==================================================================================================== B. SELECTION from the 195-row ledger 35 removed, 160 remain: a component compared with a control (ledger type is a layer comparison) 4 removed, 156 remain: not a structural row (control cannot do the task at all) and not a verdict traced to a fixed harness bug 66 removed, 90 remain: the control is a no-harness control (bare, told-bare, diligence instruction, fresh/alone), not a rival system 60 removed, 30 remain: a bounded metric with a recorded control score (headroom computable on a 0-100 scale) 9 removed, 21 remain: a standard error is recorded 6 removed, 15 remain: the harnessed model is Claude Opus 5.5 fails only 'a component compared with a control (ledger type is a layer ...': ['L119', 'L146'] fails only 'not a structural row (control cannot do the task at all) and...': ['L005', 'L100'] fails only 'the control is a no-harness control (bare, told-bare, dilige...': ['L052', 'L053', 'L056', 'L112', 'L125', 'L135', 'L142', 'L143', 'L148', 'L157', 'L158', 'L164'] fails only 'a bounded metric with a recorded control score (headroom com...': ['L009', 'L014', 'L020', 'L023', 'L024', 'L028', 'L048', 'L062', 'L073', 'L083', 'L084', 'L128', 'L129', 'L138', 'L141', 'L154', 'L162', 'L165', 'L175', 'L176', 'L180', 'L181', 'L184', 'L185', 'L186', 'L187', 'L188', 'L193', 'L194', 'L195'] fails only 'a standard error is recorded...': ['L097', 'L102'] fails only 'the harnessed model is Claude Opus 5.5...': ['L001', 'L002', 'L006', 'L007', 'L054', 'L058'] Opus 5.5 rows: ['L003', 'L004', 'L010', 'L011', 'L012', 'L016', 'L057', 'L099', 'L124', 'L126', 'L136', 'L147', 'L163', 'L166', 'L174'] weaker-model rows: [['L001', 'haiku'], ['L002', 'haiku'], ['L006', 'haiku'], ['L007', 'haiku'], ['L054', 'opus-4.8'], ['L058', 'haiku']] ==================================================================================================== A. REPRODUCTION { "k": 0.539, "k_ci": [ 0.427, 0.675 ], "zero": { "aic": 107.1, "tau": 7.09, "params": [] }, "constant": { "aic": 96.82, "tau": 4.16, "params": [ 5.705 ] }, "headroom": { "aic": 77.16, "tau": 0.98, "params": [ 0.539 ] }, "weaker_k": 0.383, "weaker_tau": 11.45, "all21_k": 0.453, "published_bf": { "lpd_head": -51.95, "lpd_zero": -54.52, "bf": 13.1, "note": "both scored with tau fitted on the weaker rows under the headroom model" } } ==================================================================================================== C. MODEL COMPARISON Opus 5.5 rows (n=15) model params tau AIC BIC LOO lpd M0 [] 7.085 107.10 107.81 -53.211 M1 [5.7053] 4.160 96.82 98.24 -48.300 M2 [0.5392] 0.980 77.16 78.57 -38.580 M2b [0.6414, 1.5926] 0.000 75.58 77.70 -41.142 M3 [7.3286] 2.639 89.39 90.81 -45.374 M5 [12.129] 1.887 83.15 84.57 -42.077 weaker-model rows (n=6) model params tau AIC BIC LOO lpd M0 [] 15.327 52.48 52.28 -26.239 M1 [8.1201] 12.927 52.68 52.26 -30.494 M2 [0.3834] 11.455 51.39 50.98 -31.762 M2b [0.7663, 10.7617] 10.882 52.80 52.17 -34.870 M3 [8.1201] 12.927 52.68 52.26 -32.262 M5 [11.637] 12.610 52.39 51.97 -32.969 all 21 rows (n=21) model params tau AIC BIC LOO lpd M0 [] 9.667 161.65 162.70 -81.000 M1 [6.3857] 6.733 152.97 155.06 -78.206 M2 [0.4529] 4.411 143.81 145.89 -78.883 M2b [0.4785, 0.5041] 4.422 145.76 148.89 -80.597 M3 [7.7262] 5.724 149.81 151.90 -78.932 M5 [11.857] 4.939 146.83 148.92 -80.150 weaker rows -> Opus 5.5 rows model params (src) tau src lpd own tau lpd tau_w lpd tau refit M0 [] 15.327 -57.172 -54.519 -52.550 M1 [8.1201] 12.927 -54.229 -52.910 -47.797 M2 [0.3834] 11.455 -51.945 -51.945 -40.273 M2b [0.7663, 10.7617] 10.882 -54.565 -54.888 -53.586 M3 [8.1201] 12.927 -53.664 -52.197 -42.894 M5 [2.4542] 12.610 -53.061 -51.847 -39.588 Bayes factors of M2 (headroom) against each model, on the destination rows: M2:M0 own tau 186.23 shared tau_w 13.12 tau refit 214700.65 M2:M1 own tau 9.82 shared tau_w 2.62 tau refit 1851.96 M2:M2b own tau 13.74 shared tau_w 18.97 tau refit 605009.84 M2:M3 own tau 5.58 shared tau_w 1.29 tau refit 13.75 M2:M5 own tau 3.05 shared tau_w 0.91 tau refit 0.5 Opus 5.5 rows -> weaker rows model params (src) tau src lpd own tau lpd tau_w lpd tau refit M0 [] 7.085 -28.663 -28.663 -25.242 M1 [5.7053] 4.160 -30.140 -30.140 -24.431 M2 [0.5392] 0.980 -37.603 -37.603 -24.003 M2b [0.6414, 1.5926] 0.000 -40.764 -40.764 -24.123 M3 [7.3286] 2.639 -32.943 -32.943 -24.349 M5 [2.4956] 1.887 -34.318 -34.318 -24.196 Bayes factors of M2 (headroom) against each model, on the destination rows: M2:M0 own tau 0.0 shared tau_w 0.0 tau refit 3.45 M2:M1 own tau 0.0 shared tau_w 0.0 tau refit 1.53 M2:M2b own tau 23.59 shared tau_w 23.59 tau refit 1.13 M2:M3 own tau 0.01 shared tau_w 0.01 tau refit 1.41 M2:M5 own tau 0.04 shared tau_w 0.04 tau refit 1.21 Per-row log-likelihood advantage of M2 at each model's MLE (Opus rows, sorted by headroom): id h y s mu_M1 mu_M2 mu_M3 M2-M1 M2-M3 L010 0.0 -1.10 0.84 5.71 0.00 0.00 2.11 0.48 L003 2.3 0.00 2.35 5.71 1.24 2.30 1.22 0.42 L016 5.0 -1.67 4.28 5.71 2.70 5.00 0.58 0.52 L004 8.0 5.75 2.64 5.71 4.31 7.33 0.43 0.24 L136 9.7 2.68 1.18 5.71 5.23 7.33 -0.10 0.54 L011 10.0 0.00 10.61 5.71 5.39 7.33 0.06 0.12 L163 10.1 4.30 1.35 5.71 5.45 7.33 0.78 0.86 L012 11.0 1.40 4.03 5.71 5.93 7.33 0.01 0.31 L099 11.0 10.80 4.46 5.71 5.93 7.33 0.07 -0.22 L147 13.1 9.30 3.62 5.71 7.06 7.33 0.42 0.10 L174 15.1 6.70 1.71 5.71 8.14 7.33 0.58 0.22 L126 15.6 10.80 2.19 5.71 8.41 7.33 0.76 0.37 L124 16.7 11.90 2.73 5.71 9.00 7.33 0.82 0.50 L166 19.3 13.20 2.78 5.71 10.41 7.33 1.20 0.99 L057 25.8 15.20 6.59 5.71 13.91 7.33 0.88 0.66 ==================================================================================================== SENSITIVITY: Opus rows excluded only because no SE is recorded id model instrument y h flags L097 opus-5.5 production streams no-swap (120 tickets) 0.0 0.0 ceiling L102 opus-5.5 wave 3 no-harm (6 streams x 120) 0.0 0.0 ceiling,audited_cross imputed s = 0.5: k [0.518] AIC M1 109.29 M2 78.88 M3 96.53 imputed s = 1.0: k [0.522] AIC M1 109.28 M2 81.61 M3 96.83 imputed s = 2.0: k [0.533] AIC M1 109.23 M2 83.95 M3 97.67 ==================================================================================================== D. HEADROOM-LAW FORECAST ADDITIONS D1. Profile-likelihood 95% CI for k (tau profiled out; cut at min nll + 1.92; grid step 0.001) opus15 n=15 k = 0.539 95% CI [0.427, 0.675] tau 0.980 grid [-0.5, 1.5] contiguous=True weaker6 n= 6 k = 0.383 95% CI [-0.058, 0.837] tau 11.455 grid [-0.5, 1.5] contiguous=True all21 n=21 k = 0.453 95% CI [0.299, 0.609] tau 4.411 grid [-0.5, 1.5] contiguous=True Opus-15 interval identical to the part-1 reproduction: True D2. Weaker rows (6) -> Opus 5.5 rows (15): parameters (and tau) fitted on the source rows, mean predicted on the destination rows model name params(src) MAE RMSE |e|/s |e|/sd bias max|e| strict best M0 zero [] 6.320 8.067 2.330 0.401 5.951 15.200 4 M1 constant [8.1201] 5.166 5.863 2.317 0.379 -2.169 9.787 0 M2 headroom [0.3834] 3.304 3.862 1.073 0.269 1.537 6.583 4 M2b headroom+shift [0.7663, 10.7617] 7.889 8.337 3.575 0.692 7.889 13.132 - M3 capped constant [8.1201] 4.021 4.614 1.457 0.291 -1.024 8.120 6 row-wise best among ['M0', 'M1', 'M2', 'M3']: strict {'M0': 4, 'M1': 0, 'M2': 4, 'M3': 6}, tied {'M0': 1, 'M1': 0, 'M2': 1, 'M3': 1} M2 closer than each other model (rows): M0: 10-4 (ties 1), M1: 9-6 (ties 0), M2b: 14-1 (ties 0), M3: 8-6 (ties 1) id model h y s mu_M0 mu_M1 mu_M2 mu_M3 err_M0 err_M1 err_M2 err_M3 best_of_M0_M1_M2_M3 L010 opus-5.5 0.0 -1.10 0.84 0.0 8.12 0.00 0.00 -1.10 -9.22 -1.10 -1.10 M0/M2/M3 L003 opus-5.5 2.3 0.00 2.35 0.0 8.12 0.88 2.30 0.00 -8.12 -0.88 -2.30 M0 L016 opus-5.5 5.0 -1.67 4.28 0.0 8.12 1.92 5.00 -1.67 -9.79 -3.58 -6.67 M0 L004 opus-5.5 8.0 5.75 2.64 0.0 8.12 3.07 8.00 5.75 -2.37 2.68 -2.25 M3 L136 opus-5.5 9.7 2.68 1.18 0.0 8.12 3.72 8.12 2.68 -5.44 -1.04 -5.44 M2 L011 opus-5.5 10.0 0.00 10.61 0.0 8.12 3.83 8.12 0.00 -8.12 -3.83 -8.12 M0 L163 opus-5.5 10.1 4.30 1.35 0.0 8.12 3.87 8.12 4.30 -3.82 0.43 -3.82 M2 L012 opus-5.5 11.0 1.40 4.03 0.0 8.12 4.22 8.12 1.40 -6.72 -2.82 -6.72 M0 L099 opus-5.5 11.0 10.80 4.46 0.0 8.12 4.22 8.12 10.80 2.68 6.58 2.68 M3 L147 opus-5.5 13.1 9.30 3.62 0.0 8.12 5.02 8.12 9.30 1.18 4.28 1.18 M3 L174 opus-5.5 15.1 6.70 1.71 0.0 8.12 5.79 8.12 6.70 -1.42 0.91 -1.42 M2 L126 opus-5.5 15.6 10.80 2.19 0.0 8.12 5.98 8.12 10.80 2.68 4.82 2.68 M3 L124 opus-5.5 16.7 11.90 2.73 0.0 8.12 6.40 8.12 11.90 3.78 5.50 3.78 M3 L166 opus-5.5 19.3 13.20 2.78 0.0 8.12 7.40 8.12 13.20 5.08 5.80 5.08 M3 L057 opus-5.5 25.8 15.20 6.59 0.0 8.12 9.89 8.12 15.20 7.08 5.31 7.08 M2 D3. Opus 5.5 rows (15) -> weaker rows (6): parameters (and tau) fitted on the source rows, mean predicted on the destination rows model name params(src) MAE RMSE |e|/s |e|/sd bias max|e| strict best M0 zero [] 14.312 16.486 2.967 1.648 8.345 29.230 1 M1 constant [5.7053] 10.508 14.461 2.049 1.577 2.640 23.605 2 M2 headroom [0.5392] 9.277 13.302 2.044 1.991 -4.981 29.438 2 M2b headroom+shift [0.6414, 1.5926] 9.296 13.535 2.106 2.106 -5.915 30.033 - M3 capped constant [7.3286] 10.112 14.254 1.955 1.733 1.016 25.229 1 row-wise best among ['M0', 'M1', 'M2', 'M3']: strict {'M0': 1, 'M1': 2, 'M2': 2, 'M3': 1}, tied {'M0': 0, 'M1': 0, 'M2': 0, 'M3': 0} M2 closer than each other model (rows): M0: 4-2 (ties 0), M1: 2-4 (ties 0), M2b: 4-2 (ties 0), M3: 3-3 (ties 0) id model h y s mu_M0 mu_M1 mu_M2 mu_M3 err_M0 err_M1 err_M2 err_M3 best_of_M0_M1_M2_M3 L054 opus-4.8 9.1 6.10 4.12 0.0 5.71 4.91 7.33 6.10 0.39 1.19 -1.23 M1 L002 haiku 19.9 6.50 4.05 0.0 5.71 10.73 7.33 6.50 0.79 -4.23 -0.83 M1 L058 haiku 21.4 -17.90 4.92 0.0 5.71 11.54 7.33 -17.90 -23.61 -29.44 -25.23 M0 L007 haiku 27.6 17.24 5.28 0.0 5.71 14.88 7.33 17.24 11.53 2.36 9.91 M2 L001 haiku 33.4 8.90 3.13 0.0 5.71 18.01 7.33 8.90 3.19 -9.11 1.57 M3 L006 haiku 36.9 29.23 5.89 0.0 5.71 19.90 7.33 29.23 23.52 9.33 21.90 M2 D4. Leave-one-out on the Opus 5.5 rows: each row predicted by each model fitted on the other 14 model name LOO MAE LOO RMSE LOO |e|/s in-sample MAE LOO lpd M0 zero 6.320 8.067 2.330 6.320 -53.211 M1 constant 5.142 5.799 2.089 4.822 -48.300 M2 headroom 2.836 3.173 1.020 2.645 -38.580 M2b headroom+shift 2.616 2.998 1.023 2.305 -41.142 M3 capped constant 4.329 4.905 1.554 4.029 -45.374 LOO row-wise strictly best among ['M0', 'M1', 'M2', 'M3']: {'M0': 5, 'M1': 1, 'M2': 5, 'M3': 3} id h y s loo_mu_M0 loo_mu_M1 loo_mu_M2 loo_mu_M3 loo_best_of_M0_M1_M2_M3 L010 0.0 -1.10 0.84 0.0 6.40 0.00 0.00 M0/M2/M3 L003 2.3 0.00 2.35 0.0 6.18 1.25 2.30 M0 L016 5.0 -1.67 4.28 0.0 6.08 2.72 5.00 M0 L004 8.0 5.75 2.64 0.0 5.73 4.28 7.54 M1 L136 9.7 2.68 1.18 0.0 6.04 5.54 8.32 M0 L011 10.0 0.00 10.61 0.0 5.79 5.41 7.42 M0 L163 10.1 4.30 1.35 0.0 5.88 5.65 7.85 M2 L012 11.0 1.40 4.03 0.0 5.96 6.06 7.68 M0 L099 11.0 10.80 4.46 0.0 5.45 5.82 7.16 M3 L147 13.1 9.30 3.62 0.0 5.49 6.97 7.22 M3 L174 15.1 6.70 1.71 0.0 5.64 8.57 7.50 M3 L126 15.6 10.80 2.19 0.0 5.24 7.94 6.86 M2 L124 16.7 11.90 2.73 0.0 5.20 8.59 6.82 M2 L166 19.3 13.20 2.78 0.0 5.08 9.87 6.64 M2 L057 25.8 15.20 6.59 0.0 5.41 13.84 7.11 M2 D5. Rows (0-100 scale, sorted by h) opus15: L010 opus-5.5 ctrl 100.0 h 0.0 delta -1.10 s 0.84 r n/a n 30 living | hourly probes AppWorld (H0-H24) L003 opus-5.5 ctrl 97.7 h 2.3 delta 0.00 s 2.35 r 0.00 n 87 lineage | AppWorld challenge k=11 single crash survival L016 opus-5.5 ctrl 95.0 h 5.0 delta -1.67 s 4.28 r -0.33 n 60 living | fresh AppWorld offline (60) L004 opus-5.5 ctrl 92.0 h 8.0 delta 5.75 s 2.64 r 0.72 n 87 lineage | AppWorld challenge k=11 single crash survival L136 opus-5.5 ctrl 90.3 h 9.7 delta 2.68 s 1.18 r 0.28 n 224 vp3.1 | vp3.1 X+Y L011 opus-5.5 ctrl 90.0 h 10.0 delta 0.00 s 10.61 r 0.00 n 16 living | hourly probes code (H0-H24) L163 opus-5.5 ctrl 89.9 h 10.1 delta 4.30 s 1.35 r 0.43 n None layer+sensor | test_challenge stream drift+52 crashes L012 opus-5.5 ctrl 89.0 h 11.0 delta 1.40 s 4.03 r 0.13 n 15 living | hourly probes tau2 pass^1 (H0-H24) L099 opus-5.5 ctrl 89.0 h 11.0 delta 10.80 s 4.46 r 0.98 n 120 sensor | UD-drift wave 2 L147 opus-5.5 ctrl 86.9 h 13.1 delta 9.30 s 3.62 r 0.71 n None vp2 | v6 silent shift FINAL L174 opus-5.5 ctrl 84.9 h 15.1 delta 6.70 s 1.71 r 0.44 n None Opus+layer | durable test_challenge stream (crash+drift+swap) L126 opus-5.5 ctrl 84.4 h 15.6 delta 10.80 s 2.19 r 0.69 n None vp3 | vp3 pooled L124 opus-5.5 ctrl 83.3 h 16.7 delta 11.90 s 2.73 r 0.71 n None vp3 | vp3 A2 L166 opus-5.5 ctrl 80.7 h 19.3 delta 13.20 s 2.78 r 0.68 n None v3 | amazon-cents v3 (212 tasks; seen in dev) L057 opus-5.5 ctrl 74.2 h 25.8 delta 15.20 s 6.59 r 0.59 n 66 a5 | Haiku->Opus a5 weaker6: L054 opus-4.8 ctrl 90.9 h 9.1 delta 6.10 s 4.12 r 0.67 n 66 a5 | a5 DOWN, unseen shard 1 (66/pair) L002 haiku ctrl 80.1 h 19.9 delta 6.50 s 4.05 r 0.33 n 168 Haiku+Opus-compiled store | AppWorld test_normal TGC L058 haiku ctrl 78.6 h 21.4 delta -17.90 s 4.92 r -0.84 n 168 online store | 168-task stream, online store L007 haiku ctrl 72.4 h 27.6 delta 17.24 s 5.28 r 0.62 n 58 lineage | AppWorld fresh_normal k=14 single crash survival L001 haiku ctrl 66.6 h 33.4 delta 8.90 s 3.13 r 0.27 n 417 Haiku+Opus-compiled store | AppWorld test_challenge TGC L006 haiku ctrl 63.1 h 36.9 delta 29.23 s 5.89 r 0.79 n 65 lineage | AppWorld challenge k=14 single crash survival HEADLINE { "opus15": { "k": 0.539, "k_ci95": [ 0.427, 0.675 ], "aic": { "headroom": 77.16, "constant": 96.82, "zero": 107.1, "capped": 89.39, "smooth_cap": 83.15 } }, "weaker6": { "k": 0.383, "k_ci95": [ -0.058, 0.837 ], "tau": 11.45 }, "all21": { "k": 0.453, "k_ci95": [ 0.299, 0.609 ] }, "forecast_bf_own_tau": { "vs_zero": 186.23, "vs_constant": 9.82, "vs_capped": 5.58, "vs_smooth_cap": 3.05 }, "forecast_bf_shared_tau_published": 13.1, "forecast_error_weaker_to_opus": { "zero": { "mae": 6.32, "rmse": 8.067, "mean_abs_err_over_s": 2.33, "strictly_best_rows": 4 }, "constant": { "mae": 5.166, "rmse": 5.863, "mean_abs_err_over_s": 2.317, "strictly_best_rows": 0 }, "headroom": { "mae": 3.304, "rmse": 3.862, "mean_abs_err_over_s": 1.073, "strictly_best_rows": 4 }, "capped constant": { "mae": 4.021, "rmse": 4.614, "mean_abs_err_over_s": 1.457, "strictly_best_rows": 6 } } } ==================================================================================================== CHECK: every part-1 value against the synthesis paper's re-test of the law leaves compared: 508; mismatches: 0 wrote evidence/headroom_forecast.json