#!/usr/bin/env python3 """ Test: Crisis Count Ceiling — Topological Invariant of Regime Crossings ====================================================================== Tests the prediction that crisis count per economic long wave is a topological invariant determined by floor(K/T), where K is CES curvature and T is information friction. Lean backing: - crisis_count_invariant (Dynamics/ConservationLaws.lean): the winding number of the trajectory around T = T* is a topological invariant; crisis count ~ floor(K/T_avg) per Kondratieff wave. Four sub-tests: 1. Recession frequency declines across Kondratieff waves (T increases over time with better institutions → lower K/T → fewer crises). 2. Great Moderation structural break: post-1984 recession frequency significantly lower (Poisson test), consistent with T increase. 3. NFCI correlation: financial stress predicts recession occurrence in 5-year windows, validating NFCI as a T proxy. 4. Recession spacing regularity: inter-recession intervals have CV < 1 (more regular than Poisson), consistent with deterministic ceiling rather than random arrival. Data: NBER recession dates (hardcoded, 1854-2024), FRED NFCI (1971-2024). Kondratieff wave boundaries follow Perez (2002, 2009): Wave 3: 1890-1929 (Age of Steel & Electricity) Wave 4: 1930-1970 (Age of Oil & Mass Production) Wave 5: 1971-2024 (Age of ICT) Review Notes (2026-03-11): Theory match: PARTIAL. The Lean theorem is a True := trivial schematic (no real proof). The prediction n = floor(K/T) requires both K and T estimates per wave, but neither is directly observable at the wave level. We test weaker implications: (1) frequency decline across waves (T increasing), (2) Great Moderation as T-shift, (3) NFCI as T proxy, (4) spacing regularity (deterministic vs stochastic crisis arrival). Data-signal alignment: ADEQUATE. NBER recession dates are the gold standard for US crisis timing. NFCI is a reasonable financial stress proxy. But Kondratieff wave boundaries are debatable and the sample is inherently small (3 waves, 7 post-1970 recessions). Known limitations: (1) Only 3 waves have adequate recession data. (2) The prediction n = floor(K/T) is essentially unfalsifiable with N=3 waves. (3) "Topological invariant" is a strong claim that can't be tested empirically — we test weaker regularity implications. (4) Previous version was tautological (set N_eff=5 to match max observed) and tested "complexity growth" which contradicts the invariant prediction. Replaced with testable frequency/regularity predictions. """ import numpy as np import pandas as pd from scipy import stats import sys, os sys.path.insert(0, os.path.join(os.path.dirname(__file__), '..', '..')) from common.data import load_fred from common.stats import verdict, log_result # ── NBER recession peak dates (full list, 1854-2024) ──────────────── # Source: NBER Business Cycle Dating Committee # https://www.nber.org/research/data/us-business-cycle-expansions-and-contractions NBER_RECESSIONS = [ # (peak_year, peak_month) (1857, 6), (1860, 10), (1865, 4), (1869, 6), (1873, 10), (1882, 3), (1887, 3), (1890, 7), (1893, 1), (1895, 12), (1899, 6), (1902, 9), (1907, 5), (1910, 1), (1913, 1), (1918, 8), (1920, 1), (1923, 5), (1926, 10), (1929, 8), (1937, 5), (1945, 2), (1948, 11), (1953, 7), (1957, 8), (1960, 4), (1969, 12), (1973, 11), (1980, 1), (1981, 7), (1990, 7), (2001, 3), (2007, 12), (2020, 2), ] # ── Kondratieff wave boundaries (Perez 2002, 2009) ────────────────── KONDRATIEFF_WAVES = [ ("Age of Steel & Electricity", 1890, 1929), ("Age of Oil & Mass Production", 1930, 1970), ("Age of ICT", 1971, 2024), ] # Great Moderation structural break (McConnell & Perez-Quiros 2000) GREAT_MODERATION_BREAK = 1984 def _recessions_in_period(start_year, end_year): """Count NBER recessions with peak in [start_year, end_year].""" return [r for r in NBER_RECESSIONS if start_year <= r[0] <= end_year] def _recession_frequency(start_year, end_year): """Recessions per decade in period.""" recs = _recessions_in_period(start_year, end_year) span = end_year - start_year if span <= 0: return 0.0 return len(recs) / (span / 10.0) _cache = {} def main(): """Run crisis count ceiling tests. Returns list of result dicts.""" results = [] # ── Test 1: Recession frequency declines across Kondratieff waves ── # The theory predicts n = floor(K/T). As T increases over time # (better institutions, central banking, regulation), the ceiling # K/T declines, so fewer crises per unit time. wave_data = [] for name, start, end in KONDRATIEFF_WAVES: recs = _recessions_in_period(start, end) span = end - start freq = len(recs) / (span / 10.0) wave_data.append({ 'wave': name, 'start': start, 'end': end, 'n_recessions': len(recs), 'span_years': span, 'frequency_per_decade': round(freq, 2), }) freqs = [w['frequency_per_decade'] for w in wave_data] # Test: frequency is monotonically non-increasing across waves. # With 3 waves, probability of monotonic decrease by chance = 1/6 ≈ 0.17 mono_decreasing = all(freqs[i] >= freqs[i+1] for i in range(len(freqs)-1)) if mono_decreasing: verd_wave = 'CONSISTENT' # 1/3! = 1/6 = 0.167 chance of this ordering by chance p_wave = 1.0 / 6.0 else: verd_wave = 'AMBIGUOUS' p_wave = 0.50 results.append(log_result( 'crisis_count_wave_frequency', freqs[-1], p_wave, verd_wave, details={'waves': wave_data, 'monotone_decreasing': mono_decreasing}, description=( "Tests that recession frequency (per decade) declines across " "Kondratieff waves, consistent with the crisis count ceiling " "n = floor(K/T) as T increases over time (better institutions, " "monetary policy). Uses NBER recession dates across 3 waves " "(1890-1929, 1930-1970, 1971-2024). Monotonic decline supports " "the theory. CAVEAT: only N=3 waves; probability of monotonic " "ordering by chance is 1/6." ) )) # ── Test 2: Great Moderation structural break ──────────────────── # Post-1984 recession frequency should be lower (Bernanke 2004: # better monetary policy ≈ higher T in CES framework). freq_pre = _recession_frequency(1948, GREAT_MODERATION_BREAK) freq_post = _recession_frequency(GREAT_MODERATION_BREAK + 1, 2024) recs_pre = _recessions_in_period(1948, GREAT_MODERATION_BREAK) recs_post = _recessions_in_period(GREAT_MODERATION_BREAK + 1, 2024) span_pre = GREAT_MODERATION_BREAK - 1948 span_post = 2024 - GREAT_MODERATION_BREAK # Poisson test: under H0 of constant rate, is post-moderation count low? combined_rate = (len(recs_pre) + len(recs_post)) / (span_pre + span_post) expected_post = combined_rate * span_post p_poisson = stats.poisson.cdf(len(recs_post), expected_post) decline = freq_post < freq_pre if decline and p_poisson < 0.10: verd_gm = 'CONSISTENT' elif decline: verd_gm = 'AMBIGUOUS' else: verd_gm = 'INCONSISTENT' results.append(log_result( 'crisis_count_great_moderation', freq_post - freq_pre, p_poisson, verd_gm, details={ 'pre_moderation_recessions': len(recs_pre), 'pre_moderation_span': span_pre, 'pre_moderation_freq_per_decade': round(freq_pre, 2), 'post_moderation_recessions': len(recs_post), 'post_moderation_span': span_post, 'post_moderation_freq_per_decade': round(freq_post, 2), 'frequency_decline': round(freq_pre - freq_post, 2), 'poisson_p': round(p_poisson, 4), 'expected_post_under_H0': round(expected_post, 1), }, description=( "Tests the Great Moderation as a T-increase in the crisis ceiling " "n = floor(K/T). Post-1984 recession frequency should be lower " "than pre-1984 (better monetary policy = higher T = lower K/T). " "Uses a Poisson test: under H0 of constant rate across the " "postwar era, is the post-1984 count significantly low? " "Consistent if frequency declined and Poisson p < 0.10." ) )) # ── Test 3: NFCI correlation with crisis occurrence ───────────── # NFCI measures financial conditions stress — a proxy for crisis # propensity. Decades with more financial stress should have more # recessions. Test in non-overlapping 5-year windows. try: nfci = load_fred('NFCI') except FileNotFoundError: nfci = None if nfci is not None and len(nfci) > 100: nfci_annual = nfci.resample('YS').mean() # Non-overlapping 5-year windows from 1972-2024 windows = [] for start_yr in range(1972, 2020, 5): end_yr = start_yr + 4 window_nfci = nfci_annual[ (nfci_annual.index.year >= start_yr) & (nfci_annual.index.year <= end_yr) ] if len(window_nfci) < 3: continue mean_nfci = float(window_nfci.mean()) n_recs = len(_recessions_in_period(start_yr, end_yr)) windows.append({ 'period': f'{start_yr}-{end_yr}', 'mean_nfci': round(mean_nfci, 3), 'n_recessions': n_recs, }) if len(windows) >= 5: nfci_vals = [w['mean_nfci'] for w in windows] rec_counts = [w['n_recessions'] for w in windows] # Spearman: higher NFCI stress → more recessions r_sp, p_sp = stats.spearmanr(nfci_vals, rec_counts) sign_ok = r_sp > 0 verd_nfci = verdict(p_sp, sign_ok, threshold=0.10) _cache['windows'] = windows _cache['r_sp'] = float(r_sp) _cache['p_sp'] = float(p_sp) _cache['nfci_vals'] = nfci_vals _cache['rec_counts'] = rec_counts results.append(log_result( 'crisis_count_nfci_correlation', float(r_sp), float(p_sp), verd_nfci, details={ 'windows': windows, 'n_windows': len(windows), 'spearman_r': round(float(r_sp), 3), }, description=( "Tests whether financial stress (NFCI) correlates with " "recession frequency in 5-year windows (1972-2024). " "NFCI > 0 means tighter financial conditions. Positive " "Spearman correlation (more stress = more recessions) " "validates NFCI as a crisis mechanism proxy. " "CAVEAT: tests NFCI as crisis correlate, not the deeper " "K/T ceiling prediction. N=10 windows." ) )) else: results.append(log_result( 'crisis_count_nfci_correlation', float('nan'), float('nan'), 'SKIPPED', details={'reason': f'Only {len(windows)} windows'}, description="Skipped: insufficient 5-year windows." )) else: results.append(log_result( 'crisis_count_nfci_correlation', float('nan'), float('nan'), 'SKIPPED', details={'reason': 'NFCI not available'}, description="Skipped: NFCI data not available." )) # ── Test 4: Recession spacing regularity ───────────────────────── # The "topological invariant" prediction implies approximately # regular recession spacing within structural regimes (deterministic # ceiling, not random arrival). Test: CV of inter-recession intervals # < 1.0 (more regular than Poisson). postwar_peaks = sorted([r[0] + r[1] / 12.0 for r in NBER_RECESSIONS if r[0] >= 1948]) if len(postwar_peaks) >= 4: intervals = np.diff(postwar_peaks) cv_intervals = float(intervals.std() / intervals.mean()) if intervals.mean() > 0 else 1.0 mean_interval = float(intervals.mean()) # Under Poisson (random timing), CV = 1.0 # Under regular spacing (topological invariant), CV < 1.0 # Under clustered timing, CV > 1.0 # Bootstrap CI for CV np.random.seed(42) n_boot = 5000 boot_cvs = np.zeros(n_boot) n_int = len(intervals) for b in range(n_boot): boot_sample = np.random.choice(intervals, size=n_int, replace=True) if boot_sample.mean() > 0: boot_cvs[b] = boot_sample.std() / boot_sample.mean() # p-value: fraction of bootstrap CVs >= 1.0 p_regular = float(np.mean(boot_cvs >= 1.0)) if cv_intervals < 0.8: verd_reg = 'CONSISTENT' elif cv_intervals < 1.0: verd_reg = 'AMBIGUOUS' else: verd_reg = 'INCONSISTENT' _cache['intervals'] = intervals _cache['cv_intervals'] = cv_intervals _cache['postwar_peaks'] = postwar_peaks _cache['mean_interval'] = mean_interval results.append(log_result( 'crisis_count_spacing_regularity', cv_intervals, p_regular, verd_reg, details={ 'mean_interval_years': round(mean_interval, 2), 'std_interval_years': round(float(intervals.std()), 2), 'cv_intervals': round(cv_intervals, 3), 'n_intervals': len(intervals), 'intervals_years': [round(float(x), 1) for x in intervals], 'poisson_cv_benchmark': 1.0, 'boot_cv_median': round(float(np.median(boot_cvs)), 3), }, description=( "Tests whether postwar recession spacing is more regular than " "a random Poisson process (CV < 1.0), consistent with the " "topological invariant prediction that crisis count is " "deterministic (floor(K/T)), not stochastic. CV < 0.8 is " "CONSISTENT (more regular than random), 0.8-1.0 AMBIGUOUS, " "> 1.0 INCONSISTENT (clustered). Uses inter-recession " "intervals from 1948-2024 NBER dates." ) )) _cache['results'] = results _cache['wave_data'] = wave_data _cache['freq_pre'] = freq_pre _cache['freq_post'] = freq_post _cache['recs_pre'] = len(recs_pre) _cache['recs_post'] = len(recs_post) _cache['span_pre'] = span_pre _cache['span_post'] = span_post _cache['p_poisson'] = p_poisson return results def figures(): """Generate figures for crisis count ceiling subtests.""" if not _cache: main() paths = [] from common.plotting import setup_figure, setup_subplots, save_figure import matplotlib.pyplot as plt # --- Figure 1: Wave frequency + Great Moderation (2-panel) --- wave_data = _cache.get('wave_data', []) if wave_data: fig, axes = setup_subplots(1, 2, width=14, height=5) # Panel A: Recession frequency per wave ax = axes[0] labels = [w['wave'].replace(' & ', '\n& ') for w in wave_data] freqs = [w['frequency_per_decade'] for w in wave_data] colors = ['#d94801', '#f16913', '#4292c6'] bars = ax.bar(labels, freqs, color=colors, edgecolor='k', linewidth=0.5) for bar, f, w in zip(bars, freqs, wave_data): ax.text(bar.get_x() + bar.get_width()/2, bar.get_height() + 0.05, f'{f:.2f}\n({w["n_recessions"]} in {w["span_years"]}yr)', ha='center', fontsize=8) ax.set_ylabel('Recessions per Decade') ax.set_title('(a) Recession Frequency by Kondratieff Wave') ax.grid(True, alpha=0.2, axis='y') # Panel B: Great Moderation pre/post ax = axes[1] fp = _cache.get('freq_pre', 0) fpo = _cache.get('freq_post', 0) bars = ax.bar(['Pre-1984\n(1948-1984)', 'Post-1984\n(1985-2024)'], [fp, fpo], color=['#d94801', '#4292c6'], edgecolor='k', linewidth=0.5) for bar, f in zip(bars, [fp, fpo]): ax.text(bar.get_x() + bar.get_width()/2, bar.get_height() + 0.03, f'{f:.2f}/decade', ha='center', fontsize=9) p_poi = _cache.get('p_poisson', 1) ax.set_ylabel('Recessions per Decade') ax.set_title(f'(b) Great Moderation Break (Poisson p={p_poi:.3f})') ax.grid(True, alpha=0.2, axis='y') fig.tight_layout() paths += save_figure(fig, 'crisis_count_waves', subfolder='dynamics') # --- Figure 2: NFCI scatter + spacing histogram (2-panel) --- nfci_vals = _cache.get('nfci_vals') rec_counts = _cache.get('rec_counts') intervals = _cache.get('intervals') if nfci_vals is not None or intervals is not None: n_panels = sum([nfci_vals is not None, intervals is not None]) fig, axes = setup_subplots(1, n_panels, width=7*n_panels, height=5) if n_panels == 1: axes = [axes] panel_idx = 0 # Panel: NFCI vs recession count if nfci_vals is not None: ax = axes[panel_idx] panel_idx += 1 ax.scatter(nfci_vals, rec_counts, s=60, c='steelblue', edgecolor='k', linewidth=0.5, zorder=5) # Fit line z = np.polyfit(nfci_vals, rec_counts, 1) x_fit = np.linspace(min(nfci_vals), max(nfci_vals), 50) ax.plot(x_fit, np.polyval(z, x_fit), 'r--', linewidth=1.5) r_sp = _cache.get('r_sp', 0) p_sp = _cache.get('p_sp', 1) ax.set_xlabel('Mean NFCI (5-year window)') ax.set_ylabel('Recession Count (5-year window)') label_chr = 'a' if n_panels == 2 else '' ax.set_title(f'({label_chr}) NFCI vs Recession Frequency\n' f'Spearman r={r_sp:.3f}, p={p_sp:.3f}') ax.grid(True, alpha=0.3) # Panel: Inter-recession intervals if intervals is not None: ax = axes[panel_idx] cv = _cache.get('cv_intervals', 0) mean_int = _cache.get('mean_interval', 0) label_chr = 'b' if n_panels == 2 else '' ax.bar(range(len(intervals)), intervals, color='#4292c6', edgecolor='k', linewidth=0.5) ax.axhline(y=mean_int, color='red', linestyle='--', linewidth=1.5, label=f'Mean = {mean_int:.1f} yr') ax.set_xlabel('Recession Interval Index') ax.set_ylabel('Years Between Recessions') ax.set_title(f'({label_chr}) Postwar Inter-Recession Intervals\n' f'CV = {cv:.3f} (< 1.0 = more regular than Poisson)') ax.legend(fontsize=8) ax.grid(True, alpha=0.2, axis='y') fig.tight_layout() paths += save_figure(fig, 'crisis_count_nfci_spacing', subfolder='dynamics') return paths if __name__ == '__main__': results = main() for r in results: print(f" {r['name']:45s} {r['verdict']:15s} " f"stat={r['statistic']:.4f}, p={r['p_value']:.4f}")

waves	[[object Object], [object Object], [object Object]]
p value	0.1667
statistic	1.3200
monotone decreasing	1

Crisis Count Wave Frequency

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