v2.0.0: Multidimensional Jet Space & Chronological Step-Operator Engine

The Log-Tower Generator is an advanced symbolic and computational engine designed to calculate the exact $n$-th order mixed partial derivatives of multidimensional Log-Tower functions.

Specifically, it provides a closed-form, algorithmic solution for evaluating complex jet space structures of the form:

$$A = h(X)\frac{\ln g(X)}{\ln f(X)}$$

In standard computational mathematics, evaluating high-order mixed partials of nested rational functions triggers combinatorial explosion. Repeatedly applying the quotient and chain rules across multiple orthogonal dimensions forces computer algebra systems to build exponentially large expression trees riddled with redundancies that quickly consume memory and processing power.

Version 2.0.0 bypasses these algebraic bottlenecks. By deploying a Chronological Step-Operator Engine, the framework maps a constrained index set ($\mathcal{A}_\alpha$) to navigate the multi-index space with full efficiency. It decouples the denominator's mathematical "drag" into a tensor cache, reducing calculation times for complex 4-D derivatives from minutes to milliseconds, opening the door for higher-order parameter sweeps.

v1.0.0: The Omega-Kernel Update

Full Changelog: v0.1.0...v1.0.0

Initial Proof of Concept & Derivation

First release establishing the F/G-sector symmetry and providing the Python generator source code.