Theta Against Gamma Is Not a Rule of Thumb, It Is One Equation
Traders treat opposite signs for theta and gamma as a law of the desk, but it is the pricing equation rearranged, and the equation names its own exceptions. At a zero rate the identity is exact and unbreakable; with a positive rate the interest on the bond leg buys the exception, and a deep in-the-money put has theta +7.0053 and gamma +0.0040317 together. The change of variables to the heat equation shows where the interest was hiding.