Grafometric Analysis of Ovals with AOT and Sample Uncertainty

by | Aug 29, 2026 | Noticias MacWinLin CPS

Executive Summary

This scientific study evaluates the discriminative capacity and accuracy of NEGA’s AOT (Analysis Oval Text) tool through a two-phase experimental framework: the characterization of samples from different authorship (different writers) and the evaluation of samples produced by the same executor (same writer).

Through standardized photographic capture and automated measurement of the major axis tilt (θ) and the aspect ratio (R) of oval structures, the algorithm integrates the arithmetic mean (μ) and sample uncertainty expressed via the standard error of the mean (±SE). The system operates under ISO/IEC 17025, ISO 5725-2, ISO 21748, and ISO 16269-4 standards, as well as ENFSI forensic laboratory network guidelines.

Homologous allographic pairs belonging to letters (“g”, “e”, “d”) and numeric digits (“0”, “8”, “9”) are analyzed individually. Phase I results confirm the model’s ability to prevent false positives through dispersion penalization, while Phase II will establish the algorithm’s tolerance to the natural intrapersonal variability of the same writer.

1. Introduction

  1. Computerized graphometric analysis in modern forensic handwriting examination demands going beyond merely qualitative assessments to provide judicial reports with objective, traceable, and reproducible mathematical backing. Closed or oval structures constitute highly automated elements of motor habit, reflecting the writer’s psychomotor consistency and gestural dynamism.

    However, the evaluation of quantitative data in questioned document examination faces a critical risk when limited to comparing simple arithmetic means. Human handwriting exhibits an intrinsic variability stemming from the neuromuscular system. In accordance with international testing standards (ISO/IEC 17025) and recommendations for forensic laboratories from ENFSI (European Network of Forensic Science Institutes), measurement uncertainty must be formally integrated into the estimation of results.

    The NEGA software and its AOT tool address this requirement through a statistical-morphometric model that evaluates both the intermodular distance between means and the overlap zones of dispersion intervals defined by standard error (±SE). To validate the robustness and specificity of this model, this study articulates two complementary scenarios:

    • Phase I (Different Hand): Aimed at verifying system specificity and its capacity to prevent false positives when analyzing handwritings from different writers that display superficial similarities.

    • Phase II (Same Hand): Aimed at calibrating system sensitivity and its tolerance toward the natural dispersion inherent to the same writer.

2. Objectives

2.1. General Objective

To validate the efficacy and precision of the AOT algorithm in discriminating between samples of divergent authorship (different hands) and correlating samples of coincident authorship (same hand), through the quantitative analysis of axial inclination and aspect ratio weighted by sample uncertainty.

2.2. Specific Objectives

  • To establish a photographic capture and inspection protocol in accordance with strict metrological criteria (orthogonality, scale, and resolution at 600 DPI – 1200 DPI).
  • To quantify morphometric metrics in homologous allographic pairs (IND_n ↔ DUB_n) for both experimental scenarios.
  • To demonstrate the impact of dispersion penalization (±SE) pursuant to ISO 21748 and ISO 5725-2 standards.
  • To evaluate the algorithm’s tolerance toward intrapersonal variability in samples belonging to the same writer.
  • To preserve forensic specificity by analyzing each grapheme individually, avoiding aggregated or combined averages across dissimilar letters. 

3. Methodology, Operating Protocol, and ISO Regulatory Framework

The analytical procedure using the AOT (Analysis Oval Text) tool follows a strict technical protocol divided into three consecutive stages:

  • 1. Capture and Photo Extraction: Orthogonal Digital Capture | Between 600 DPI (min) and 1200 DPI (ideal)

  • 2. Vectorial Scan: AOT Detection Radar (1/90°) | Fitted Ellipse

  • 3. Statistical Model: Means, SE, and ISO Standards

3.1. Step I: Photographic Capture and Controlled Digitization

To guarantee the metrological validity of the angular (θ) and proportional (R) variables, photographic sample collection adheres to the following operational requirements:

  • Geometry and Perpendicularity (Orthogonality): Photographic captures or scans are performed in a plane strictly parallel to the paper substrate (90° relative to the optical axis) to prevent perspective distortions that alter the Aspect Ratio (R) or axial inclination (θ).

  • Scale and Spatial Resolution: Mandatory inclusion of a certified millimeter scale in the focal plane, with a minimum resolution of 600 DPI in an uncompressed lossy format (TIFF/PNG) or an ideal resolution of 1200 DPI used in tests. Intermediate resolutions (e.g., 800 DPI) are fully valid, provided that no software interpolation is applied by the capture hardware.

  • Neutral and Diffuse Illumination: Use of technical diffuse lighting (5000K – 6500K) to eliminate cast shadows in the ink groove that could distort edge reading.

  • Sample Selection Criteria: Individual isolation of allographs with closed oval structures (“g”, “e”, “d”, “0”, “8”, “9”). Collapsed, blinded, or retouched ovals are discarded.

3.2. Step II: Segmentation, Vectorization, and Scanning in AOT

Once images are imported into the AOT module, the algorithm executes vectorial processing:

  • Perimeter Scan Resolution (1/90° Radar): The software scans the oval perimeter using a radar at 1/90° intervals (0.011° steps), calculating the figure’s true centroid via moments of inertia and fitting the bounding ellipse of minimum deviation.

  • Axial Inclination (θ): Angular orientation in degrees of the fitted ellipse’s major axis relative to the horizontal (0° ≤ θ < 180°).

  • Aspect Ratio (R): Eccentricity or degree of flattening of the ellipse structure, defined by the formula:

    Aspect Ratio (R) = Major Axis / Minor Axis

3.3. Step III: Statistical Modeling, Dispersion Control, and International Standards

For each sample (IND_n and DUB_n), AOT calculates the arithmetic mean (μ) and the Standard Error of the Mean (SE):

SE = s / √n

(Where “s” represents the sample standard deviation and “n” the number of ovals analyzed).

The algorithm’s statistical model is grounded in the international regulatory framework:

  • Uncertainty Estimation (GUM / ISO 21748): In compliance with the Guide to the Expression of Uncertainty in Measurement (GUM) and ISO 21748, AOT similarity evaluates the probabilistic overlap of Gaussian distributions. If a sample exhibits high dispersion or motor hesitation (high SE), the algorithm applies a penalty, automatically reducing the final similarity percentage.

  • Dispersion Control via Coefficient of Variation (ISO 5725-2): Following the repeatability criteria of the ISO 5725-2 standard, the software evaluates the Coefficient of Variation:

    CV (%) = (s / μ) × 100

    A value of CV > 20% triggers an automatic technical alert due to high sample inconsistency.

  • Outlier Treatment (ISO 16269-4): Pursuant to ISO 16269-4, the software integrates an algorithm for automatic outlier detection, allowing atypical samples to be isolated without skewing the overall project mean.

  • Forensic Laboratory Validation (ISO/IEC 17025 & ENFSI): Guarantees the metrological traceability and repeatability required in judicial expert reports.

3.4. Overall Verdict Matrix and Interpretation Criteria

To convert individual measurements into a unified overall report, the AOT protocol establishes a categorization system based on three similarity ranges per homologous allographic pair:

3.4.1. Classification Thresholds per Grapheme

  • ■ 0% – 60% → “INVALID” → Certain Divergence / Different Hand: Insurmountable biomechanical discrepancy, incompatibility of motor habits, or axis reversal.

  • ■ 60% – 80% → “INDETERMINATE” → Zone of Uncertainty / Inconclusive: Partial overlap or moderate dispersion that prevents confirming or ruling out authorship on its own.

  • ■  80% – 100% → “VALID” → High Compatibility / Same Hand: Consistent geometric and biomechanical alignment with the same writer.

3.4.2. Decision Rules for the Overall Verdict

The Overall Report Verdict is determined by combining two criteria:

  1. Sample Percentage Distribution: Proportion of analyzed graphemes falling into each of the three ranges.
  2. Essential Discrepancy Principle (Veto Criterion): Pursuant to the core principles of forensic handwriting examination, the presence of more than 30% of graphemes in the “INVALID” category (< 60%) or the existence of antagonistic axial reversals in automated structures automatically triggers an overall verdict of DIFFERENT HAND / NON-MATCHING, regardless of whether other graphemes fall within the inconclusive range.

4. Results: Phase I – Samples from Different Hands (Audited Data)

The data obtained after processing the six homologous allographic pairs belonging to different writers are detailed below:

4.1. Individual Breakdown of Phase I Comparisons

4.1.1 Comparison IND-1 / DUB-1 (Letter “g”)

Metrics:

  • IND Angle (μ ± SE): 39.7° ± 1.1°

  • DUB Angle (μ ± SE): 56.9° ± 9.3°

  • IND Aspect Ratio (μ ± SE): 2.00:1 ± 0.04

  • DUB Aspect Ratio (μ ± SE): 1.39:1 ± 0.03

  • Angle Sim. (%): 29.3%

  • Aspect Ratio Sim. (%): 48.4%

  • Overall AOT Similarity (%): 35.5%

Analysis:

A marked morphometric and dimensional divergence is observed between both samples, with no zone of interference or overlap in any of the analyzed variables:

  • Inclination Angle: The dispersion interval of the known sample (38.6° to 40.8°) and that of the questioned sample (47.6° to 66.2°) are completely disjoint. Despite the high variability observed in the questioned sample (±9.3°), a clear separation of 6.8° persists between their error margins; thus, there is no angular interference zone, resulting in a 29.3% degree of correspondence.

  • Aspect Ratio: The known sample (1.96:1 to 2.04:1) reflects a markedly compressed and verticalized elliptical structure, contrasting with the wider and more rounded execution of the questioned sample (1.36:1 to 1.42:1). Both intervals are manifestly distant and show no interference zone, placing morphological similarity at 48.4%.

The total absence of overlap in the evaluated parameters and the low overall AOT similarity index (35.5%, below the 60.0% threshold) confirm disparate and incompatible graphic execution patterns, resulting in an INVALID rating.

4.1.2 Comparison IND-2 / DUB-2 (Letter “e”)

Metrics:

  • IND Angle (μ ± SE): 19.5° ± 0.5°

  • DUB Angle (μ ± SE): 18.1° ± 0.8°

  • IND Aspect Ratio (μ ± SE): 4.15:1 ± 0.16

  • DUB Aspect Ratio (μ ± SE): 2.49:1 ± 0.04

  • Angle Sim. (%): 49.8%

  • Aspect Ratio Sim. (%): 45.6%

  • Overall AOT Similarity (%): 47.6%

Analysis:

A significant graphic divergence is confirmed between both samples, with no zone of interference or overlap in any of the analyzed variables:

  • Inclination Angle: Despite the proximity of the mean values (19.5° vs. 18.1°), the dispersion interval of the known sample (19.0° to 20.0°) and that of the questioned sample (17.3° to 18.9°) are disjoint with a separation of 0.1°. The absence of an angular interference zone is confirmed, placing the degree of correspondence at 49.8%.

  • Aspect Ratio: The known sample (3.99:1 to 4.31:1) exhibits an extraordinarily compressed and stylized ellipse, whereas the questioned sample (2.45:1 to 2.53:1) displays a markedly more open oval structure. Both ranges are manifestly distant without an interference zone, setting the dimensional similarity at 45.6%.

The lack of overlap in the evaluated parameters and the low overall AOT similarity index (47.6%, below the 60.0% validity threshold) evidence a decisive morphometric discrepancy, rating the comparison as INVALID.

4.1.3 Comparison IND-3 / DUB-3 (Letter “d”)

Metrics:

  • IND Angle (μ ± SE): 34.4° ± 0.8°

  • DUB Angle (μ ± SE): 40.1° ± 10.6°

  • IND Aspect Ratio (μ ± SE): 2.88:1 ± 0.07

  • DUB Aspect Ratio (μ ± SE): 1.53:1 ± 0.01

  • Angle Sim. (%): 78.3%

  • Aspect Ratio Sim. (%): 46.2%

  • Overall AOT Similarity (%): 56.3%

Analysis:

The comparison displays a differentiated behavior depending on the evaluated morphometric variable, with an interference zone identified exclusively in the angular inclination:

  • Inclination Angle: The known dispersion interval (33.6° to 35.2°) is comfortably encompassed within the broad dispersion range of the questioned sample (29.5° to 50.7°), driven by the marked intra-script variability of the latter (±10.6°). A clear angular interference and overlap zone is confirmed, reaching a 78.3% similarity degree.

  • Aspect Ratio: Clear incompatibility is evidenced in the oval dimensionality. The known sample (2.81:1 to 2.95:1) describes a markedly stylized and compressed ellipse, whereas the questioned sample (1.52:1 to 1.54:1) presents a significantly more open and rounded structure. Both intervals are entirely mutually exclusive and lack an interference zone, placing dimensional correspondence at 46.2%.

Despite the angular overlap, the absence of interference in the aspect ratio and the structural divergence of the ellipse reduce the overall AOT similarity index to 56.3% (below the 60.0% threshold), resulting in an INVALID rating.

4.1.4 Comparison IND-4 / DUB-4 (Number “0”)

Metrics:

  • IND Angle (μ ± SE): 23.6° ± 1.0°

  • DUB Angle (μ ± SE): 125.3° ± 16.1°

  • IND Aspect Ratio (μ ± SE): 1.96:1 ± 0.04

  • DUB Aspect Ratio (μ ± SE): 1.60:1 ± 0.02

  • Angle Sim. (%): 0.0%

  • Aspect Ratio Sim. (%): 49.1%

  • Overall AOT Similarity (%): 0.0%

Analysis:

An absolute morphometric incompatibility is evidenced between both samples, with no zone of interference or overlap in any of the analyzed parameters:

  • Inclination Angle: The dispersion ranges of the known sample (22.6° to 24.6°) and questioned sample (109.2° to 141.4°) are diametrically opposed, reflecting a clear antagonistic axial reversal with a deviation of more than 100° between their mean values. There is not the slightest angular interference zone, yielding a null result of 0.0% correspondence.

  • Aspect Ratio: The interval of the known sample (1.92:1 to 2.00:1) describes a more stylized and compressed ellipse, whereas the questioned sample (1.58:1 to 1.62:1) exhibits a markedly wider and rounder stroke. Both ranges are completely disjoint and lack an interference zone, limiting aspect ratio correspondence to 49.1%.

The total absence of overlap in both parameters and the overall AOT similarity value of 0.0% ratify an irreconcilable graphic divergence, resulting in an INVALID rating.

4.1.5 Comparison IND-5 / DUB-5 (Number “8”).

Metrics:

  • IND Angle (μ ± SE): 31.1° ± 5.5°

  • DUB Angle (μ ± SE): 120.9° ± 9.6°

  • IND Aspect Ratio (μ ± SE): 2.17:1 ± 0.03

  • DUB Aspect Ratio (μ ± SE): 1.57:1 ± 0.03

  • Angle Sim. (%): 0.0%

  • Aspect Ratio Sim. (%): 48.4%

  • Overall AOT Similarity (%): 0.0%

Analysis:

An absolute morphometric incompatibility is confirmed between both samples, with no zone of interference or overlap in any of the analyzed parameters:

  • Inclination Angle: The dispersion intervals of the known sample (25.6° to 36.6°) and questioned sample (111.3° to 130.5°) are diametrically distant with a net separation exceeding 74°, reflecting a severe axial reversal in the digit’s structure. There is not the slightest angular interference zone, yielding a null correspondence of 0.0%.
  • Aspect Ratio: The range of the known sample (2.14:1 to 2.20:1) corresponds to a markedly stylized and compressed ellipse, whereas the questioned sample (1.54:1 to 1.60:1) exhibits a noticeably wider and rounder oval morphology. Both intervals are mutually exclusive and lack an interference zone, placing dimensional similarity at 48.4%.

The total lack of overlap in the evaluated variables and the overall AOT similarity index of 0.0% (below the 60.0% threshold) result in an INVALID rating.

4.1.6 Comparison IND-6 / DUB-6 (Number “9”)

Metrics:

  • IND Angle (μ ± SE): 32.6° ± 1.1°

  • DUB Angle (μ ± SE): 20.8° ± 5.5°

  • IND Aspect Ratio (μ ± SE): 2.10:1 ± 0.03

  • DUB Aspect Ratio (μ ± SE): 2.07:1 ± 0.05

  • Angle Sim. (%): 34.5%

  • Aspect Ratio Sim. (%): 91.1%

  • Overall AOT Similarity (%): 45.6%

Analysis:

The comparison displays a differentiated behavior depending on the evaluated morphometric variable, with an interference zone identified exclusively in the aspect ratio:

  • Inclination Angle: A clear separation exists between the mean orientation values (32.6° vs. 20.8°). The dispersion intervals of the known sample (31.5° to 33.7°) and the questioned sample (15.3° to 26.3°) are disjoint, maintaining a net distance of 5.2°. The absence of an angular interference zone is confirmed, limiting the correspondence of this parameter to 34.5%.

  • Aspect Ratio: High coincidence is observed in the ellipse proportions (2.10:1 vs. 2.07:1). The dispersion ranges of the known sample (2.07:1 to 2.13:1) and questioned sample (2.02:1 to 2.12:1) overlap extensively within the 2.07:1 to 2.12:1 segment, confirming a clear dimensional interference and overlap zone, which supports the 91.1% aspect ratio similarity.

Despite the high morphological compatibility of the ellipse, the total absence of interference in graphic inclination reduces the overall AOT similarity index to 45.6% (below the 60.0% threshold), resulting in an INVALID rating.

5. Results: Phase I – Samples from the Same Hand (Audited Data)

The data obtained after processing a pair of homologous analyses belonging to the same writer are detailed below:

5.1. Individual Breakdown of Phase II Comparison

5.1.1 Comparison IND-1 / DUB-7 (Letter “g”)

Metrics:

  • IND Angle (μ ± SE): 39.7° ± 1.1°

  • DUB Angle (μ ± SE): 38.1° ± 1.1°

  • IND Aspect Ratio (μ ± SE): 2.00:1 ± 0.04

  • DUB Aspect Ratio (μ ± SE): 2.01:1 ± 0.05

  • Angle Sim. (%): 87.1%

  • Aspect Ratio Sim. (%): 97.4%

  • Overall AOT Similarity (%): 91.8%

Analysis:

An extremely high morphometric and dimensional concordance is observed between both samples, with simultaneous interference and overlap zones confirmed in both analyzed variables:

  • Inclination Angle: The angular means display close proximity (39.7° vs. 38.1°). The dispersion intervals of the known sample (38.6° to 40.8°) and questioned sample (37.0° to 39.2°) clearly overlap within the 38.6° to 39.2° segment, confirming the existence of an angular interference zone, which supports the 87.1% degree of similarity.

  • Aspect Ratio: The elliptical morphology reflects a virtually identical dimensional correspondence (2.00:1 vs. 2.01:1). The dispersion range of the known sample (1.96:1 to 2.04:1) is almost fully integrated into the questioned interval (1.96:1 to 2.06:1), confirming an extensive dimensional interference zone, which yields a high 97.4% aspect ratio similarity.

The simultaneous presence of interference zones in both variables and the outstanding overall AOT similarity index (91.8%, clearly above the 80.0% validity threshold) confirm biomechanical identity and identical graphic habits, resulting in a VALID rating.

5.1.2 Comparison IND-2 / DUB-8 (Letter “e”)

Metrics:

  • IND Angle (μ ± SE): 19.5° ± 0.5°

  • DUB Angle (μ ± SE): 18.7° ± 0.7°

  • IND Aspect Ratio (μ ± SE): 4.15:1 ± 0.16

  • DUB Aspect Ratio (μ ± SE): 4.02:1 ± 0.06

  • Angle Sim. (%): 88.0%

  • Aspect Ratio Sim. (%): 88.8%

  • Overall AOT Similarity (%): 88.4%

Analysis:

An extremely high morphometric and dimensional concordance is observed between both samples, with simultaneous interference and overlap zones confirmed in both analyzed variables:

  • Inclination Angle: The angular means display great proximity (19.5° vs. 18.7°). The dispersion intervals of the known sample (19.0° to 20.0°) and questioned sample (18.0° to 19.4°) overlap within the 19.0° to 19.4° segment, confirming the existence of an angular interference zone, which supports the 88.0% degree of similarity.

  • Aspect Ratio: The elliptical morphology reflects highly equivalent proportions (4.15:1 vs. 4.02:1). The dispersion ranges of the known sample (3.99:1 to 4.31:1) and questioned sample (3.96:1 to 4.08:1) overlap within the 3.99:1 to 4.08:1 interval, confirming a clear dimensional interference zone, which yields an 88.8% aspect ratio similarity.

The simultaneous presence of interference zones in both variables and the high overall AOT similarity index (88.4%, clearly above the 80.0% validity threshold) confirm biomechanical identity and single-origin graphic production, resulting in a VALID rating.

5.1.3 Comparison IND-3 / DUB-9 (Letter “d”)

Metrics:

  • IND Angle (μ ± SE): 34.4° ± 0.8°

  • DUB Angle (μ ± SE): 34.9° ± 1.0°

  • IND Aspect Ratio (μ ± SE): 2.88:1 ± 0.07

  • DUB Aspect Ratio (μ ± SE): 2.80:1 ± 0.07

  • Angle Sim. (%): 93.5%

  • Aspect Ratio Sim. (%): 89.0%

  • Overall AOT Similarity (%): 91.2%

Analysis:

An extremely high morphometric and dimensional concordance is observed between both samples, with simultaneous interference and overlap zones confirmed in both analyzed variables:

  • Inclination Angle: The angular means display a virtually identical match (34.4° vs. 34.9°, with a difference of only 0.5°). The dispersion intervals of the known sample (33.6° to 35.2°) and questioned sample (33.9° to 35.9°) overlap extensively within the 33.9° to 35.2° segment, confirming the existence of an angular interference zone, which supports the 93.5% degree of similarity.

  • Aspect Ratio: The elliptical morphology reflects highly equivalent proportions (2.88:1 vs. 2.80:1). The dispersion ranges of the known sample (2.81:1 to 2.95:1) and questioned sample (2.73:1 to 2.87:1) overlap within the 2.81:1 to 2.87:1 interval, confirming a clear dimensional interference zone, which yields an 89.0% aspect ratio similarity.

The simultaneous presence of interference zones in both variables and the high overall AOT similarity index (91.2%, clearly above the 80.0% validity threshold) confirm biomechanical identity and single-origin graphic production, resulting in a VALID rating.

5.1.4 Comparison IND-4 / DUB-10 (Number “0”)

Metrics:

  • IND Angle (μ ± SE): 23.6° ± 1.0°

  • DUB Angle (μ ± SE): 24.3° ± 1.2°

  • IND Aspect Ratio (μ ± SE): 1.96:1 ± 0.04

  • DUB Aspect Ratio (μ ± SE): 1.96:1 ± 0.04

  • Angle Sim. (%): 92.3%

  • Aspect Ratio Sim. (%): 99.4%

  • Overall AOT Similarity (%): 95.6%

Analysis:

An extraordinarily high morphometric and dimensional concordance is observed between both samples, with simultaneous interference and overlap zones confirmed in both analyzed variables:

  • Inclination Angle: The angular means display close proximity (23.6° vs. 24.3°, with a difference of only 0.7°). The dispersion intervals of the known sample (22.6° to 24.6°) and questioned sample (23.1° to 25.5°) overlap extensively within the 23.1° to 24.6° segment, confirming the existence of an angular interference zone, which supports the 92.3% degree of similarity.

  • Aspect Ratio: The elliptical morphology reflects identical proportions in its mean values (1.96:1 vs. 1.96:1). The dispersion ranges of the known sample (1.92:1 to 2.00:1) and questioned sample (1.92:1 to 2.00:1) coincide completely in their entirety, confirming a perfect dimensional interference and overlap zone, which yields an outstanding 99.4% aspect ratio similarity.

The simultaneous presence of interference zones in both variables and the remarkable overall AOT similarity index (95.6%, well above the 80.0% validity threshold) confirm biomechanical identity and single-origin graphic production, resulting in a VALID rating.

5.1.5 Comparison IND-5 / DUB-11 (Number “8”)

Metrics:

  • IND Angle (μ ± SE): 31.1° ± 5.5°

  • DUB Angle (μ ± SE): 31.6° ± 6.1°

  • IND Aspect Ratio (μ ± SE): 2.17:1 ± 0.03

  • DUB Aspect Ratio (μ ± SE): 2.15:1 ± 0.03

  • Angle Sim. (%): 97.8%

  • Aspect Ratio Sim. (%): 93.5%

  • Overall AOT Similarity (%): 95.6%

Analysis:

An extraordinarily high morphometric and dimensional concordance is observed between both samples, with simultaneous interference and overlap zones confirmed in both analyzed variables:

  • Inclination Angle: The angular means display a virtually identical match (31.1° vs. 31.6°, with a deviation of only 0.5°). The dispersion intervals of the known sample (25.6° to 36.6°) and questioned sample (25.5° to 37.7°) overlap almost entirely (25.6° to 36.6°), confirming the existence of an extensive angular interference zone, which supports the 97.8% degree of similarity.

  • Aspect Ratio: The elliptical morphology of the digit reflects highly equivalent proportions in its mean values (2.17:1 vs. 2.15:1). The dispersion ranges of the known sample (2.14:1 to 2.20:1) and questioned sample (2.12:1 to 2.18:1) overlap extensively within the 2.14:1 to 2.18:1 segment, confirming a clear dimensional interference zone, which yields a 93.5% aspect ratio similarity.

The simultaneous presence of interference zones in both variables and the remarkable overall AOT similarity index (95.6%, well above the 80.0% validity threshold) confirm biomechanical identity and single-origin graphic production, resulting in a VALID rating.

5.1.6 Comparison IND-6 / DUB-12 (Number “9”)

Metrics:

  • IND Angle (μ ± SE): 32.6° ± 1.1°

  • DUB Angle (μ ± SE): 32.2° ± 1.2°

  • IND Aspect Ratio (μ ± SE): 2.10:1 ± 0.03

  • DUB Aspect Ratio (μ ± SE): 2.11:1 ± 0.03

  • Angle Sim. (%): 95.5%

  • Aspect Ratio Sim. (%): 97.6%

  • Overall AOT Similarity (%): 96.5%

Analysis:

An extraordinarily high morphometric and dimensional concordance is observed between both samples, with simultaneous interference and overlap zones confirmed in both analyzed variables:

  • Inclination Angle: The angular means display a virtually identical match (32.6° vs. 32.2°, with a difference of only 0.4°). The dispersion intervals of the known sample (31.5° to 33.7°) and questioned sample (31.0° to 33.4°) overlap extensively within the 31.5° to 33.4° segment, confirming the existence of an angular interference zone, which supports the 95.5% degree of similarity.

  • Aspect Ratio: The elliptical morphology reflects virtually identical proportions in its mean values (2.10:1 vs. 2.11:1). The dispersion ranges of the known sample (2.07:1 to 2.13:1) and questioned sample (2.08:1 to 2.14:1) overlap almost entirely within the 2.08:1 to 2.13:1 interval, confirming an optimal dimensional interference and overlap zone, which yields an outstanding 97.6% aspect ratio similarity.

The simultaneous presence of interference zones in both variables and the remarkable overall AOT similarity index (96.5%, well above the 80.0% validity threshold) confirm biomechanical identity and single-origin graphic production, resulting in a VALID rating.

6. OVERALL VERDICT PHASE I: INVALID CATEGORY / NON-MATCHING AUTHORSHIP (DIFFERENT HAND)

 

Rationale (Comparisons C1 to C6):

100.0% of the Phase I comparisons (6 out of 6) fell below the validity threshold of 60.0% (INVALID), yielding an overall mean similarity of just 30.83% (with values ranging between 0.0% and 56.3%).

A radical biomechanical incompatibility is confirmed in the circular structures (digits “0” and “8” in C4 and C5), registering 0.0% total similarity as a result of an antagonistic axial reversal (angular deviations of 101.7° and 89.8°, respectively). In no comparison within this phase was a simultaneous interference or overlap zone identified across both parameters (inclination and aspect ratio). The presence of isolated interference zones in a single variable (C3 in angle with 78.3%; C6 in aspect ratio with 91.1%) proved insufficient, as they were penalized by the discrepancy in the remaining variable. No comparison reached the validity threshold (≥ 80.0%), categorically confirming that the samples were executed by a different hand.

7. OVERALL VERDICT PHASE II: VALID CATEGORY / MATCHING AUTHORSHIP (SAME HAND)

Rationale (Comparisons C7 to C12):

100.0% of the Phase II comparisons (6 out of 6) comfortably exceeded the 80.0% validity threshold (VALID), yielding an overall mean similarity of 93.18% (with values ranging between 88.4% and 96.5%).

An extraordinary stability and consistency in the writer’s graphic motor automatism is verified: the maximum angular deviation across the entire series was only 1.6° (C7), reaching angular coincidence between 87.1% and 97.8%. In terms of aspect ratio, the elliptical structures exhibited virtually identical proportions (as in C10, with 1.96:1 vs. 1.96:1 and a 99.4% dimensional similarity). Furthermore, 100.0% of the Phase II comparisons demonstrated full and simultaneous interference and overlap zones across both morphometric variables. The complete two-dimensional correspondence conclusively confirms single-origin graphic production and gestural identity (same executing hand).

8. Comparative Discussion

The cross-analysis between the audited results of Phase I (Different Hand / Comparisons C1 to C6) and the results obtained in Phase II (Same Hand / Comparisons C7 to C12) allows for the articulation of three fundamental axes of expert discussion:

  • Discrimination Capacity for Reversal and Axial Deviation: Phase I demonstrated massive angular discordances in circular structures (digits “0” and “8”, with antagonistic axial deviations of 101.7° and 89.8° that yielded 0.0% similarity), as well as net angular divergences in graphemes such as “g” (deviation of 17.2° / C1) and “9” (deviation of 11.8° / C6). In contrast, Phase II (Comparisons C7 to C12) confirmed that matching authorship maintains an extraordinarily close gestural parallelism, recording minimal angular discrepancies in all cases (between 0.4° and 1.6°) and angular correspondence levels from 87.1% to 97.8%. This validates the high sensitivity of the AOT model in detecting true biomechanical directionality and distinguishing intrapersonal discrepancies from interpersonal divergences.

  • Intrapersonal vs. Interpersonal Consistency of Aspect Ratio: Phase I revealed clear interpersonal differentiation: the known writer consistently exhibited a habit of greater elliptical compression and stylization (high aspect ratios between 1.96:1 and 4.15:1 compared to wider or rounder questioned strokes, from 1.39:1 to 2.49:1). Conversely, Phase II ratified the intrapersonal consistency of graphic motor automatisms across all evaluated structures (“g”, “e”, “d”, “0”, “8”, “9”), achieving virtually superimposable dimensional proportions (e.g., 1.96:1 vs. 1.96:1 in C10 or 2.10:1 vs. 2.11:1 in C12) with aspect ratio similarities ranging between 88.8% and 99.4%.

  • Validation of Interference Zones and Standard Error (SE) Control: Phase I demonstrated that integrating standard error (±SE) and requiring simultaneous two-dimensional overlap are essential for neutralizing false positives. Comparisons such as C3 (letter “d”) or C6 (number “9”) presented isolated overlap or coincidence in a single parameter (78.3% angular in “d” and 91.1% dimensional in “9”), but the lack of interference in the complementary variable kept the overall rating as INVALID (56.3% and 45.6%, respectively). Phase II decisively showed that when single-origin graphic production exists, 100% of the samples (6 out of 6) converge simultaneously on both axes (inclination and proportion), reaching overall averages between 88.4% and 96.5% (VALID) without penalties arising from the natural variability of human signature or handwriting.

9. Final Conclusion

The results obtained throughout this experimental and comparative study conclusively demonstrate the scientific validity, metrological reliability, and discriminative precision of the AOT (Analysis Oval Text) tool within forensic handwriting examination and questioned document analysis.

9.1 Demonstration of Scientific Validity and Empirical Robustness

  • Absolute Specificity (100.0% in Phase I – Different Hand): The tool demonstrated a critical capability to rule out false positives, correctly classifying 100% of the comparisons executed by different hands (C1 to C6) as INVALID, with a mean similarity of just 30.83% and precisely identifying biomechanical incompatibility and antagonistic axial reversals (0.0% in digits “0” and “8”).

  • Sensitivity and Repeatability (100.0% in Phase II – Same Hand): In all single-origin graphic comparisons (C7 to C12), the system verified the consistency of the writer’s gestural automatism, reaching an overall mean similarity of 93.18% (range of 88.4% to 96.5%) and confirming simultaneous interference and overlap zones in 100% of the samples across both angular and dimensional axes.

  • Metrological Control via Standard Error (SE): The incorporation of standard error and dispersion interval analysis eliminates traditional expert subjectivity, ensuring that partial or isolated coincidences in a single parameter do not distort the final verdict unless comprehensive geometric compatibility is verified.

9.2 Compliance with International ISO Standards and Regulations

The architecture and foundation of the NEGA software and its AOT tool satisfy the most rigorous expert quality and technical standardization requirements:

  • ISO/IEC 17025 Standard (Validation of Testing and Calibration Methods): Complies with the demands of repeatability, reproducibility, quantification of measurement uncertainty (±SE), and objective mathematical traceability in the handling of documentary evidence.

  • ISO 21043 Standard (Forensic Sciences): Aligns with international standards for forensic examination, interpretation, and reporting processes, transforming oval analysis into a quantitative, auditable procedure free from cognitive biases or subjective interpretations.

  • Scientific Criteria for Judicial Admissibility (Daubert / Frye Standard): The AOT methodology provides a known, measurable error rate, verifiable statistical validation, and empirical foundations reproducible by third-party experts or courts.

9.3 Expert Recommendation

Based on the foregoing, it is strongly recommended that the AOT (Analysis Oval Text) tool be adopted and implemented in forensic offices, criminalistics laboratories, and courts of law as a benchmark biometric-morphometric instrument. Its use elevates handwriting expert evidence to the level of objective scientific evidence, providing unquestionable mathematical support for confirming or ruling out authorship.