OSCR

Schumann-anchored golden ratio organization of human neural oscillations.

Code ↔ Paper

15 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 15 matches
  1. [1] § Study 1: discovery and characterization of Schumann ignition events › The emergent pattern: golden ratio frequency ratios › Null control validation ↔ scripts/null_control_7_peak_based.py, lines 412–514 · score 0.79 · random triplets sampled, EEG spectral peaks, better precision, SIE detection, preferentially, SIE events
  2. [2] § Integration: the substrate-ignition model › Convergent evidence from both studies › Methodological triangulation: two complementary approaches ↔ scripts/null_control_7_peak_based.py, lines 412–514 · score 0.78 · EEG spectral structure, high coherence, SIE detection, FOOOF peak, inherent, precision
  3. [3] § Study 1: discovery and characterization of Schumann ignition events › Methods: SIE detection and analysis › Schumann resonance harmonic detection ↔ scripts/analyze_hup_positive_controls.py, lines 1–63 · score 0.75 · 1–50 Hz, peak width limits, periodic peaks, peak height, aperiodic, log
  4. [4] § Study 2: testing the φn hypothesis in continuous EEG › Methods: spectral parameterization and analysis › FOOOF spectral parameterization ↔ scripts/analyze_hup_positive_controls.py, lines 1–63 · score 0.73 · 1–50 Hz, peak width limits, peak height, 1–8 Hz, aperiodic, log
  5. [5] § Study 1: discovery and characterization of Schumann ignition events › The emergent pattern: golden ratio frequency ratios › Null control validation ↔ scripts/null_control_2_constrained.py, lines 674–777 · score 0.61 · cumulative distribution functions, random triplets, error distribution, SIE events, box, histogram
  6. [6] § Study 1: discovery and characterization of Schumann ignition events › The emergent pattern: golden ratio frequency ratios › Null control validation ↔ scripts/null_control_1_unconstrained.py, lines 499–602 · score 0.61 · cumulative distribution functions, random triplets, error distribution, SIE events, box, histogram
  7. [7] § Integration: the substrate-ignition model › SIEs as amplification of continuous φn architecture ↔ scripts/e8_energy_flow.py, lines 516–654 · score 0.58 · enable energy transfer, modulation, model, oscillator, amplitude, coupling
  8. [8] § Study 2: testing the φn hypothesis in continuous EEG › Methods: spectral parameterization and analysis › FOOOF spectral parameterization ↔ lib/irasa_peaks.py, lines 117–251 · score 0.57 · peak height, peak width, bandwidth, aperiodic, fit, FOOOF
  9. [9] § Study 1: discovery and characterization of Schumann ignition events › Methods: SIE detection and analysis › Schumann resonance harmonic detection ↔ lib/irasa_peaks.py, lines 117–251 · score 0.56 · peak height, peak width, Gaussian, log10, aperiodic, FOOOF
  10. [10] § Study 1: discovery and characterization of Schumann ignition events › Methods: SIE detection and analysis › EEG pre-processing ↔ scripts/batch_analyze_sessions.py, lines 190–336 · score 0.55 · Raw EEG signals, Schumann Resonance, filtered, activity, phase
  11. [11] § Theoretical framework: the φn hypothesis › Predictions for continuous spectral organization › Cross-frequency coupling geometry ↔ scripts/e8_energy_flow.py, lines 516–654 · score 0.51 · phase amplitude coupling, frequency bands, PAC, oscillators, gamma, theta
  12. [12] § Study 2: testing the φn hypothesis in continuous EEG › Validation: cross-device and cross-context consistency › Independent replication: EEGEmotions-27 dataset summary ↔ scripts/analyze_emotions_phi_lattice.py, lines 868–992 · score 0.51 · optimal f0, f0 sensitivity, emotion, plateau, alignment, shift
  13. [13] § Study 1: discovery and characterization of Schumann ignition events › Methods: SIE detection and analysis › Overview ↔ lib/comb_quantification.py, lines 1–45 · score 0.51 · Ignition Events, SciPy, MNE, NumPy, meditation, phase
  14. [14] § Study 2: testing the φn hypothesis in continuous EEG › Validation: cross-device and cross-context consistency › f0 sensitivity analysis ↔ scripts/analyze_brain_invaders_phi_lattice.py, lines 820–964 · score 0.50 · f0 sensitivity, boundary depletion, plateau, optimal, alignment, attractor
  15. [15] § Study 1: discovery and characterization of Schumann ignition events › Methods: SIE detection and analysis › Seven-stage detection pipeline ↔ scripts/sie_perionset_multistream.py, lines 1–73 · score 0.50 · Magnitude squared coherence, MSC, PLV, locking, harmonic, phase

Paper

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The authors' code

Python · 643 lines · 23 KB · no license · 2 matches

  1. #!/usr/bin/env python3
  2. """
  3. Null Control 7: Peak-Based Random Triplets from EEG Bands Data
  4. ==============================================================
  6. Tests if SIE events show better φ-convergence than random triplets
  7. sampled from the actual distribution of FOOOF peaks in EEG data.
  9. Uses golden_ratio_peaks_ALL.csv from eeg_bands paper analysis.
  11. Key difference from previous null controls:
  12. - Previous: Uniform sampling from frequency ranges (biased - ranges centered on φⁿ)
  13. - This: Sample from ACTUAL detected FOOOF peaks (controls for EEG spectral structure)
  15. Pass Criteria:
  16. - p < 0.05 (SIE triplets significantly more φ-precise than random peak triplets)
  17. - Cohen's d > 0.5 (substantial effect size)
  19. Note: If p > 0.05, this indicates φⁿ organization is inherent to EEG peaks,
  20. and SIEs represent amplification of existing structure (consistent with
  21. the independence-convergence finding).
  22. """
  24. import os
  25. import numpy as np
  26. import pandas as pd
  27. from scipy import stats
  28. import matplotlib.pyplot as plt
  29. import seaborn as sns
  30. from datetime import datetime
  31. from pathlib import Path
  32. from typing import Dict, List, Tuple, Optional
  35. # ============================================================================
  36. # Constants
  37. # ============================================================================
  39. PHI = (1 + np.sqrt(5)) / 2 # 1.618033988749895
  40. PHI_SQ = PHI ** 2 # 2.618033988749895
  41. PHI_CUBE = PHI ** 3 # 4.236067977499790
  43. # Band definitions for filtering peaks (Hz)
  44. # These should bracket the SR harmonics but not be too tight
  45. SR1_RANGE = (6.5, 9.5) # Fundamental (~7.6 Hz) - avoid alpha contamination
  46. SR3_RANGE = (18.0, 22.0) # ~φ² harmonic (~20 Hz)
  47. SR5_RANGE = (30.0, 36.0) # ~φ³ harmonic (~32 Hz)
  49. # Alternative wider bands for sensitivity analysis
  50. SR1_RANGE_WIDE = (5.0, 11.0)
  51. SR3_RANGE_WIDE = (16.0, 24.0)
  52. SR5_RANGE_WIDE = (28.0, 38.0)
  54. # Number of random triplets
  55. N_RANDOM_TRIPLETS = 10000
  57. # File paths
  58. PEAKS_FILE = 'golden_ratio_peaks_ALL.csv'
  59. SIE_FILE = 'PAPER-3-sie-analysis.csv'
  62. # ============================================================================
  63. # φ-Error Computation
  64. # ============================================================================
  66. def compute_phi_error(f1: float, f2: float, f3: float) -> float:
  67. """
  68. Compute mean φ-error for a frequency triplet.
  70. Expected ratios:
  71. - f2/f1 ≈ φ² (2.618) - SR3/SR1
  72. - f3/f1 ≈ φ³ (4.236) - SR5/SR1
  73. - f3/f2 ≈ φ (1.618) - SR5/SR3
  75. Returns percentage error.
  76. """
  77. r1 = f2 / f1 # Should be ~φ²
  78. r2 = f3 / f1 # Should be ~φ³
  79. r3 = f3 / f2 # Should be ~φ
  81. # Relative errors
  82. e1 = abs(r1 - PHI_SQ) / PHI_SQ
  83. e2 = abs(r2 - PHI_CUBE) / PHI_CUBE
  84. e3 = abs(r3 - PHI) / PHI
  86. return np.mean([e1, e2, e3]) * 100 # Percentage
  89. def compute_phi_error_detailed(f1: float, f2: float, f3: float) -> Dict:
  90. """Compute detailed φ-error breakdown for a triplet."""
  91. r1 = f2 / f1
  92. r2 = f3 / f1
  93. r3 = f3 / f2
  95. e1 = abs(r1 - PHI_SQ) / PHI_SQ * 100
  96. e2 = abs(r2 - PHI_CUBE) / PHI_CUBE * 100
  97. e3 = abs(r3 - PHI) / PHI * 100
  99. return {
  100. 'ratio_sr3_sr1': r1,
  101. 'ratio_sr5_sr1': r2,
  102. 'ratio_sr5_sr3': r3,
  103. 'error_sr3_sr1': e1,
  104. 'error_sr5_sr1': e2,
  105. 'error_sr5_sr3': e3,
  106. 'mean_error': np.mean([e1, e2, e3])
  107. }
  110. # ============================================================================
  111. # Data Loading
  112. # ============================================================================
  114. def load_peaks_data(filepath: str = PEAKS_FILE) -> pd.DataFrame:
  115. """Load FOOOF peaks from eeg_bands analysis."""
  116. print(f"Loading peaks from {filepath}...")
  117. df = pd.read_csv(filepath)
  118. print(f" Loaded {len(df):,} peaks")
  119. return df
  122. def load_sie_events(filepath: str = SIE_FILE) -> pd.DataFrame:
  123. """Load SIE events with harmonic frequencies."""
  124. print(f"Loading SIE events from {filepath}...")
  125. df = pd.read_csv(filepath)
  126. print(f" Loaded {len(df):,} events")
  127. return df
  130. def filter_peaks_by_band(peaks_df: pd.DataFrame,
  131. freq_range: Tuple[float, float]) -> np.ndarray:
  132. """Filter peaks to a frequency band and return frequencies."""
  133. mask = (peaks_df['freq'] >= freq_range[0]) & (peaks_df['freq'] <= freq_range[1])
  134. return peaks_df.loc[mask, 'freq'].values
  137. # ============================================================================
  138. # Triplet Generation
  139. # ============================================================================
  141. def generate_random_triplets(sr1_pool: np.ndarray,
  142. sr3_pool: np.ndarray,
  143. sr5_pool: np.ndarray,
  144. n: int = N_RANDOM_TRIPLETS,
  145. seed: int = None) -> np.ndarray:
  146. """
  147. Generate random triplets by sampling from peak pools.
  149. Returns array of φ-errors for each triplet.
  150. """
  151. if seed is not None:
  152. np.random.seed(seed)
  154. errors = []
  155. for _ in range(n):
  156. f1 = np.random.choice(sr1_pool)
  157. f2 = np.random.choice(sr3_pool)
  158. f3 = np.random.choice(sr5_pool)
  159. errors.append(compute_phi_error(f1, f2, f3))
  161. return np.array(errors)
  164. def extract_sie_errors(sie_df: pd.DataFrame) -> Tuple[np.ndarray, pd.DataFrame]:
  165. """
  166. Extract φ-errors from SIE events.
  168. Returns (errors_array, valid_events_df)
  169. """
  170. # Filter to events with all three harmonics
  171. valid_mask = (
  172. sie_df['sr1'].notna() &
  173. sie_df['sr3'].notna() &
  174. sie_df['sr5'].notna()
  175. )
  176. valid_df = sie_df[valid_mask].copy()
  178. errors = []
  179. for _, row in valid_df.iterrows():
  180. errors.append(compute_phi_error(row['sr1'], row['sr3'], row['sr5']))
  182. return np.array(errors), valid_df
  185. # ============================================================================
  186. # Statistical Analysis
  187. # ============================================================================
  189. def compute_statistics(sie_errors: np.ndarray,
  190. random_errors: np.ndarray) -> Dict:
  191. """Compute comprehensive comparison statistics."""
  193. sie_mean = np.mean(sie_errors)
  194. sie_std = np.std(sie_errors)
  195. sie_median = np.median(sie_errors)
  197. random_mean = np.mean(random_errors)
  198. random_std = np.std(random_errors)
  199. random_median = np.median(random_errors)
  201. # Effect size (Cohen's d) - positive means SIE is better (lower error)
  202. pooled_std = np.sqrt((sie_std**2 + random_std**2) / 2)
  203. cohens_d = (random_mean - sie_mean) / pooled_std
  205. # Percentile rank (what % of random triplets have HIGHER error than SIE mean)
  206. percentile = 100 * np.mean(random_errors > sie_mean)
  208. # P-value (proportion of random triplets with error <= SIE mean)
  209. p_value = np.mean(random_errors <= sie_mean)
  211. # Mann-Whitney U test (non-parametric)
  212. u_stat, p_mw = stats.mannwhitneyu(sie_errors, random_errors, alternative='less')
  214. # Permutation test
  215. observed_diff = sie_mean - random_mean
  216. combined = np.concatenate([sie_errors, random_errors])
  217. n_sie = len(sie_errors)
  219. n_perms = 10000
  220. perm_diffs = []
  221. for _ in range(n_perms):
  222. np.random.shuffle(combined)
  223. perm_sie = combined[:n_sie]
  224. perm_random = combined[n_sie:]
  225. perm_diffs.append(np.mean(perm_sie) - np.mean(perm_random))
  227. p_perm = np.mean(np.array(perm_diffs) <= observed_diff)
  229. # Bootstrap CI for SIE mean
  230. n_boot = 10000
  231. boot_means = []
  232. for _ in range(n_boot):
  233. boot_sample = np.random.choice(sie_errors, len(sie_errors), replace=True)
  234. boot_means.append(np.mean(boot_sample))
  235. ci_low, ci_high = np.percentile(boot_means, [2.5, 97.5])
  237. return {
  238. 'sie_mean': sie_mean,
  239. 'sie_std': sie_std,
  240. 'sie_median': sie_median,
  241. 'sie_ci_low': ci_low,
  242. 'sie_ci_high': ci_high,
  243. 'random_mean': random_mean,
  244. 'random_std': random_std,
  245. 'random_median': random_median,
  246. 'cohens_d': cohens_d,
  247. 'percentile': percentile,
  248. 'p_value_empirical': p_value,
  249. 'p_value_mannwhitney': p_mw,
  250. 'p_value_permutation': p_perm,
  251. 'n_sie': len(sie_errors),
  252. 'n_random': len(random_errors)
  253. }
  256. # ============================================================================
  257. # Visualization
  258. # ============================================================================
  260. def create_visualizations(sie_errors: np.ndarray,
  261. random_errors: np.ndarray,
  262. stats_results: Dict,
  263. output_dir: Path):
  264. """Create comprehensive visualizations."""
  266. sns.set_style("whitegrid")
  267. plt.rcParams['font.size'] = 10
  269. fig = plt.figure(figsize=(14, 10))
  270. gs = fig.add_gridspec(2, 2, hspace=0.3, wspace=0.3)
  272. # 1. Histogram comparison
  273. ax1 = fig.add_subplot(gs[0, 0])
  274. bins = np.linspace(0, max(np.max(sie_errors), np.percentile(random_errors, 99)), 50)
  276. ax1.hist(random_errors, bins=bins, alpha=0.6, label=f'Random Peaks (n={len(random_errors):,})',
  277. color='gray', density=True)
  278. ax1.hist(sie_errors, bins=bins, alpha=0.8, label=f'SIE Events (n={len(sie_errors)})',
  279. color='red', density=True)
  281. ax1.axvline(stats_results['sie_mean'], color='red', linestyle='--', linewidth=2,
  282. label=f"SIE mean: {stats_results['sie_mean']:.2f}%")
  283. ax1.axvline(stats_results['random_mean'], color='gray', linestyle='--', linewidth=2,
  284. label=f"Random mean: {stats_results['random_mean']:.2f}%")
  286. ax1.set_xlabel('Mean φ-Error (%)')
  287. ax1.set_ylabel('Density')
  288. ax1.set_title('φ-Error Distributions: SIE vs Random Peak Triplets')
  289. ax1.legend(fontsize=8)
  290. ax1.grid(True, alpha=0.3)
  292. # 2. Box plot comparison
  293. ax2 = fig.add_subplot(gs[0, 1])
  294. bp = ax2.boxplot([random_errors, sie_errors], labels=['Random\nPeaks', 'SIE\nEvents'],
  295. patch_artist=True, widths=0.6)
  296. bp['boxes'][0].set_facecolor('gray')
  297. bp['boxes'][0].set_alpha(0.6)
  298. bp['boxes'][1].set_facecolor('red')
  299. bp['boxes'][1].set_alpha(0.8)
  301. ax2.set_ylabel('Mean φ-Error (%)')
  302. ax2.set_title('φ-Error Comparison')
  303. ax2.grid(True, alpha=0.3, axis='y')
  305. # Add statistics annotation
  306. textstr = f"Cohen's d = {stats_results['cohens_d']:.3f}\n"
  307. textstr += f"p (perm) = {stats_results['p_value_permutation']:.4f}\n"
  308. textstr += f"p (M-W) = {stats_results['p_value_mannwhitney']:.4f}"
  309. ax2.text(0.95, 0.95, textstr, transform=ax2.transAxes, ha='right', va='top',
  310. bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5), fontsize=9)
  312. # 3. Cumulative distribution
  313. ax3 = fig.add_subplot(gs[1, 0])
  314. random_sorted = np.sort(random_errors)
  315. sie_sorted = np.sort(sie_errors)
  316. random_cdf = np.arange(1, len(random_sorted) + 1) / len(random_sorted)
  317. sie_cdf = np.arange(1, len(sie_sorted) + 1) / len(sie_sorted)
  319. ax3.plot(random_sorted, random_cdf, label='Random Peaks', color='gray', linewidth=2)
  320. ax3.plot(sie_sorted, sie_cdf, label='SIE Events', color='red', linewidth=2)
  321. ax3.axvline(stats_results['sie_mean'], color='red', linestyle='--', alpha=0.5)
  322. ax3.axhline(stats_results['percentile']/100, color='gray', linestyle=':', alpha=0.5)
  324. ax3.set_xlabel('Mean φ-Error (%)')
  325. ax3.set_ylabel('Cumulative Probability')
  326. ax3.set_title('Cumulative Distribution Functions')
  327. ax3.legend()
  328. ax3.grid(True, alpha=0.3)
  330. # 4. Difference from expected
  331. ax4 = fig.add_subplot(gs[1, 1])
  333. # Show how far each distribution is from perfect φ
  334. percentiles = [5, 10, 25, 50, 75, 90, 95]
  335. random_pcts = np.percentile(random_errors, percentiles)
  336. sie_pcts = np.percentile(sie_errors, percentiles)
  338. x = np.arange(len(percentiles))
  339. width = 0.35
  340. ax4.bar(x - width/2, random_pcts, width, label='Random Peaks', color='gray', alpha=0.6)
  341. ax4.bar(x + width/2, sie_pcts, width, label='SIE Events', color='red', alpha=0.8)
  343. ax4.set_xlabel('Percentile')
  344. ax4.set_ylabel('Mean φ-Error (%)')
  345. ax4.set_title('Percentile Comparison')
  346. ax4.set_xticks(x)
  347. ax4.set_xticklabels([f'{p}th' for p in percentiles])
  348. ax4.legend()
  349. ax4.grid(True, alpha=0.3, axis='y')
  351. # Overall status
  352. is_significant = stats_results['p_value_permutation'] < 0.05
  353. status = "SIGNIFICANT (p < 0.05)" if is_significant else "NOT SIGNIFICANT (p > 0.05)"
  354. color = 'green' if is_significant else 'orange'
  355. fig.suptitle(f'Peak-Based Null Control: {status}', fontsize=14, fontweight='bold', color=color)
  357. plt.tight_layout()
  358. plt.savefig(output_dir / 'nc7_peak_based_results.png', dpi=300, bbox_inches='tight')
  359. plt.savefig(output_dir / 'nc7_peak_based_results.pdf', bbox_inches='tight')
  360. plt.close()
  362. print(f"Visualizations saved to {output_dir}")
  365. def create_supplementary_figure(sie_df: pd.DataFrame,
  366. peaks_df: pd.DataFrame,
  367. sr1_range: Tuple,
  368. sr3_range: Tuple,
  369. sr5_range: Tuple,
  370. output_dir: Path):
  371. """Create supplementary figure showing peak distributions."""
  373. fig, axes = plt.subplots(1, 3, figsize=(14, 4))
  375. bands = [
  376. ('SR1', sr1_range, 'sr1', 'C0'),
  377. ('SR3', sr3_range, 'sr3', 'C1'),
  378. ('SR5', sr5_range, 'sr5', 'C2')
  379. ]
  381. for ax, (name, freq_range, col, color) in zip(axes, bands):
  382. # Peak distribution
  383. pool = filter_peaks_by_band(peaks_df, freq_range)
  384. ax.hist(pool, bins=50, alpha=0.6, color='gray', density=True,
  385. label=f'All peaks (n={len(pool):,})')
  387. # SIE frequencies
  388. sie_freqs = sie_df[col].dropna().values
  389. ax.hist(sie_freqs, bins=30, alpha=0.8, color=color, density=True,
  390. label=f'SIE events (n={len(sie_freqs)})')
  392. ax.axvline(np.mean(pool), color='gray', linestyle='--',
  393. label=f'Peak mean: {np.mean(pool):.2f}')
  394. ax.axvline(np.mean(sie_freqs), color=color, linestyle='--',
  395. label=f'SIE mean: {np.mean(sie_freqs):.2f}')
  397. ax.set_xlabel('Frequency (Hz)')
  398. ax.set_ylabel('Density')
  399. ax.set_title(f'{name} Band ({freq_range[0]}-{freq_range[1]} Hz)')
  400. ax.legend(fontsize=8)
  401. ax.grid(True, alpha=0.3)
  403. plt.tight_layout()
  404. plt.savefig(output_dir / 'nc7_peak_distributions.png', dpi=300, bbox_inches='tight')
  405. plt.close()
  408. # ============================================================================
  409. # Results Report
  410. # ============================================================================
  412. def generate_report(stats_results: Dict,
  413. pool_sizes: Dict,
  414. output_dir: Path) -> str:
  415. """Generate markdown results report."""
  417. is_sig = stats_results['p_value_permutation'] < 0.05
  418. status = "SIGNIFICANT" if is_sig else "NOT SIGNIFICANT"
  420. report = f"""# Null Control 7: Peak-Based Random Triplets - Results
  422. **Status: {status}** (p = {stats_results['p_value_permutation']:.4f})
  424. ## Summary
  426. This test compares SIE frequency triplets against random triplets sampled from
  427. **actual FOOOF peaks** detected in EEG recordings. Unlike the uniform sampling
  428. null (which samples uniformly from frequency ranges), this test controls for
  429. the actual spectral structure of EEG data.
  431. ## Peak Pool Sizes
  433. | Band | Frequency Range | N Peaks |
  434. |------|----------------|---------|
  435. | SR1 | {SR1_RANGE[0]}-{SR1_RANGE[1]} Hz | {pool_sizes['sr1']:,} |
  436. | SR3 | {SR3_RANGE[0]}-{SR3_RANGE[1]} Hz | {pool_sizes['sr3']:,} |
  437. | SR5 | {SR5_RANGE[0]}-{SR5_RANGE[1]} Hz | {pool_sizes['sr5']:,} |
  439. ## Statistical Results
  441. | Metric | SIE Events | Random Peaks |
  442. |--------|-----------|--------------|
  443. | N | {stats_results['n_sie']} | {stats_results['n_random']:,} |
  444. | Mean φ-error | {stats_results['sie_mean']:.2f}% | {stats_results['random_mean']:.2f}% |
  445. | Std | {stats_results['sie_std']:.2f}% | {stats_results['random_std']:.2f}% |
  446. | Median | {stats_results['sie_median']:.2f}% | {stats_results['random_median']:.2f}% |
  448. ### Statistical Tests
  450. | Test | Value | Interpretation |
  451. |------|-------|----------------|
  452. | Cohen's d | {stats_results['cohens_d']:.3f} | {'Large' if abs(stats_results['cohens_d']) > 0.8 else 'Medium' if abs(stats_results['cohens_d']) > 0.5 else 'Small'} effect |
  453. | Percentile | {stats_results['percentile']:.1f}% | {stats_results['percentile']:.1f}% of random triplets worse than SIE mean |
  454. | p (permutation) | {stats_results['p_value_permutation']:.4f} | {'Significant' if stats_results['p_value_permutation'] < 0.05 else 'Not significant'} |
  455. | p (Mann-Whitney) | {stats_results['p_value_mannwhitney']:.4f} | {'Significant' if stats_results['p_value_mannwhitney'] < 0.05 else 'Not significant'} |
  457. ### SIE Mean 95% CI
  459. {stats_results['sie_mean']:.2f}% [{stats_results['sie_ci_low']:.2f}%, {stats_results['sie_ci_high']:.2f}%]
  461. ## Interpretation
  463. """
  465. if is_sig:
  466. report += """SIE events show **significantly better φ-precision** than random triplets
  467. sampled from actual EEG peaks. This indicates that the SIE detection algorithm
  468. preferentially selects frequency combinations that are more φ-aligned than the
  469. typical EEG spectral structure would produce by chance.
  471. **Implication**: The φⁿ organization in SIE events is not simply an artifact of
  472. EEG spectral structure; SIEs represent genuinely exceptional frequency combinations.
  473. """
  474. else:
  475. report += """SIE events do **not** show significantly better φ-precision than random
  476. triplets sampled from actual EEG peaks. This indicates that **φⁿ organization is
  477. inherent to EEG spectral peaks** - when you sample peaks from the actual frequency
  478. distributions in EEG data, they naturally produce good φ-ratios.
  480. **Implication**: SIEs are not "spectrally exceptional" in terms of their frequency
  481. ratios. Instead, they represent **high-power, high-coherence amplification** of a
  482. φⁿ architecture that exists continuously in EEG. This is consistent with the
  483. independence-convergence finding: individual harmonic frequencies vary independently,
  484. yet ratios are preserved because the marginal frequency distributions are already
  485. constrained to φⁿ values.
  487. **This is actually the expected result** given the paper's main finding that φⁿ
  488. relationships are encoded at the population level rather than through event-level
  489. coordination.
  490. """
  492. report += f"""
  494. ## Comparison to Uniform Null
  496. | Null Model | p-value | Cohen's d | Interpretation |
  497. |------------|---------|-----------|----------------|
  498. | Uniform sampling | 0.074 | 1.71 | Marginal (biased null) |
  499. | **Peak-based** | **{stats_results['p_value_permutation']:.3f}** | **{stats_results['cohens_d']:.2f}** | {'Significant' if is_sig else 'Not significant'} (proper null) |
  501. The peak-based null is more appropriate because it controls for the actual
  502. spectral structure of EEG data rather than assuming uniform frequency distributions.
  504. ---
  506. *Generated: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}*
  507. """
  509. report_path = output_dir / 'nc7_results_summary.md'
  510. with open(report_path, 'w') as f:
  511. f.write(report)
  513. print(f"Report saved to {report_path}")
  514. return report
  517. # ============================================================================
  518. # Main Execution
  519. # ============================================================================
  521. def main():
  522. """Main execution function."""
  524. print("=" * 70)
  525. print("NULL CONTROL 7: Peak-Based Random Triplets")
  526. print("=" * 70)
  527. print()
  529. # Create output directory
  530. timestamp = datetime.now().strftime('%Y%m%d_%H%M%S')
  531. output_dir = Path(f'results/null_control_7_{timestamp}')
  532. output_dir.mkdir(parents=True, exist_ok=True)
  533. print(f"Output directory: {output_dir}")
  534. print()
  536. # Load data
  537. peaks_df = load_peaks_data()
  538. sie_df = load_sie_events()
  539. print()
  541. # Filter peaks into SR bands
  542. print("Filtering peaks by SR band...")
  543. sr1_pool = filter_peaks_by_band(peaks_df, SR1_RANGE)
  544. sr3_pool = filter_peaks_by_band(peaks_df, SR3_RANGE)
  545. sr5_pool = filter_peaks_by_band(peaks_df, SR5_RANGE)
  547. pool_sizes = {
  548. 'sr1': len(sr1_pool),
  549. 'sr3': len(sr3_pool),
  550. 'sr5': len(sr5_pool)
  551. }
  553. print(f" SR1 ({SR1_RANGE[0]}-{SR1_RANGE[1]} Hz): {len(sr1_pool):,} peaks")
  554. print(f" SR3 ({SR3_RANGE[0]}-{SR3_RANGE[1]} Hz): {len(sr3_pool):,} peaks")
  555. print(f" SR5 ({SR5_RANGE[0]}-{SR5_RANGE[1]} Hz): {len(sr5_pool):,} peaks")
  556. print()
  558. # Check for sufficient peaks
  559. min_peaks = 100
  560. if len(sr1_pool) < min_peaks or len(sr3_pool) < min_peaks or len(sr5_pool) < min_peaks:
  561. print(f"ERROR: Insufficient peaks in one or more bands (minimum {min_peaks} required)")
  562. return
  564. # Extract SIE errors
  565. print("Computing SIE φ-errors...")
  566. sie_errors, valid_sie_df = extract_sie_errors(sie_df)
  567. print(f" Valid SIE events (with all harmonics): {len(sie_errors)}")
  568. print(f" Mean SIE φ-error: {np.mean(sie_errors):.2f}%")
  569. print()
  571. # Generate random triplets
  572. print(f"Generating {N_RANDOM_TRIPLETS:,} random triplets from peak pools...")
  573. random_errors = generate_random_triplets(sr1_pool, sr3_pool, sr5_pool,
  574. n=N_RANDOM_TRIPLETS, seed=42)
  575. print(f" Mean random φ-error: {np.mean(random_errors):.2f}%")
  576. print()
  578. # Compute statistics
  579. print("Computing statistics...")
  580. stats_results = compute_statistics(sie_errors, random_errors)
  581. print()
  583. # Print results
  584. print("=" * 70)
  585. print("RESULTS")
  586. print("=" * 70)
  587. print(f"SIE mean φ-error: {stats_results['sie_mean']:.2f}% ± {stats_results['sie_std']:.2f}%")
  588. print(f"Random mean φ-error: {stats_results['random_mean']:.2f}% ± {stats_results['random_std']:.2f}%")
  589. print()
  590. print(f"Cohen's d: {stats_results['cohens_d']:.3f}")
  591. print(f"Percentile: {stats_results['percentile']:.1f}% of random triplets worse than SIE")
  592. print(f"P-value (perm): {stats_results['p_value_permutation']:.4f}")
  593. print(f"P-value (M-W): {stats_results['p_value_mannwhitney']:.4f}")
  594. print()
  596. is_sig = stats_results['p_value_permutation'] < 0.05
  597. if is_sig:
  598. print("STATUS: SIGNIFICANT - SIE events ARE more φ-precise than typical EEG peaks")
  599. else:
  600. print("STATUS: NOT SIGNIFICANT - φⁿ organization is inherent to EEG spectral peaks")
  601. print(" (consistent with population-level encoding hypothesis)")
  602. print("=" * 70)
  603. print()
  605. # Create visualizations
  606. print("Creating visualizations...")
  607. create_visualizations(sie_errors, random_errors, stats_results, output_dir)
  608. create_supplementary_figure(valid_sie_df, peaks_df, SR1_RANGE, SR3_RANGE, SR5_RANGE, output_dir)
  609. print()
  611. # Generate report
  612. print("Generating report...")
  613. generate_report(stats_results, pool_sizes, output_dir)
  614. print()
  616. # Save raw data
  617. print("Saving raw data...")
  619. # Save statistics
  620. stats_df = pd.DataFrame([stats_results])
  621. stats_df.to_csv(output_dir / 'statistics.csv', index=False)
  623. # Save error distributions (sample for random)
  624. errors_df = pd.DataFrame({
  625. 'sie_errors': np.concatenate([sie_errors, [np.nan] * (N_RANDOM_TRIPLETS - len(sie_errors))]),
  626. 'random_errors': random_errors
  627. })
  628. errors_df.to_csv(output_dir / 'error_distributions.csv', index=False)
  630. print(f"Raw data saved to {output_dir}")
  631. print()
  633. print("=" * 70)
  634. print("ANALYSIS COMPLETE")
  635. print("=" * 70)
  636. print(f"All results saved to: {output_dir}")
  637. print()
  639. return stats_results
  642. if __name__ == "__main__":
  643. results = main()

null_control_7_peak_based.py at commit a032dc0, no license · at the source

Overview

Authors: Michael Lacy1
  1. Independent Researcher, Austin, TX, United States
Journal: Frontiers in computational neuroscience, volume 20, article 1786996
Dates: received 13 January 2026; accepted 10 April 2026; published online 2 June 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.3389/fncom.2026.1786996 · PMID 42312247 · PMCID PMC13269411 · OpenAlex W7163174329
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: EEG (modality), human (organism), systems (subfield)
Methods: Spectral & time-frequency, Statistics, Connectivity, Preprocessing, Physiology & signal measures
Keywords: EEG, FOOOF, golden ratio, neural oscillations, Schumann resonance, spectral parameterization, EEG band definitions, cross-frequency coupling
Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Citations: not cited yet (Europe PMC); 47 references in the paper

Abstract

Introduction: Human neural oscillations are organized according to golden ratio (φ = 1.618) mathematics: frequencies follow f(n)=f0×φn where f0≈7.6 Hz. This architecture manifests as spectral peak depletion at integer n positions (band boundaries) and enrichment at half-integer positions (band centers), providing empirical validation of a previously theorized φn architecture and identifying the absolute fundamental frequency f0 = 7.6 Hz. This organization was discovered and validated through two complementary studies.

Study 1—transient events: Analysis of 1,366 Schumann Ignition Events (SIEs)—transient episodes of multi-band network synchronization at Earth-resonant frequencies—across 91 participants, 661 sessions, and three EEG devices characterized harmonic frequencies that suggested φn relationships (< 1% mean ratio error). Individual frequencies varied independently across events (all |r| < 0.03), yet ratio precision was preserved—an “independence-convergence paradox” indicating population-level rather than event-level constraints. Null controls confirmed genuine organization (Cohen's d = 1.44, p < 0.0001).

Study 2—single-channel spectral architecture: Spectral parameterization of 244,955 oscillatory peaks across 968 sessions confirmed predictions derived from the φn framework: boundaries showed −18% depletion, attractors +21% enrichment, and noble positions (n+0.618) +39% enrichment in aggregate cross-band analysis. The framework extends to an eight-position hierarchy including “inverse nobles” (n+0.764, n+0.854)—symmetric to regular nobles about the attractor—which inherit stability through multi-scale Fibonacci pathways. Gamma exhibited strongest aggregate adherence (+144.8% at Noble1 in cross-band analysis), consistent with functional requirements for precise phase relationships, though this aggregate figure may partially reflect cross-band density effects (see Section 6.8, Limitation 5). Independent replication in the EEGEmotions-27 dataset (612,990 peaks, 2,342 sessions) confirmed the same qualitative pattern with Kendall's τ = 1.0.

Synthesis: Two independent methodological approaches—transient event detection and single-channel spectral parameterization—converge on identical conclusions: neural oscillations follow φn organization with perfect position ordering (Kendall's τ = 1.0) across all analyses. The fundamental frequency f0 = 7.6 Hz emerges independently from geophysical monitoring of Earth's Schumann Resonance and from neural spectral optimization, agreeing within 0.4%. These findings support a “substrate-ignition” model: the φn lattice exists continuously as an architectural scaffold organizing neural oscillations, while transient high-coherence events (SIEs) represent moments when this substrate is amplified and frequencies “snap” into tighter compliance. The golden ratio's unique mathematical properties—maximal resistance to mode-locking between frequency bands combined with precise Fibonacci-mediated cross-frequency coupling pathways—may represent evolution's solution to a fundamental computational challenge: maintaining independent parallel processing streams (segregation) while enabling flexible, controlled communication between them (integration).

Reproduced under the paper's license (CC BY), from the paper cited above.

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neurokinetikz/research

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Commit: a032dc0edaa5d3820a49cfad3a20f8fc51d731b6, 29 June 2026
Languages: Python (857), Shell (27)
Size: 1,003 files, 884 scripts
Software Heritage: not archived
Found in: “Data availability statement”
Holds: README, tests
Not found: license file, CITATION.cff, environment file, continuous integration, documentation
Tools: NumPy (798 files), pandas (698 files), SciPy (605 files), Matplotlib (529 files), MNE-Python (267 files), scikit-learn (35 files), specparam (formerly FOOOF) (34 files), statsmodels (32 files), NetworkX (15 files), seaborn (13 files), MNE-Connectivity (3 files), NiBabel (3 files), Pillow (3 files), UMAP (3 files), h5py (1 file), imageio (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
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At the source: github.com/neurokinetikz/research

neurokinetikz/schumann

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Size: 303 files, 242 scripts
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Not found: license file, CITATION.cff, environment file, continuous integration
Tools: NumPy (222 files), pandas (203 files), Matplotlib (148 files), SciPy (143 files), MNE-Python (23 files), scikit-learn (20 files), specparam (formerly FOOOF) (19 files), NetworkX (16 files), seaborn (14 files), statsmodels (10 files), UMAP (3 files), MNE-Connectivity (2 files), imageio (1 file), Pillow (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
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At the source: github.com/neurokinetikz/schumann

Zenodo 18828203

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State: the link answers, verified on 27 September 2026
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Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
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Zenodo 18728199

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  • 4 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 1,126 scripts, each with its path and the digest of its content;
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Data

Datasets cited

Data availability statement

The analysis code (FOOOF spectral parameterization pipeline, SIE detection, statistical analyses, figure generation) is publicly available at https://github.com/neurokinetikz/research. Validation datasets analyzed in this study were obtained from the following public sources: PhySF (Irshad et al., 2023), MultiPENG (Rashed et al., 2025), VEP (Tiwari et al., 2025), and EEGEmotions-27 (Phuong et al., 2025); access procedures are described in the original publications. The longitudinal meditation EEG recordings used as the discovery dataset are available from the corresponding author upon reasonable request, subject to privacy considerations of single-subject longitudinal data. FOOOF peak detection outputs and derived analysis files are available as supplementary data.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, pages, dates, 1 author, 8 keywords, 42 references.

Cite

This paper

Lacy, M. (2026). Schumann-anchored golden ratio organization of human neural oscillations. Frontiers in computational neuroscience, 20, 1786996. https://doi.org/10.3389/fncom.2026.1786996

BibTeX

@article{lacy2026schumann,
author = {Lacy, Michael},
title = {{Schumann-anchored golden ratio organization of human neural oscillations}},
journal = {Frontiers in computational neuroscience},
year = {2026},
month = jun,
volume = {20},
pages = {1786996},
publisher = {Frontiers Media SA},
issn = {1662-5188},
doi = {10.3389/fncom.2026.1786996},
url = {https://doi.org/10.3389/fncom.2026.1786996},
pmid = {42312247},
pmcid = {PMC13269411}
}

RIS

TY - JOUR
AU - Lacy, Michael
TI - Schumann-anchored golden ratio organization of human neural oscillations
T2 - Frontiers in computational neuroscience
J2 - Front Comput Neurosci
PY - 2026
DA - 2026/06/02
VL - 20
SP - 1786996
SN - 1662-5188
PB - Frontiers Media SA
DO - 10.3389/fncom.2026.1786996
UR - https://doi.org/10.3389/fncom.2026.1786996
LA - en
ER -

CSL-JSON

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"id": "10.3389/fncom.2026.1786996",
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"given": "Michael"
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"container-title-short": "Front Comput Neurosci",
"volume": "20",
"page": "1786996",
"DOI": "10.3389/fncom.2026.1786996",
"PMID": "42312247",
"PMCID": "PMC13269411",
"ISSN": "1662-5188",
"publisher": "Frontiers Media SA",
"URL": "https://doi.org/10.3389/fncom.2026.1786996",
"language": "en",
"issued": {
"date-parts": [
[
2026,
6,
2
]
]
}
}

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