Parametric Temporal Signatures of Angular Geometric Configurations: Magnetic-Field Dynamics and Acoustic Correlates in a Single-Session Study

Integrated Exploratory Study Parametric Temporal Signatures of Angular Geometric Configurations: Magnetic-Field Dynamics and Acoustic Correlates in a Single-Session Study A unified examination of electromagnetic transient signatures and state-dependent vocal parameters during exposure to screen-displayed and mobile-displayed angular configurations (66°, 58°, 38°, 32°) Functional reference: Wafa, M. A.-B. (2010). Angular Geometric Fields and Their Neuropsychological Effects (doctoral dissertation; unpublished observations). Correspondence: [Email] | Conflict of interest: none | Funding: none Abstract Background. Prior observational reports (Wafa, 2010) described that angular geometric configurations displayed on a screen are accompanied by distinct neurofunctional states (alertness, cognition, meditation, relaxation, drowsiness). Whether these configurations possess measurable physical correlates in the electromagnetic or acoustic domains remained unexamined. Objective. To test (1) whether screen-displayed angular configurations (66°, 58°, 38°, 32°) alter the local magnetic field relative to a blank white screen (SHAM), using a parametric temporal (trajectory-based) analytic framework; and (2) whether the same configurations, when displayed on a mobile device placed on the subject's body, produce measurable changes in vocal acoustic parameters. Methods. Electromagnetic arm: Five conditions were presented in fixed order on a 15-inch LCD. Magnetic-field readings were obtained with a handheld S8602 meter (0.01–99.99 µT; resolution 0.01 µT) in averaging mode, fixed on the screen for 45 s per condition, manually transcribed at ≈1 Hz. Acoustic arm: The 66° configuration was displayed on a mobile phone placed on the subject's thigh across four physiological states (post-breakfast fatigued, 6 PM extended wakefulness, 7 PM extended wakefulness, 9 PM post-heavy-meal fatigue); the 58° configuration was tested once in a rested state. Vocal parameters (local shimmer, APQ3/5/11, DDA shimmer, Harmony-to-Noise Ratio, fundamental frequency F₀) were recorded before and after 3-minute exposure. Results — Electromagnetic. Steady-state (final-10-s) means showed little separation (0.177–0.212 µT). Parametric temporal analysis revealed two distinct classes: Homeostatic (SHAM, 66°; A₀ ≈ 0.20 µT, CV 7.5–8.7%) and Transient (58°, 38°, 32°; A₀ = 0.280–0.316 µT with exponential-like decay). Within the Transient class: 38° decayed fastest (τ = 8.7 s) settling below baseline (B₀ = 0.175 µT); 32° showed highest onset with slowest decay (τ = 22.3 s); 58° showed biphasic response (τ = 18.4 s). Kruskal–Wallis: H = 27.22, p < 0.0001. Transient energy (AUC₀₋₁₅) separated active from homeostatic configurations by ~10×. Results — Acoustic. For 66° (electromagnetically homeostatic), acoustic responses were state-dependent: APQ11 changes ranged from −36.8% (post-meal fatigue) to +28.4% (evening wakefulness), while F₀ consistently increased across all sessions (+2.2% to +9.4%). Harmony showed variable changes (−2.8% to +4.4%). For 58° (electromagnetically transient), tested in a rested state, acoustic changes were minimal (APQ11 −18.8%, F₀ +1.7%, Harmony −1.5%). Jitter values (0.52–0.84 Hz) were recorded for the 58° session. Conclusion. Angular geometric configurations generate angle-dependent parametric temporal magnetic signatures (A₀, τ, B₀) independent of the observer. Acoustic correlates of 66° exposure are state-dependent and do not parallel the electromagnetic homeostasis, suggesting that vocal parameters may reflect the subject's physiological state rather than a direct configuration effect. All findings are exploratory and require randomized, replicated confirmation. magnetic field geometric configurations parametric temporal signature acoustic correlates shimmer APQ11 fundamental frequency transient dynamics EMF display screen exploratory study 1. Introduction Visual patterned stimuli modulate cortical activity through bottom-up sensory processing and top-down attentional mechanisms (Hubel & Wiesel, 1962; Engel & Singer, 2001). Wafa (2010) reported observational findings that angular geometric configurations displayed on a screen are associated with distinct functional states: 66° (alertness, cognition, insight, relaxation), 58° (cognition with some meditation), 38° (calm, relaxation, enhanced focus), 32° (drowsiness, reduced focus), 52° (organized learning), and 24° (drowsiness with inner peace). These observations were qualitative and lacked measurable physical correlates. The prevailing assumption in related literature is that any geometric effect must be static—a permanent raise or lower of the field. This ignores temporal dynamics evolving over the recording window and may explain why steady-state-only comparisons have been inconsistent. We adopt a two-directional, trajectory-based approach: the effect may be an increase, a decrease, or a change in the parametric temporal dynamics of the field. The electromagnetic rationale rests on Ampère's law: varying currents in display circuitry generate magnetic fields proportional to current draw; rendering a new geometric pattern may alter instantaneous load and pixel-switching transients, producing a brief magnetic pulse that decays as the system stabilizes. Additionally, if geometric configurations modulate neurofunctional states as Wafa suggested, such modulation might manifest in vocal acoustic parameters—since voice production is sensitive to neurological, muscular, and autonomic state. Shimmer (amplitude perturbation), APQ11 (amplitude perturbation quotient over 11 periods), Harmony-to-Noise Ratio (HNR), and fundamental frequency (F₀) are established markers of vocal stability that respond to fatigue, alertness, and relaxation (Buder, 2000; Teixeira & Fernandes, 2015). Objectives Measure the local magnetic field at ≈1 Hz for 45 s across five conditions (SHAM, 66°, 58°, 38°, 32°) and characterize parametric temporal trajectories (A₀, τ, B₀). Measure vocal acoustic parameters before and after exposure to 66° and 58° configurations displayed on a mobile device. Quantify transient response energy and decay kinetics for the magnetic data. Describe, without claiming causality, the parallel between magnetic signatures, acoustic responses, and Wafa's functional taxonomy. Generate testable predictions for future confirmatory work. 2. Materials and Methods 2.1 Stimuli Geometric configurations were generated in AutoCAD using the Polar Array command at 58°, 66°, 38°, and 32°, each consisting of intersecting lines forming a radial pattern. A blank white screen served as the control (SHAM). For electromagnetic measurements, stimuli were displayed on a 15-inch LCD monitor at identical brightness and resolution. For acoustic measurements, the same image files were opened on a mobile phone (WhatsApp viewer) and placed horizontally on the subject's thigh. 2.2 Electromagnetic Instrumentation Magnetic-field readings were obtained with a handheld S8602 tri-function EMF meter (magnetic range 0.01–99.99 µT, display resolution 0.01 µT; electric range 1–1999 V/m). The magnetic channel was operated in averaging (AVG) mode (≈0.4 s moving-average window); recorded transient amplitudes are conservative lower bounds. The electric channel read 0 V/m throughout. The device was fixed in position on the screen surface. 2.3 Acoustic Instrumentation Vocal acoustic parameters were extracted using automated analysis software providing: local shimmer (dimensionless and dB), APQ3, APQ5, APQ11 (amplitude perturbation quotients), DDA shimmer, Harmony-to-Noise Ratio (HNR, in dB), and fundamental frequency (F₀, in Hz). For the 58° session, additional jitter values (in Hz) were recorded. 2.4 Electromagnetic Procedure Five 45-s recordings were captured in fixed order: 58° → 66° → SHAM → 38° → 32°. The device was not moved between conditions. Recordings began immediately after the display switch. No stabilization period was applied between conditions. 2.5 Acoustic Procedure The 66° configuration image was opened on a mobile phone placed on the subject's thigh within what was described as the subject's "electromagnetic halo" region. The phone remained in place for 3 minutes. Vocal recordings were taken before placement and after the 3-minute exposure period. This was repeated across four sessions at different times of day and under different physiological conditions. The 58° configuration was tested once in a rested morning state. A single subject (the author) was used throughout; the transcriber/analyst was not blinded. 2.6 Data Extraction — Electromagnetic Automated OCR extraction was developed and abandoned due to low recognition rates (41–80%). The final dataset was manually transcribed second-by-second (≈1 Hz) from video recordings. Recorded digits represent the displayed value with two implied decimal places (e.g., "26" = 0.26 µT). 2.7 Statistical Analysis Non-parametric tests were chosen: Kruskal–Wallis H for overall comparison; two-sided Mann–Whitney U for pairwise comparisons against SHAM (effect size r = Z/√N). Temporal analyses: (i) first 10 s vs last 10 s drift; (ii) transient energy AUC₀₋₁₅ (summed deviation above SHAM median over first 15 s); (iii) exponential decay modeling B(t) = B₀ + A·e−t/τ; (iv) parametric characterization by (A₀, τ, B₀); (v) dynamic range; (vi) inter-condition continuity checks. Acoustic data were analyzed descriptively (percentage change before→after) given the single-subject, non-randomized design. All tests are exploratory. 3. Results — Electromagnetic Domain 3.1 Descriptive Statistics Condition | N | Mean (µT) | Median (µT) | SD | CV% | Min | Max | IQR SHAM | 46 | 0.197 | 0.200 | 0.017 | 8.7 | 0.16 | 0.24 | 0.028 66° | 49 | 0.204 | 0.200 | 0.015 | 7.5 | 0.18 | 0.24 | 0.020 58° | 46 | 0.245 | 0.225 | 0.058 | 23.9 | 0.17 | 0.37 | 0.078 38° | 51 | 0.209 | 0.190 | 0.056 | 26.8 | 0.16 | 0.3