exp dt=A/k (V_hyp diverges)

Sympy-exact symbolic witness of temporal-discounting canonical forms (hyperbolic + exponential), their half-value delays, ratio, and integrated-area contrast. Setup: A (reward magnitude), k (discount rate), t (delay) — all positive…