{ "$schema": "spectral-verdict/1", "generated": "2026-08-19", "manifest": "scripts/spectral/analysis-manifest.yaml", "manifest_sha256": "1765eca3cacd12fbf44d8645a24bb9e57970aa70fb3a8dc33a477898e9df4572", "seed": 20260819, "draws": 99999, "alpha": 0.05, "gate_min_periods": 3.0, "versions": { "python": "3.14.6", "numpy": "2.5.2", "scipy": "1.18.0" }, "headline": { "eligible_primary": 0, "total_primary": 9, "text": "0 of the 9 paired constructions reach the 3.0-period eligibility gate for a spectral test." }, "primary": [ { "cycle_id": "schlesinger_jr", "period_years": 30, "series_id": "stimson_policy_mood", "span_years": 72, "cycles_covered": 2.4, "eligible": false, "state": "INSUFFICIENT_DATA", "p": null, "p_ar2": null, "lrt": null, "lrt_ar2": null, "phi": null, "phi_ar2": null, "holm_family": "primary", "holm_significant": null, "holm_significant_ar2": null, "lay_text": "The US Policy Mood (Stimson) record spans 72 years — 2.4 of the 3.0 full periods this site requires before testing a 30-year claim. No test was run and no p-value exists: the honest verdict is that the record is too short to test the claim at all." }, { "cycle_id": "kondratiev", "period_years": 54, "series_id": "us_tfp_growth_annual", "span_years": 77, "cycles_covered": 1.43, "eligible": false, "state": "INSUFFICIENT_DATA", "p": null, "p_ar2": null, "lrt": null, "lrt_ar2": null, "phi": null, "phi_ar2": null, "holm_family": "primary", "holm_significant": null, "holm_significant_ar2": null, "lay_text": "The US TFP growth (annual, unsmoothed) record spans 77 years — 1.4 of the 3.0 full periods this site requires before testing a 54-year claim. No test was run and no p-value exists: the honest verdict is that the record is too short to test the claim at all." }, { "cycle_id": "perez", "period_years": 55, "series_id": "perez_tech_diffusion", "span_years": 158, "cycles_covered": 2.87, "eligible": false, "state": "INSUFFICIENT_DATA", "p": null, "p_ar2": null, "lrt": null, "lrt_ar2": null, "phi": null, "phi_ar2": null, "holm_family": "primary", "holm_significant": null, "holm_significant_ar2": null, "lay_text": "The US Technology-Diffusion Intensity (HATCH) record spans 158 years — 2.9 of the 3.0 full periods this site requires before testing a 55-year claim. No test was run and no p-value exists: the honest verdict is that the record is too short to test the claim at all." }, { "cycle_id": "huntington", "period_years": 60, "series_id": "dw_nominate_polarization", "span_years": 144, "cycles_covered": 2.4, "eligible": false, "state": "INSUFFICIENT_DATA", "p": null, "p_ar2": null, "lrt": null, "lrt_ar2": null, "phi": null, "phi_ar2": null, "holm_family": "primary", "holm_significant": null, "holm_significant_ar2": null, "lay_text": "The US House Polarization (DW-NOMINATE) record spans 144 years — 2.4 of the 3.0 full periods this site requires before testing a 60-year claim. No test was run and no p-value exists: the honest verdict is that the record is too short to test the claim at all." }, { "cycle_id": "dalio", "period_years": 75, "series_id": "us_world_gdp_share", "span_years": 152, "cycles_covered": 2.03, "eligible": false, "state": "INSUFFICIENT_DATA", "p": null, "p_ar2": null, "lrt": null, "lrt_ar2": null, "phi": null, "phi_ar2": null, "holm_family": "primary", "holm_significant": null, "holm_significant_ar2": null, "lay_text": "The US Share of World GDP record spans 152 years — 2.0 of the 3.0 full periods this site requires before testing a 75-year claim. No test was run and no p-value exists: the honest verdict is that the record is too short to test the claim at all." }, { "cycle_id": "strauss_howe", "period_years": 84, "series_id": "vdem_libdem", "span_years": 236, "cycles_covered": 2.81, "eligible": false, "state": "INSUFFICIENT_DATA", "p": null, "p_ar2": null, "lrt": null, "lrt_ar2": null, "phi": null, "phi_ar2": null, "holm_family": "primary", "holm_significant": null, "holm_significant_ar2": null, "lay_text": "The US Liberal Democracy Index (V-Dem) record spans 236 years — 2.8 of the 3.0 full periods this site requires before testing a 84-year claim. No test was run and no p-value exists: the honest verdict is that the record is too short to test the claim at all." }, { "cycle_id": "modelski", "period_years": 110, "series_id": "leading_power_gdp_share", "span_years": 152, "cycles_covered": 1.38, "eligible": false, "state": "INSUFFICIENT_DATA", "p": null, "p_ar2": null, "lrt": null, "lrt_ar2": null, "phi": null, "phi_ar2": null, "holm_family": "primary", "holm_significant": null, "holm_significant_ar2": null, "lay_text": "The Leading Economy's Share of World GDP record spans 152 years — 1.4 of the 3.0 full periods this site requires before testing a 110-year claim. No test was run and no p-value exists: the honest verdict is that the record is too short to test the claim at all." }, { "cycle_id": "khaldun", "period_years": 120, "series_id": "conflict_deaths", "span_years": 211, "cycles_covered": 1.76, "eligible": false, "state": "INSUFFICIENT_DATA", "p": null, "p_ar2": null, "lrt": null, "lrt_ar2": null, "phi": null, "phi_ar2": null, "holm_family": "primary", "holm_significant": null, "holm_significant_ar2": null, "lay_text": "The Deaths in conventional wars (Project Mars, log) record spans 211 years — 1.8 of the 3.0 full periods this site requires before testing a 120-year claim. No test was run and no p-value exists: the honest verdict is that the record is too short to test the claim at all." }, { "cycle_id": "turchin", "period_years": 150, "series_id": "wid_top1_wealth_1913", "span_years": 111, "cycles_covered": 0.74, "eligible": false, "state": "INSUFFICIENT_DATA", "p": null, "p_ar2": null, "lrt": null, "lrt_ar2": null, "phi": null, "phi_ar2": null, "holm_family": "primary", "holm_significant": null, "holm_significant_ar2": null, "lay_text": "The US top 1% wealth share (1913 onward) record spans 111 years — 0.7 of the 3.0 full periods this site requires before testing a 150-year claim. No test was run and no p-value exists: the honest verdict is that the record is too short to test the claim at all." } ], "cross_grid": [ { "period_source_cycle_id": "schlesinger_jr", "period_years": 30, "series_id": "dw_nominate_polarization", "span_years": 144, "cycles_covered": 4.8, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.58515, "p_ar2": 0.502, "lrt": 1.2266, "lrt_ar2": 1.5681, "phi": [ 0.98 ], "phi_ar2": [ 1.0, -0.05 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 30-year period against US House Polarization (DW-NOMINATE). Harmonic regression at the exact 30-year period finds no significant power above an AR(1) red-noise null (p = 0.5851, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.5020)." }, { "period_source_cycle_id": "schlesinger_jr", "period_years": 30, "series_id": "vdem_libdem", "span_years": 236, "cycles_covered": 7.87, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.09377, "p_ar2": 0.18473, "lrt": 5.0822, "lrt_ar2": 3.8277, "phi": [ 0.98 ], "phi_ar2": [ 1.45, -0.5 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 30-year period against US Liberal Democracy Index (V-Dem). Harmonic regression at the exact 30-year period finds no significant power above an AR(1) red-noise null (p = 0.0938, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.1847)." }, { "period_source_cycle_id": "schlesinger_jr", "period_years": 30, "series_id": "conflict_deaths", "span_years": 211, "cycles_covered": 7.03, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.23921, "p_ar2": 0.19252, "lrt": 3.3805, "lrt_ar2": 3.9496, "phi": [ 0.87 ], "phi_ar2": [ 0.9, -0.05 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 30-year period against Deaths in conventional wars (Project Mars, log). Harmonic regression at the exact 30-year period finds no significant power above an AR(1) red-noise null (p = 0.2392, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.1925)." }, { "period_source_cycle_id": "schlesinger_jr", "period_years": 30, "series_id": "us_world_gdp_share", "span_years": 152, "cycles_covered": 5.07, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.1828, "p_ar2": 0.49806, "lrt": 3.9181, "lrt_ar2": 1.6786, "phi": [ 0.98 ], "phi_ar2": [ 1.1, -0.15 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 30-year period against US Share of World GDP. Harmonic regression at the exact 30-year period finds no significant power above an AR(1) red-noise null (p = 0.1828, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.4981)." }, { "period_source_cycle_id": "schlesinger_jr", "period_years": 30, "series_id": "leading_power_gdp_share", "span_years": 152, "cycles_covered": 5.07, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.9169, "p_ar2": 0.97683, "lrt": 0.2009, "lrt_ar2": 0.0573, "phi": [ 0.975 ], "phi_ar2": [ 1.15, -0.2 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 30-year period against Leading Economy's Share of World GDP. Harmonic regression at the exact 30-year period finds no significant power above an AR(1) red-noise null (p = 0.9169, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.9768)." }, { "period_source_cycle_id": "schlesinger_jr", "period_years": 30, "series_id": "wid_top1_wealth_1913", "span_years": 111, "cycles_covered": 3.7, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.10329, "p_ar2": 0.11949, "lrt": 5.882, "lrt_ar2": 5.7788, "phi": [ 0.97 ], "phi_ar2": [ 1.0, -0.05 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 30-year period against US top 1% wealth share (1913 onward). Harmonic regression at the exact 30-year period finds no significant power above an AR(1) red-noise null (p = 0.1033, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.1195)." }, { "period_source_cycle_id": "schlesinger_jr", "period_years": 30, "series_id": "perez_tech_diffusion", "span_years": 158, "cycles_covered": 5.27, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.45268, "p_ar2": 0.29145, "lrt": 1.8953, "lrt_ar2": 2.9967, "phi": [ 0.615 ], "phi_ar2": [ 0.7, -0.1 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 30-year period against US Technology-Diffusion Intensity (HATCH). Harmonic regression at the exact 30-year period finds no significant power above an AR(1) red-noise null (p = 0.4527, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.2914)." }, { "period_source_cycle_id": "turchin_fathers_sons", "period_years": 50, "series_id": "vdem_libdem", "span_years": 236, "cycles_covered": 4.72, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.97408, "p_ar2": 0.72739, "lrt": 0.0626, "lrt_ar2": 0.8297, "phi": [ 0.98 ], "phi_ar2": [ 1.45, -0.5 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 50-year period against US Liberal Democracy Index (V-Dem). Harmonic regression at the exact 50-year period finds no significant power above an AR(1) red-noise null (p = 0.9741, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.7274)." }, { "period_source_cycle_id": "turchin_fathers_sons", "period_years": 50, "series_id": "conflict_deaths", "span_years": 211, "cycles_covered": 4.22, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.95785, "p_ar2": 0.9405, "lrt": 0.1135, "lrt_ar2": 0.1619, "phi": [ 0.87 ], "phi_ar2": [ 0.9, -0.05 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 50-year period against Deaths in conventional wars (Project Mars, log). Harmonic regression at the exact 50-year period finds no significant power above an AR(1) red-noise null (p = 0.9578, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.9405)." }, { "period_source_cycle_id": "turchin_fathers_sons", "period_years": 50, "series_id": "perez_tech_diffusion", "span_years": 158, "cycles_covered": 3.16, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.34084, "p_ar2": 0.31835, "lrt": 2.6011, "lrt_ar2": 2.8437, "phi": [ 0.615 ], "phi_ar2": [ 0.7, -0.1 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 50-year period against US Technology-Diffusion Intensity (HATCH). Harmonic regression at the exact 50-year period finds no significant power above an AR(1) red-noise null (p = 0.3408, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.3184)." }, { "period_source_cycle_id": "turchin_fathers_sons", "period_years": 50, "series_id": "us_world_gdp_share", "span_years": 152, "cycles_covered": 3.04, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.13662, "p_ar2": 0.3038, "lrt": 5.6595, "lrt_ar2": 3.7726, "phi": [ 0.98 ], "phi_ar2": [ 1.1, -0.15 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 50-year period against US Share of World GDP. Harmonic regression at the exact 50-year period finds no significant power above an AR(1) red-noise null (p = 0.1366, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.3038)." }, { "period_source_cycle_id": "turchin_fathers_sons", "period_years": 50, "series_id": "leading_power_gdp_share", "span_years": 152, "cycles_covered": 3.04, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.39828, "p_ar2": 0.53287, "lrt": 2.6222, "lrt_ar2": 1.9795, "phi": [ 0.975 ], "phi_ar2": [ 1.15, -0.2 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 50-year period against Leading Economy's Share of World GDP. Harmonic regression at the exact 50-year period finds no significant power above an AR(1) red-noise null (p = 0.3983, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.5329)." }, { "period_source_cycle_id": "kondratiev", "period_years": 54, "series_id": "vdem_libdem", "span_years": 236, "cycles_covered": 4.37, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.79618, "p_ar2": 0.78614, "lrt": 0.5637, "lrt_ar2": 0.6366, "phi": [ 0.98 ], "phi_ar2": [ 1.45, -0.5 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 54-year period against US Liberal Democracy Index (V-Dem). Harmonic regression at the exact 54-year period finds no significant power above an AR(1) red-noise null (p = 0.7962, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.7861). At this record length a 54-year and a 55-year period are indistinguishable (they differ by 0.000337 cycles per year), so read this as one result for the ~54–55-year band, not as separating Kondratiev from Perez." }, { "period_source_cycle_id": "kondratiev", "period_years": 54, "series_id": "conflict_deaths", "span_years": 211, "cycles_covered": 3.91, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.81398, "p_ar2": 0.83313, "lrt": 0.5559, "lrt_ar2": 0.496, "phi": [ 0.87 ], "phi_ar2": [ 0.9, -0.05 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 54-year period against Deaths in conventional wars (Project Mars, log). Harmonic regression at the exact 54-year period finds no significant power above an AR(1) red-noise null (p = 0.8140, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.8331). At this record length a 54-year and a 55-year period are indistinguishable (they differ by 0.000337 cycles per year), so read this as one result for the ~54–55-year band, not as separating Kondratiev from Perez." }, { "period_source_cycle_id": "perez", "period_years": 55, "series_id": "vdem_libdem", "span_years": 236, "cycles_covered": 4.29, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.7431, "p_ar2": 0.75473, "lrt": 0.7251, "lrt_ar2": 0.7439, "phi": [ 0.98 ], "phi_ar2": [ 1.45, -0.5 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 55-year period against US Liberal Democracy Index (V-Dem). Harmonic regression at the exact 55-year period finds no significant power above an AR(1) red-noise null (p = 0.7431, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.7547). At this record length a 54-year and a 55-year period are indistinguishable (they differ by 0.000337 cycles per year), so read this as one result for the ~54–55-year band, not as separating Kondratiev from Perez." }, { "period_source_cycle_id": "perez", "period_years": 55, "series_id": "conflict_deaths", "span_years": 211, "cycles_covered": 3.84, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.7798, "p_ar2": 0.78867, "lrt": 0.6726, "lrt_ar2": 0.6559, "phi": [ 0.87 ], "phi_ar2": [ 0.9, -0.05 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 55-year period against Deaths in conventional wars (Project Mars, log). Harmonic regression at the exact 55-year period finds no significant power above an AR(1) red-noise null (p = 0.7798, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.7887). At this record length a 54-year and a 55-year period are indistinguishable (they differ by 0.000337 cycles per year), so read this as one result for the ~54–55-year band, not as separating Kondratiev from Perez." }, { "period_source_cycle_id": "huntington", "period_years": 60, "series_id": "vdem_libdem", "span_years": 236, "cycles_covered": 3.93, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.60032, "p_ar2": 0.35467, "lrt": 1.2973, "lrt_ar2": 2.8976, "phi": [ 0.98 ], "phi_ar2": [ 1.45, -0.5 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 60-year period against US Liberal Democracy Index (V-Dem). Harmonic regression at the exact 60-year period finds no significant power above an AR(1) red-noise null (p = 0.6003, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.3547)." }, { "period_source_cycle_id": "huntington", "period_years": 60, "series_id": "conflict_deaths", "span_years": 211, "cycles_covered": 3.52, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.74994, "p_ar2": 0.65525, "lrt": 0.8097, "lrt_ar2": 1.1648, "phi": [ 0.87 ], "phi_ar2": [ 0.9, -0.05 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 60-year period against Deaths in conventional wars (Project Mars, log). Harmonic regression at the exact 60-year period finds no significant power above an AR(1) red-noise null (p = 0.7499, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.6552)." }, { "period_source_cycle_id": "dalio", "period_years": 75, "series_id": "vdem_libdem", "span_years": 236, "cycles_covered": 3.15, "eligible": true, "state": "NO_SIGNIFICANT_TARGET_POWER", "p": 0.14929, "p_ar2": 0.2659, "lrt": 5.4814, "lrt_ar2": 3.9642, "phi": [ 0.98 ], "phi_ar2": [ 1.45, -0.5 ], "holm_family": "cross_grid", "holm_significant": false, "holm_significant_ar2": false, "lay_text": "Re-pairing, not the site's claim: this cell tests the 75-year period against US Liberal Democracy Index (V-Dem). Harmonic regression at the exact 75-year period finds no significant power above an AR(1) red-noise null (p = 0.1493, 99,999 bootstrap draws, Holm-corrected within a family of 19 tests); an AR(2) null agrees (p = 0.2659)." } ] }