1. Introduction and Scope of the Study

This technical study aims to validate the efficacy of the Fibonacci Digital Modeller (FDM) tool, integrated into the NEGA software, for identifying authorship in isolated characters. Unlike signature analysis, where the global gesture prevails, this study evaluates grapheme architecture and intrinsic proportionality in letters and numbers.

This report documents the results of a series of stress and validation tests performed with FDM technology on isolated alphanumeric characters. The objective is to demonstrate that identifying authorship in letters and numbers does not rely on subjective interpretation, but rather on the detection of universal biometric constants (Golden Ratio) present in the author’s micro-gestures.

Although this study focuses on the Western Latin alphabet, the Fibonacci Digital Modeling (FDM) architecture is transcultural and universal. Since the system analyzes human intrinsic proportionality and biomotor imprinting, its efficacy is equally valid for any writing system (including Arabic, Chinese, Hebrew, and Cyrillic, among others). The algorithm transcends the specific shape of the character to focus on the author’s geometric constant, leaving the scope of application to the expert’s professional judgment based on the nature of the analyzed script.

A detailed explanation of the tool’s parameters has been omitted, as they were previously covered in our signature analysis. You may consult those details in: Scientific Signature Analysis with the FDM (Fibonacci Digital Modeller) Tool.

3. Methodology

3.1. Tooling and Software

The study was conducted using the Fibonacci Digital Modeller (FDM) with the newly enhanced EVO 2 calculation module, part of the NEGA 6 v3.7.0. software suite.

3.2. Interpretation Criteria

The FDM system classifies results into three distinct ranges:

• ■ 0% – 60% → Clear Divergence: Indicates different authorship or forgery (tracing).

• ■ 60% – 80% → Indeterminate Zone: Reflects potential evolutionary changes or structural variations.

• ■ 80% – 100% → Proportional Coincidence: Indicates common authorship (same hand).

4. Same Authorship Executions (Authenticity)

The FDM tool is currently calibrated to validate authenticity in geometric proportionality when results are equal to or greater than 80%. In the software interface, these successful matches are highlighted with a cyan blue background.

In cases where the samples were executed by the same author, the system yielded consistency levels exceeding 87%, demonstrating a remarkably high stability in the subject’s Golden Ratio proportionality.

Key results:

• Letters: Similarity of 94.47% (C7) and 87.11% (C8).

• Numbers: Similarity of 95.25% (C9) and 97.17% (C10).

4.1 Comparison C7 – KNOWN-4 / QUEST-4: Letters – Same Authorship (Authenticity)

4.2 Comparison C8 – KNOWN-5 / QUEST-5: Letters – Same Authorship (Authenticity)

4.3 Comparison C9 – KNOWN-4 / QUEST-4 Numerals Same Authorship (Authenticity)

4.4 Comparison C10 – KNOWN-6 / QUEST-6: Numerals – Same Authorship (Authenticity)

5. Different Authorship Executions (Divergence)

The FDM tool is currently calibrated to identify structural divergence when geometric proportionality results are equal to or below 60%. In the software interface, these results are highlighted with a gray background.

When comparing characters from different authors, similarity metrics dropped drastically below 20%. This evidence confirms that every individual possesses a unique and unrepeatable graphic architecture.

Key Results:

• Letters: Similarity of 14.26% (C1) and a minimum of 3.81% (C2).

• Numerals: Similarity of 17.51% (C4) and 13.28% (C5).

5.1 Comparison C1 – KNOWN-1 / QUEST-1: Letters – Different Authorship (Divergence)

5.2 Comparison C2 – KNOWN-2 / QUEST-2: Letters – Different Authorship (Divergence)

5.3 Comparison C4 – KNOWN-1 / QUEST-1: Numerals – Different Authorship (Divergence)

5.4 Comparison C5 – KNOWN-2 / QUEST-2: Numerals – Different Authorship (Divergence)

6. Detection of Forgery by Tracing (Absolute Identity)

The FDM tool is currently calibrated to identify structural divergence when geometric proportionality results are equal to or below 60%. In the software interface, these results are highlighted with a gray background.

The software detected with absolute precision all attempts at reproduction via tracing or digital cloning. In these cases, the Gradient Range is 0.000000 (or nearly zero), indicating a total absence of natural variability.

Tracing Cases (C3 for Letters and C6 for Numerals):

Both cases present a residual Fibonacci Similarity of 0.08%, an Accuracy of 100.00%, and a Confidence level of 0%. This specific combination—maximum accuracy paired with a zero gradient—is the unequivocal scientific indicator of tracing. It should be noted that certain cases may still be classified as tracing even when the gradient values are slightly higher but remain within the low range.

6.1 Comparison C3 – KNOWN-3 / QUEST-3: Forgery by Tracing – Letters (Divergence)

6.2 Comparison C6 – KNOWN-3 / QUEST-3: Forgery by Tracing – Numerals (Divergence)

7. Results and Conclusions

7.1 Optimization of the Indeterminacy Range in Alphanumeric Characters

Unlike signature analysis—where the complexity of flourishes and gesture variability can create ranges of doubt or indeterminacy (between 60% and 80%)—the analysis of letters and numbers using the FDM tool presents a much more defined dichotomy. Due to the simplified and structural nature of alphanumeric graphemes, a polarization of results is observed:

• Favorable Results (≥ 80%): These identify solid morphological consistency and clear common authorship.

• Unfavorable Results (< 60%): This includes forgery by tracing and authorship divergence, where the architecture of the character breaks drastically from the known pattern.

The absence of indeterminate cases in the analyzed sample reinforces the diagnostic efficiency of the tool for text and figures, allowing the forensic expert to issue conclusions with a higher degree of certainty compared to complex or ornamental strokes.

8. Considerations on the Expert’s Role and Technological Support