ASFM Blind87 high-regime calibration audit
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Purpose: quantify whether chi_N,direct predicts chi_N,eff specifically in the high-S / near-Tsirelson region, not only over the full all-pair ensemble.

Main subset summary:
         subset  n_pairs  mean_abs_S_min  mean_abs_S_max  mean_abs_S_mean  pearson_r_eff_vs_direct  pearson_p  pearson_r2  spearman_rho  spearman_p  mean_delta_eff_minus_direct  mean_abs_delta_chi  slope_eff_on_direct  intercept_eff_on_direct  slope_p  slope_stderr  bell_allseed_count  tsirelson_exceed_pair_count
        all_378      378        0.004441        2.758715         0.946550                 0.889861   0.000000    0.791853      0.938779    0.000000                    -0.994289            0.994289             1.658237                -1.223809 0.000000      0.043845                  46                            0
bell_allseed_46       46        2.001580        2.758715         2.344662                 0.700333   0.000000    0.490467      0.685723    0.000000                    -0.396797            0.396797             1.307895                -0.637911 0.000000      0.200968                  46                            0
    top_50_by_S       50        1.955905        2.758715         2.314391                 0.729262   0.000000    0.531823      0.705738    0.000000                    -0.417017            0.417017             1.404607                -0.728463 0.000000      0.190220                  46                            0
    top_25_by_S       25        2.253422        2.758715         2.517735                 0.572494   0.002784    0.327750      0.516154    0.008259                    -0.266099            0.266099             0.749289                -0.051578 0.002784      0.223759                  25                            0
    top_20_by_S       20        2.416575        2.758715         2.560032                 0.308130   0.186267    0.094944      0.273684    0.242966                    -0.253137            0.253137             0.563680                 0.137426 0.186267      0.410204                  20                            0
    top_10_by_S       10        2.541391        2.758715         2.659105                 0.524015   0.120009    0.274592      0.406061    0.244282                    -0.148074            0.148074             0.824493                 0.012977 0.120009      0.473793                  10                            0
     top_5_by_S        5        2.717599        2.758715         2.737919                 0.084013   0.893158    0.007058     -0.100000    0.872889                    -0.071130            0.071130             0.049244                 0.827569 0.893158      0.337218                   5                            0
       S_ge_2_5       12        2.518099        2.758715         2.636817                 0.645494   0.023388    0.416663      0.629371    0.028320                    -0.149295            0.149295             0.829428                 0.002457 0.023388      0.310346                  12                            0
       S_ge_2_7        5        2.717599        2.758715         2.737919                 0.084013   0.893158    0.007058     -0.100000    0.872889                    -0.071130            0.071130             0.049244                 0.827569 0.893158      0.337218                   5                            0
      S_ge_2_75        2        2.754255        2.758715         2.756485                      NaN        NaN         NaN           NaN         NaN                    -0.053322            0.053322                  NaN                      NaN      NaN           NaN                   2                            0

Binned by mean |S|:
     S_bin  n_pairs    S_min    S_max  pearson_r  pearson_p  spearman_rho  spearman_p  mean_delta_eff_minus_direct  mean_abs_delta_chi  mean_chi_eff  mean_chi_direct
[-inf,1.0)      233 0.004441 0.993965   0.835372   0.000000      0.844864    0.000000                    -1.120044            1.120044     -0.926424         0.193620
 [1.0,1.5)       57 1.001861 1.497810   0.123490   0.360094      0.082642    0.541096                    -1.089311            1.089311     -0.620409         0.468902
 [1.5,2.0)       42 1.515684 1.974416   0.546464   0.000181      0.541366    0.000214                    -0.822089            0.822089     -0.252070         0.570019
 [2.0,2.5)       34 2.001580 2.483036   0.633320   0.000058      0.568831    0.000448                    -0.484151            0.484151      0.261347         0.745498
 [2.5,2.7)        7 2.518099 2.662474   0.612485   0.143717      0.821429    0.023449                    -0.205126            0.205126      0.644829         0.849955
[2.7,2.75)        3 2.717599 2.731637  -0.379480   0.752206     -0.500000    0.666667                    -0.083003            0.083003      0.857156         0.940159
[2.75,inf)        2 2.754255 2.758715        NaN        NaN           NaN         NaN                    -0.053322            0.053322      0.899559         0.952881

Top-N rolling correlation:
 top_N_by_S  pearson_r  pearson_p  pearson_r2  spearman_rho  spearman_p
          5   0.084013   0.893158    0.007058     -0.100000    0.872889
         10   0.524015   0.120009    0.274592      0.406061    0.244282
         15   0.321650   0.242377    0.103459      0.232143    0.405099
         20   0.308130   0.186267    0.094944      0.273684    0.242966
         25   0.572494   0.002784    0.327750      0.516154    0.008259
         30   0.584877   0.000688    0.342081      0.604449    0.000404
         40   0.688994   0.000001    0.474713      0.696060    0.000001
         50   0.729262   0.000000    0.531823      0.705738    0.000000
         75   0.775342   0.000000    0.601155      0.721821    0.000000
        100   0.830269   0.000000    0.689346      0.794371    0.000000
        150   0.844921   0.000000    0.713892      0.780360    0.000000
        200   0.874946   0.000000    0.765530      0.849296    0.000000
        300   0.888616   0.000000    0.789638      0.915616    0.000000
        378   0.889861   0.000000    0.791853      0.938779    0.000000

High-stat confirmation calibration subsets:
                    subset  n_pairs  pearson_r_eff_vs_direct  pearson_p  pearson_r2  spearman_rho  spearman_p  mean_abs_delta_chi  mean_delta_eff_minus_direct
     top5_highstats_50seed        5                 0.103684   0.868223    0.010750     -0.100000    0.872889            0.070888                    -0.070888
top10_moderatestats_20seed       10                 0.527261   0.117317    0.278005      0.406061    0.244282            0.147158                    -0.147158

Conclusion: Full-ensemble chi calibration is strong, but high-S-region calibration remains incomplete and statistically weak in the top subsets. This supports wording that Blind87 validates blind Bell-violating, Tsirelson-safe resonance classes, while direct chi_N calibration near the Tsirelson approach remains an open calibration target.
