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    "The worked comparison is infinite-temperature and central-window; it is not a low-temperature Schwarzian calculation.",
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    "Delete-one-realization intervals quantify evaluation-ensemble Monte Carlo scatter while conditioning on a frozen training map.",
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              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.3725,
              "matched_gue": {
                "jackknife_standard_error": 0.011573512960273244,
                "mean": 0.3982055175608143,
                "normal_approximation_95_high": 0.4208891861375574,
                "normal_approximation_95_low": 0.3755218489840712
              },
              "syk": {
                "jackknife_standard_error": 0.012299732061752198,
                "mean": 0.40560644861305567,
                "normal_approximation_95_high": 0.42971348047358254,
                "normal_approximation_95_low": 0.3814994167525288
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.016888742138848226,
                "mean_difference": 0.007400931052241377,
                "normal_approximation_95_high": 0.04050225738856785,
                "normal_approximation_95_low": -0.025700395284085097
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              "tau_interval": [
                0.25,
                0.5
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "plateau": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 1.0,
              "matched_gue": {
                "jackknife_standard_error": 0.005969222713475165,
                "mean": 1.0026301267946929,
                "normal_approximation_95_high": 1.0143295883288026,
                "normal_approximation_95_low": 0.9909306652605832
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              "syk": {
                "jackknife_standard_error": 0.005702887064270037,
                "mean": 1.0007082369937135,
                "normal_approximation_95_high": 1.0118856902475821,
                "normal_approximation_95_low": 0.9895307837398448
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.008255576337899513,
                "mean_difference": -0.0019218898009794039,
                "normal_approximation_95_high": 0.01425874249292471,
                "normal_approximation_95_low": -0.018102522094883517
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              "tau_interval": [
                1.5,
                3.0
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              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "ramp_plateau_corner": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.9487500000000001,
              "matched_gue": {
                "jackknife_standard_error": 0.018041498416669816,
                "mean": 0.9310576605414387,
                "normal_approximation_95_high": 0.9664183476652479,
                "normal_approximation_95_low": 0.8956969734176294
              },
              "syk": {
                "jackknife_standard_error": 0.016690625269625396,
                "mean": 0.9320574404285097,
                "normal_approximation_95_high": 0.9647704648364296,
                "normal_approximation_95_low": 0.8993444160205898
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.024577889189467784,
                "mean_difference": 0.0009997798870710062,
                "normal_approximation_95_high": 0.04917155751444419,
                "normal_approximation_95_low": -0.04717199774030218
              },
              "tau_interval": [
                0.8,
                1.2
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            }
          }
        },
        "central_24_of_64": {
          "curve_rms_syk_minus_matched_gue_tau_0p1_3": 0.07349292230585211,
          "retained_level_count": 24,
          "source_window": "nested central slice of the primary independently trained 32-level unfolded window",
          "window_summaries": {
            "early_connected": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.0725,
              "matched_gue": {
                "jackknife_standard_error": 0.0037126424081612352,
                "mean": 0.08231578915246239,
                "normal_approximation_95_high": 0.08959243455993446,
                "normal_approximation_95_low": 0.07503914374499032
              },
              "syk": {
                "jackknife_standard_error": 0.004244099503910894,
                "mean": 0.08730132912657634,
                "normal_approximation_95_high": 0.095619611301046,
                "normal_approximation_95_low": 0.07898304695210669
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.005638802554618663,
                "mean_difference": 0.004985539974113953,
                "normal_approximation_95_high": 0.01603738989709898,
                "normal_approximation_95_low": -0.006066309948871074
              },
              "tau_interval": [
                0.05,
                0.1
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "early_ramp": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.17250000000000001,
              "matched_gue": {
                "jackknife_standard_error": 0.005476792485070491,
                "mean": 0.18198918395074815,
                "normal_approximation_95_high": 0.19272349997228594,
                "normal_approximation_95_low": 0.17125486792921035
              },
              "syk": {
                "jackknife_standard_error": 0.005810920302716107,
                "mean": 0.18951656549282,
                "normal_approximation_95_high": 0.20090576000317617,
                "normal_approximation_95_low": 0.17812737098246384
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.007985114319096681,
                "mean_difference": 0.007527381542071859,
                "normal_approximation_95_high": 0.023177918019936426,
                "normal_approximation_95_low": -0.008123154935792708
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              "tau_interval": [
                0.1,
                0.25
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "late_ramp": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.6475000000000001,
              "matched_gue": {
                "jackknife_standard_error": 0.014442488303581478,
                "mean": 0.6815027638528176,
                "normal_approximation_95_high": 0.7098095207749783,
                "normal_approximation_95_low": 0.6531960069306569
              },
              "syk": {
                "jackknife_standard_error": 0.012926562675725155,
                "mean": 0.6695837282058644,
                "normal_approximation_95_high": 0.6949193254941854,
                "normal_approximation_95_low": 0.6442481309175434
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.019382504766116748,
                "mean_difference": -0.01191903564695318,
                "normal_approximation_95_high": 0.02606997562481158,
                "normal_approximation_95_low": -0.04990804691871794
              },
              "tau_interval": [
                0.5,
                0.8
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "middle_ramp": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.3725,
              "matched_gue": {
                "jackknife_standard_error": 0.009906853796004618,
                "mean": 0.39103444405633125,
                "normal_approximation_95_high": 0.41045152069660423,
                "normal_approximation_95_low": 0.3716173674160583
              },
              "syk": {
                "jackknife_standard_error": 0.009564866237345525,
                "mean": 0.3835222868792041,
                "normal_approximation_95_high": 0.40226908022134444,
                "normal_approximation_95_low": 0.36477549353706373
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.013770708706298432,
                "mean_difference": -0.007512157177127166,
                "normal_approximation_95_high": 0.019477935928809916,
                "normal_approximation_95_low": -0.03450225028306425
              },
              "tau_interval": [
                0.25,
                0.5
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "plateau": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 1.0,
              "matched_gue": {
                "jackknife_standard_error": 0.004631524559532496,
                "mean": 1.0012675922990846,
                "normal_approximation_95_high": 1.010345213629281,
                "normal_approximation_95_low": 0.9921899709688882
              },
              "syk": {
                "jackknife_standard_error": 0.004722874773172683,
                "mean": 1.0043860565530471,
                "normal_approximation_95_high": 1.0136427210119583,
                "normal_approximation_95_low": 0.9951293920941359
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.006614874592055665,
                "mean_difference": 0.0031184642539625607,
                "normal_approximation_95_high": 0.01608338021664074,
                "normal_approximation_95_low": -0.009846451708715622
              },
              "tau_interval": [
                1.5,
                3.0
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "ramp_plateau_corner": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.9487500000000001,
              "matched_gue": {
                "jackknife_standard_error": 0.015857518907766745,
                "mean": 0.9476076079408354,
                "normal_approximation_95_high": 0.9786877738842211,
                "normal_approximation_95_low": 0.9165274419974497
              },
              "syk": {
                "jackknife_standard_error": 0.013859684806772432,
                "mean": 0.9320935285493658,
                "normal_approximation_95_high": 0.9592580116077167,
                "normal_approximation_95_low": 0.9049290454910148
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.02106066876557481,
                "mean_difference": -0.015514079391469648,
                "normal_approximation_95_high": 0.025764072879384606,
                "normal_approximation_95_low": -0.0567922316623239
              },
              "tau_interval": [
                0.8,
                1.2
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            }
          }
        },
        "central_32_of_64": {
          "curve_rms_syk_minus_matched_gue_tau_0p1_3": 0.07633229942206268,
          "retained_level_count": 32,
          "source_window": "nested central slice of the primary independently trained 32-level unfolded window",
          "window_summaries": {
            "early_connected": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.0725,
              "matched_gue": {
                "jackknife_standard_error": 0.0033115068429126083,
                "mean": 0.07754145288852053,
                "normal_approximation_95_high": 0.08403188703518719,
                "normal_approximation_95_low": 0.07105101874185388
              },
              "syk": {
                "jackknife_standard_error": 0.0037532415673091997,
                "mean": 0.08815485053177699,
                "normal_approximation_95_high": 0.09551106882898168,
                "normal_approximation_95_low": 0.0807986322345723
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.005005287187887888,
                "mean_difference": 0.010613397643256459,
                "normal_approximation_95_high": 0.02042358026379648,
                "normal_approximation_95_low": 0.0008032150227164341
              },
              "tau_interval": [
                0.05,
                0.1
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "early_ramp": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.17250000000000001,
              "matched_gue": {
                "jackknife_standard_error": 0.004933873415968082,
                "mean": 0.17441377657276066,
                "normal_approximation_95_high": 0.18408399077233772,
                "normal_approximation_95_low": 0.1647435623731836
              },
              "syk": {
                "jackknife_standard_error": 0.004874080679344266,
                "mean": 0.18564202081506354,
                "normal_approximation_95_high": 0.1951950434043208,
                "normal_approximation_95_low": 0.17608899822580626
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.006935399725578448,
                "mean_difference": 0.01122824424230287,
                "normal_approximation_95_high": 0.0248213779228256,
                "normal_approximation_95_low": -0.002364889438219858
              },
              "tau_interval": [
                0.1,
                0.25
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "late_ramp": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.6475000000000001,
              "matched_gue": {
                "jackknife_standard_error": 0.01188228331965754,
                "mean": 0.665909660215572,
                "normal_approximation_95_high": 0.6891985075762018,
                "normal_approximation_95_low": 0.6426208128549421
              },
              "syk": {
                "jackknife_standard_error": 0.011659705758388083,
                "mean": 0.6575262375173689,
                "normal_approximation_95_high": 0.6803788408741438,
                "normal_approximation_95_low": 0.6346736341605941
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.016647444105952123,
                "mean_difference": -0.008383422698203025,
                "normal_approximation_95_high": 0.02424496818410673,
                "normal_approximation_95_low": -0.04101181358051278
              },
              "tau_interval": [
                0.5,
                0.8
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "middle_ramp": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.3725,
              "matched_gue": {
                "jackknife_standard_error": 0.008347530570882741,
                "mean": 0.37849861499001314,
                "normal_approximation_95_high": 0.39485947426879037,
                "normal_approximation_95_low": 0.3621377557112359
              },
              "syk": {
                "jackknife_standard_error": 0.008939294233932743,
                "mean": 0.3840906628902821,
                "normal_approximation_95_high": 0.40161135763599687,
                "normal_approximation_95_low": 0.3665699681445673
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.012230790981479698,
                "mean_difference": 0.005592047900268959,
                "normal_approximation_95_high": 0.02956395772640646,
                "normal_approximation_95_low": -0.018379861925868542
              },
              "tau_interval": [
                0.25,
                0.5
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "plateau": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 1.0,
              "matched_gue": {
                "jackknife_standard_error": 0.004171228468758922,
                "mean": 1.0001670391236366,
                "normal_approximation_95_high": 1.0083424966936922,
                "normal_approximation_95_low": 0.9919915815535809
              },
              "syk": {
                "jackknife_standard_error": 0.004153973667740798,
                "mean": 1.0018755712623892,
                "normal_approximation_95_high": 1.010017210043889,
                "normal_approximation_95_low": 0.9937339324808895
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.0058868195293272614,
                "mean_difference": 0.0017085321387526609,
                "normal_approximation_95_high": 0.013246486399721123,
                "normal_approximation_95_low": -0.0098294221222158
              },
              "tau_interval": [
                1.5,
                3.0
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            },
            "ramp_plateau_corner": {
              "interval_scope": "marginal normal approximation from independent delete-one-realization jackknife standard errors; no simultaneous or multiplicity control across windows, preprocessing choices, or retained-level counts",
              "large_matrix_gue_mean": 0.9487500000000001,
              "matched_gue": {
                "jackknife_standard_error": 0.013566066396127787,
                "mean": 0.9607803651434714,
                "normal_approximation_95_high": 0.987369366691761,
                "normal_approximation_95_low": 0.9341913635951818
              },
              "syk": {
                "jackknife_standard_error": 0.011947481481313863,
                "mean": 0.9391654344926085,
                "normal_approximation_95_high": 0.9625820679019429,
                "normal_approximation_95_low": 0.915748801083274
              },
              "syk_minus_matched_gue": {
                "contrast": "SYK minus independently generated GUE",
                "jackknife_standard_error": 0.018077070316024256,
                "mean_difference": -0.02161493065086295,
                "normal_approximation_95_high": 0.013815476114542674,
                "normal_approximation_95_low": -0.05704533741626858
              },
              "tau_interval": [
                0.8,
                1.2
              ],
              "tau_interval_convention": "lower inclusive, upper exclusive"
            }
          }
        }
      },
      "retained_level_counts": [
        16,
        24,
        32
      ],
      "scope": "nested central windows vary the energy-window width; they do not test sparse-edge scaling"
    },
    "safe_claim": "finite q=4, N_chi=14 even-parity SYK has a positive connected ramp and a unit-scale plateau that can be compared descriptively with identically processed dimension-64 GUE spectra; the calculation does not identify a large-N_chi limit or a Thouless time"
  }
}