This paper establishes the rigorous mathematical proofs and algorithmic architecture for the Forensic A-Index. While traditional evaluation metrics (such as the h-index) model academic impact as an unbounded, unweighted function—leaving them highly vulnerable to paper mills and citation cartels—the ASAI framework transitions bibliometrics into a strictly bounded, topology-aware forensic audit. This document formalizes the global publication ecosystem as a time-evolving bipartite multigraph. It establishes strict mathematical boundary conditions via a Topological Density penalty (K-Factor), an L1-normalized Conservation of Impact law, and Citation Intent Entropy. Through game-theoretic modeling and Fokker-Planck stochastic diffusion equations, this work demonstrates how the A-Index fundamentally breaks the Nash equilibrium of reciprocal cartel formation by driving the expected payoff of artificial edge creation below zero. Ultimately, this establishes the framework as a mathematically unfakeable ledger of scientific truth. Note: This document represents Part 2 of the foundational ASAI architecture. For the executive framework and practical applications, please refer to Part 1: "The Science of Truth: A New Citation Algorithm for Restoring Integrity in Scientific Metrics."
E. Shalaan (Sun,) studied this question.