{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T13:57:07Z","timestamp":1772632627021,"version":"3.50.1"},"reference-count":28,"publisher":"Frontiers Media SA","license":[{"start":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T00:00:00Z","timestamp":1772582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["frontiersin.org"],"crossmark-restriction":true},"short-container-title":["Front. Hum. Neurosci."],"abstract":"<jats:sec>\n                    <jats:title>Background<\/jats:title>\n                    <jats:p>The golden ratio (\u03d5 \u2248 1. 618) has been proposed as an organizing principle for EEG frequency bands, potentially minimizing spurious cross-frequency synchronization. However, whether individual differences in \u03d5-organization have functional correlates remains unexplored.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Objective<\/jats:title>\n                    <jats:p>We investigated whether proximity of theta-alpha frequency ratios to \u03d5 is associated with theta-alpha frequency convergence near the 8 Hz boundary.<\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Methods<\/jats:title>\n                    <jats:p>\n                      We developed the Phi Coupling Index (PCI), which quantifies spectral frequency ratio proximity (note: \u201ccoupling\u201d here refers to frequency ratio relationships, not phase-amplitude coupling), quantifying proximity to \u03d5 vs. harmonic 2:1 organization. Spectral centroids were computed from eyes-closed resting-state EEG across two independent datasets (\n                      <jats:italic>N<\/jats:italic>\n                      = 320): PhysioNet EEGBCI (\n                      <jats:italic>N<\/jats:italic>\n                      = 109) and LEMON Mind-Brain-Body (\n                      <jats:italic>N<\/jats:italic>\n                      = 211). We performed comprehensive validation including: (1) null model simulation, (2) per-dataset replication, (3) robust statistics, (4) \u03d5-specificity parameter sweep, (5) epsilon sensitivity analysis, and (6) frontal theta validation.\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Results<\/jats:title>\n                    <jats:p>\n                      Across 320 subjects, 80.0% showed \u03d5-organization (PCI &amp;gt; 0). PCI was strongly associated with theta-alpha convergence [\n                      <jats:italic>r<\/jats:italic>\n                      = 0.54,\n                      <jats:italic>p<\/jats:italic>\n                      &amp;lt; 10\n                      <jats:sup>\u221225<\/jats:sup>\n                      ; Spearman \u03c1 = 0.82 (higher rank correlation reflects monotonic association with bounded transform)]. This effect: (1) exceeded null model expectation by &amp;gt;5 SD; (2) replicated across both datasets (\n                      <jats:italic>r<\/jats:italic>\n                      = 0.50-0.63); (3) was robust to outliers; (4) showed \u03d5-specificity in parameter sweep; (5) remained qualitatively consistent across epsilon values (\n                      <jats:italic>r<\/jats:italic>\n                      = 0.41-0.78); and (6) critically, frontal theta analysis yielded even stronger effects (\n                      <jats:italic>r<\/jats:italic>\n                      = 0.718, p \u2248 10\n                      <jats:sup>\u221235<\/jats:sup>\n                      ), providing evidence against volume conduction artifacts. Demographic controls in LEMON (partial correlation controlling for age) yielded\n                      <jats:italic>r<\/jats:italic>\n                      = 0.490, virtually identical to uncorrected\n                      <jats:italic>r<\/jats:italic>\n                      = 0.497, indicating age does not substantially confound the effect. However, pre-planned exploratory subgroup analyses revealed meaningful individual differences: the association was stronger in younger adults (age &amp;lt; 40:\n                      <jats:italic>r<\/jats:italic>\n                      = 0.574,\n                      <jats:italic>N<\/jats:italic>\n                      = 142) than older adults (\n                      <jats:italic>r<\/jats:italic>\n                      = 0.344,\n                      <jats:italic>N<\/jats:italic>\n                      = 69; note: reduced statistical power in older subgroup), and notably stronger in females (\n                      <jats:italic>r<\/jats:italic>\n                      = 0.680,\n                      <jats:italic>N<\/jats:italic>\n                      = 77) than males (\n                      <jats:italic>r<\/jats:italic>\n                      = 0.429,\n                      <jats:italic>N<\/jats:italic>\n                      = 134), consistent with known sex differences in alpha oscillation characteristics. High-\u03d5 subjects (PCI &amp;gt; median) showed frequency profiles converging toward the 8 Hz boundary (\u03b8 = 6.24 Hz, \u03b1 = 9.75 Hz) compared to low-\u03d5 subjects (\u03b8 = 5.85 Hz, \u03b1 = 10.20 Hz), with no age confound (mean ages 37.7 vs. 35.7 years).\n                    <\/jats:p>\n                  <\/jats:sec>\n                  <jats:sec>\n                    <jats:title>Conclusions<\/jats:title>\n                    <jats:p>\n                      PCI demonstrates a robust association with theta-alpha convergence that exceeds structural expectations, replicates across datasets, and shows specificity to the golden ratio. The striking frontal theta validation (\n                      <jats:italic>r<\/jats:italic>\n                      = 0.718) provides converging evidence against a simple spatial-mixing explanation and is consistent with neurophysiological organization.\n                    <\/jats:p>\n                  <\/jats:sec>","DOI":"10.3389\/fnhum.2026.1781338","type":"journal-article","created":{"date-parts":[[2026,3,4]],"date-time":"2026-03-04T07:02:46Z","timestamp":1772607766000},"update-policy":"https:\/\/doi.org\/10.3389\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Golden ratio organization in human EEG is associated with theta-alpha frequency convergence: a multi-dataset validation study"],"prefix":"10.3389","volume":"20","author":[{"given":"Andrei","family":"Ursachi","sequence":"first","affiliation":[{"name":"Independent Researcher","place":["Bucharest, Romania"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1965","published-online":{"date-parts":[[2026,3,4]]},"reference":[{"key":"B1","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1016\/j.conb.2014.08.002","article-title":"Untangling cross-frequency coupling in neuroscience","volume":"31","author":"Aru","year":"2015","journal-title":"Curr. 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