The Science of Truth: A Rigorous Mathematical Framework for Integrity-Aware Scientific Metrics via the Forensic A-Index
Bibliographic record
Abstract
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."
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.013 | 0.050 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.006 | 0.004 |
| Science and technology studies | 0.002 | 0.011 |
| Scholarly communication | 0.007 | 0.016 |
| Open science | 0.003 | 0.007 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".