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lattice-analysis/results/phi_analysis.json
T
zeekayandHanzo Dev dbc56f1364 chore: initial commit — tree had no git at all 
Lattice analysis rig. No history, no remote, not on GitHub.

Excludes three compiled analysis binaries (lattice_test, round2,
kurtosis_sweep — 6.1 MB each) that are build output, not source; committing
them was what made the initial push fail.

Co-authored-by: Hanzo Dev <[email protected]>
2026-07-28 11:57:48 -07:00

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{
"analysis": "Phi-Geometric Analysis of RLWE Lattice Noise",
"methodology": "In2Infinity Brillouin Zone Theory applied to cryptographic lattice noise",
"key_constants": {
"phi": 1.618033988749895,
"sqrt_1.25": 1.118033988749895,
"sqrt_2": 1.4142135623730951,
"sqrt_5": 2.23606797749979,
"silver_ratio": 2.414213562373095
},
"results": [
{
"test": "phi_frequencies",
"domain": "NTT",
"mean_psd": 8.384719993440745e+29,
"anomalies": [
{
"label": "1/sqrt5",
"target_freq": 0.4472135954999579,
"actual_freq": 0.4453125,
"power": 7.5357975061989175e+28,
"ratio_to_mean": 0.08987536270852303,
"anomaly": "SUPPRESSED \u2014 0.09x mean power"
},
{
"label": "1/sqrt2",
"target_freq": 0.7071067811865475,
"actual_freq": 0.70703125,
"power": 3.2500438339332216e+29,
"ratio_to_mean": 0.3876150708044738,
"anomaly": "SUPPRESSED \u2014 0.39x mean power"
}
],
"frequencies": [
{
"label": "1/phi",
"target_freq": 0.6180339887498948,
"actual_freq": 0.6171875,
"power": 1.1732401068470693e+30,
"ratio_to_mean": 1.399259734093541,
"anomaly": null
},
{
"label": "1/sqrt5",
"target_freq": 0.4472135954999579,
"actual_freq": 0.4453125,
"power": 7.5357975061989175e+28,
"ratio_to_mean": 0.08987536270852303,
"anomaly": "SUPPRESSED \u2014 0.09x mean power"
},
{
"label": "1/sqrt2",
"target_freq": 0.7071067811865475,
"actual_freq": 0.70703125,
"power": 3.2500438339332216e+29,
"ratio_to_mean": 0.3876150708044738,
"anomaly": "SUPPRESSED \u2014 0.39x mean power"
},
{
"label": "1/sqrt1.25",
"target_freq": 0.8944271909999159,
"actual_freq": 0.89453125,
"power": 1.1520778336106792e+30,
"ratio_to_mean": 1.374020640536517,
"anomaly": null
},
{
"label": "phi/3",
"target_freq": 0.5393446629166316,
"actual_freq": 0.5390625,
"power": 1.2008732439157517e+30,
"ratio_to_mean": 1.4322162753856764,
"anomaly": null
},
{
"label": "2/sqrt5",
"target_freq": 0.8944271909999159,
"actual_freq": 0.89453125,
"power": 1.1520778336106792e+30,
"ratio_to_mean": 1.374020640536517,
"anomaly": null
},
{
"label": "silver/4",
"target_freq": 0.6035533905932737,
"actual_freq": 0.60546875,
"power": 1.0438437133317756e+30,
"ratio_to_mean": 1.2449356855665552,
"anomaly": null
}
],
"verdict": "FOUND 2 phi-related frequency anomalies"
},
{
"test": "phi_frequencies",
"domain": "Direct",
"mean_psd": 20.748513370029723,
"anomalies": [],
"frequencies": [
{
"label": "1/phi",
"target_freq": 0.6180339887498948,
"actual_freq": 0.6171875,
"power": 26.043810434485703,
"ratio_to_mean": 1.2552133239629975,
"anomaly": null
},
{
"label": "1/sqrt5",
"target_freq": 0.4472135954999579,
"actual_freq": 0.4453125,
"power": 19.78949545224035,
"ratio_to_mean": 0.9537789575240301,
"anomaly": null
},
{
"label": "1/sqrt2",
"target_freq": 0.7071067811865475,
"actual_freq": 0.70703125,
"power": 19.120636096065812,
"ratio_to_mean": 0.9215424621064512,
"anomaly": null
},
{
"label": "1/sqrt1.25",
"target_freq": 0.8944271909999159,
"actual_freq": 0.89453125,
"power": 17.56088385052746,
"ratio_to_mean": 0.8463682933493131,
"anomaly": null
},
{
"label": "phi/3",
"target_freq": 0.5393446629166316,
"actual_freq": 0.5390625,
"power": 25.814514234599876,
"ratio_to_mean": 1.2441621129293898,
"anomaly": null
},
{
"label": "2/sqrt5",
"target_freq": 0.8944271909999159,
"actual_freq": 0.89453125,
"power": 17.56088385052746,
"ratio_to_mean": 0.8463682933493131,
"anomaly": null
},
{
"label": "silver/4",
"target_freq": 0.6035533905932737,
"actual_freq": 0.60546875,
"power": 22.18683363710978,
"ratio_to_mean": 1.0693216059111803,
"anomaly": null
}
],
"verdict": "No significant phi-related frequency anomalies detected"
},
{
"test": "phi_autocorrelation",
"domain": "NTT",
"lag_results": [
{
"label": "sqrt_1.25 (lag=1)",
"phi_value": 1.118033988749895,
"lag": 1,
"autocorrelation": -0.012352674781169658,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "sqrt_1.25 (lag=2)",
"phi_value": 1.118033988749895,
"lag": 2,
"autocorrelation": -0.028011197734772283,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "sqrt_2 (lag=1)",
"phi_value": 1.4142135623730951,
"lag": 1,
"autocorrelation": -0.012352674781169658,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "sqrt_2 (lag=2)",
"phi_value": 1.4142135623730951,
"lag": 2,
"autocorrelation": -0.028011197734772283,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "phi (lag=1)",
"phi_value": 1.618033988749895,
"lag": 1,
"autocorrelation": -0.012352674781169658,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "phi (lag=2)",
"phi_value": 1.618033988749895,
"lag": 2,
"autocorrelation": -0.028011197734772283,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "sqrt_5 (lag=2)",
"phi_value": 2.23606797749979,
"lag": 2,
"autocorrelation": -0.028011197734772283,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "sqrt_5 (lag=3)",
"phi_value": 2.23606797749979,
"lag": 3,
"autocorrelation": -0.002777527591138098,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "phi_sq (lag=2)",
"phi_value": 2.618033988749895,
"lag": 2,
"autocorrelation": -0.028011197734772283,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "phi_sq (lag=3)",
"phi_value": 2.618033988749895,
"lag": 3,
"autocorrelation": -0.002777527591138098,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "zone_4 (lag=3)",
"phi_value": 3.0,
"lag": 3,
"autocorrelation": -0.002777527591138098,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "zone_4 (lag=3)",
"phi_value": 3.0,
"lag": 3,
"autocorrelation": -0.002777527591138098,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "phi_cubed (lag=4)",
"phi_value": 4.23606797749979,
"lag": 4,
"autocorrelation": -0.028732597395625465,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "phi_cubed (lag=5)",
"phi_value": 4.23606797749979,
"lag": 5,
"autocorrelation": -0.07065912131571873,
"threshold": 0.06125,
"significant": "True"
},
{
"label": "2*phi (lag=3)",
"phi_value": 3.23606797749979,
"lag": 3,
"autocorrelation": -0.002777527591138098,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "2*phi (lag=4)",
"phi_value": 3.23606797749979,
"lag": 4,
"autocorrelation": -0.028732597395625465,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "sqrt5*phi (lag=3)",
"phi_value": 3.6180339887498953,
"lag": 3,
"autocorrelation": -0.002777527591138098,
"threshold": 0.06125,
"significant": "False"
},
{
"label": "sqrt5*phi (lag=4)",
"phi_value": 3.6180339887498953,
"lag": 4,
"autocorrelation": -0.028732597395625465,
"threshold": 0.06125,
"significant": "False"
}
],
"anomalies": [
{
"label": "phi_cubed (lag=5)",
"phi_value": 4.23606797749979,
"lag": 5,
"autocorrelation": -0.07065912131571873,
"threshold": 0.06125,
"significant": "True"
}
],
"verdict": "FOUND 1 significant autocorrelation values at phi-related lags"
},
{
"test": "zone_kurtosis",
"domain": "NTT",
"measured_kurtosis": -1.1925365596921327,
"abs_kurtosis": 1.1925365596921327,
"matches": [],
"sqrt_1.25_proximity": {
"sqrt_1.25": 1.118033988749895,
"difference": 0.07450257094223778,
"note": "|kurtosis| - \u221a1.25 = 0.0745 \u2014 VERY CLOSE to \u221a1.25!"
},
"verdict": "SIGNIFICANT: |kurtosis| = 1.1925 \u2248 \u221a1.25 = 1.1180 (diff=0.0745). The Sandreckoner vector length appears in the noise distribution."
},
{
"test": "zone_progression",
"domain": "NTT",
"zones": [
{
"zone": 1,
"freq_range": "0.000 \u2014 0.333",
"mean_power": 7.898543293186512e+29,
"total_power": 6.7927472321404e+31,
"variance": 1.94245809693927e+59
},
{
"zone": 2,
"freq_range": "0.333 \u2014 0.471",
"mean_power": 8.540579304190821e+29,
"total_power": 2.9892027564667875e+31,
"variance": 2.4334752355401413e+59
},
{
"zone": 3,
"freq_range": "0.471 \u2014 0.745",
"mean_power": 8.811994007812861e+29,
"total_power": 6.168395805469003e+31,
"variance": 1.80156297958962e+59
},
{
"zone": 4,
"freq_range": "0.745 \u2014 1.000",
"mean_power": 8.610401761510719e+29,
"total_power": 5.596761144981967e+31,
"variance": 2.9813902903488364e+59
}
],
"max_power_ratio": 1.1156479974496456,
"verdict": "OK: Energy roughly uniform across zones"
}
],
"charts": {
"phi_psd": "results/charts/phi_psd_markers.png",
"phi_kurtosis": "results/charts/phi_kurtosis_comparison.png",
"phi_zones": "results/charts/phi_zone_energy.png"
}
}
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