============================================================================================================== H. HEADLINE REPRODUCTION: models fitted on the 6 weaker rows (own tau), scored on the 15 Opus 5.5 rows M0 zero params [] tau 15.327 M1 constant params [8.1201] tau 12.927 M2 law k*h params [0.3834] tau 11.455 M3 capped min(c,h) params [8.1201] tau 12.927 M5 smooth cap params [2.4542] tau 12.610 weak6 -> Opus15 (own tau) n=15 BF law vs zero 186.18 const 9.81 capped 5.58 smooth 3.05 | MAE law 3.30 const 5.17 capped 4.02 zero 6.32 weak6 -> Opus15 (shared tau_w = law's weak tau) n=15 BF law vs zero 13.11 const 2.62 capped 1.29 smooth 0.91 | MAE law 3.30 const 5.17 capped 4.02 zero 6.32 ============================================================================================================== A. FAMILY OVERLAP: does the forecast need the component families shared with the weaker rows? L001 line 2 haiku store compiled by Opus 5.5, carried down to Haiku | contrast: Haiku+Opus-compiled store - Haiku bare | instrument: AppWorld test_challenge TGC L002 line 3 haiku store compiled by Opus 5.5, carried down to Haiku | contrast: Haiku+Opus-compiled store - Haiku bare | instrument: AppWorld test_normal TGC L006 line 7 haiku crash recovery (lineage) | contrast: lineage - bare_notice | instrument: AppWorld challenge k=14 single crash survival L007 line 8 haiku crash recovery (lineage) | contrast: lineage - bare_notice | instrument: AppWorld fresh_normal k=14 single crash survival L054 line 55 opus-4.8 handoff brief a5 (Opus 5.5 -> Opus 4.8) | contrast: a5 - Opus 4.8 alone | instrument: a5 DOWN, unseen shard 1 (66/pair) L058 line 59 haiku online store (Haiku's own) | contrast: online store - fresh | instrument: 168-task stream, online store L003 line 4 opus-5.5 crash recovery (lineage) | contrast: lineage - bare_notice | instrument: AppWorld challenge k=11 single crash survival L004 line 5 opus-5.5 crash recovery (lineage) | contrast: lineage - bare | instrument: AppWorld challenge k=11 single crash survival L010 line 11 opus-5.5 store built by Opus 4.8, carried up | contrast: living - bare (AppWorld probes H0-H41, item-paired) | instrument: hourly probes AppWorld (H0-H24) L011 line 12 opus-5.5 store built by Opus 4.8, carried up | contrast: living - bare | instrument: hourly probes code (H0-H24) L012 line 13 opus-5.5 store built by Opus 4.8, carried up | contrast: living - bare | instrument: hourly probes tau2 pass^1 (H0-H24) L016 line 17 opus-5.5 store built by Opus 4.8, carried up | contrast: living - bare | instrument: fresh AppWorld offline (60) L057 line 58 opus-5.5 handoff brief a5 (Haiku -> Opus 5.5) | contrast: a5 - fresh | instrument: Haiku->Opus a5 L099 line 100 opus-5.5 API-change sensor | contrast: sensor - bare | instrument: UD-drift wave 2 L124 line 126 opus-5.5 claim learner | contrast: vp3 - prior | instrument: vp3 A2 L126 line 128 opus-5.5 claim learner | contrast: vp3 - prior | instrument: vp3 pooled L136 line 138 opus-5.5 claim learner | contrast: vp3.1 - prior | instrument: vp3.1 X+Y L147 line 149 opus-5.5 claim learner | contrast: vp2 - prior | instrument: v6 silent shift FINAL L163 line 165 opus-5.5 crash recovery layer + API-change sensor | contrast: layer+sensor - bare | instrument: test_challenge stream drift+52 crashes L166 line 168 opus-5.5 API-change sensor | contrast: v3 - drifted bare | instrument: amazon-cents v3 (212 tasks; seen in dev) L174 line 176 opus-5.5 crash recovery (durable layer) | contrast: Opus+layer - Opus alone | instrument: durable test_challenge stream (crash+drift+swap) novel: sensor + claim learner + Opus-4.8 store (no weaker n=10 BF law vs zero 28.60 const 4.30 capped 2.92 smooth 1.98 | MAE law 3.94 const 5.47 capped 4.34 zero 6.29 same, shared tau_w n=10 BF law vs zero 5.30 const 1.84 capped 1.13 smooth 0.90 | MAE law 3.94 const 5.47 capped 4.34 zero 6.29 novel strict: sensor + claim learner (no crash, store or h n= 6 BF law vs zero 11.57 const 1.50 capped 1.50 smooth 1.21 | MAE law 4.67 const 3.47 capped 3.47 zero 9.78 same, shared tau_w n= 6 BF law vs zero 5.77 const 0.81 capped 0.81 smooth 0.73 | MAE law 4.67 const 3.47 capped 3.47 zero 9.78 novel + handoff brief L057 (the ten novel rows and L057) n=11 BF law vs zero 50.44 const 4.91 capped 3.33 smooth 2.08 | MAE law 4.06 const 5.62 capped 4.59 zero 7.09 same, shared tau_w n=11 BF law vs zero 9.48 const 1.96 capped 1.20 smooth 0.89 | MAE law 4.06 const 5.62 capped 4.59 zero 7.09 shared: crash recovery + handoff brief (family has a weake n= 5 BF law vs zero 6.51 const 2.28 capped 1.91 smooth 1.54 | MAE law 2.04 const 4.56 capped 3.37 zero 6.39 same, shared tau_w n= 5 BF law vs zero 2.47 const 1.43 capped 1.14 smooth 1.00 | MAE law 2.04 const 4.56 capped 3.37 zero 6.39 shared crash recovery only n= 4 BF law vs zero 3.69 const 2.00 capped 1.68 smooth 1.47 | MAE law 1.23 const 3.93 capped 2.45 zero 4.19 same, shared tau_w n= 4 BF law vs zero 1.38 const 1.34 capped 1.07 smooth 1.02 | MAE law 1.23 const 3.93 capped 2.45 zero 4.19 per-row log BF of the law (own tau): id family h y | vs zero, const, capped L010 store built by Opus 4.8, carried u h 0.0 y -1.10 | 0.29 0.37 0.12 L003 crash recovery (lineage) h 2.3 y 0.00 | 0.28 0.30 0.13 L016 store built by Opus 4.8, carried u h 5.0 y -1.67 | 0.23 0.32 0.18 L004 crash recovery (lineage) h 8.0 y 5.75 | 0.32 0.11 0.10 L136 claim learner h 9.7 y 2.68 | 0.30 0.20 0.20 L011 store built by Opus 4.8, carried u h 10.0 y 0.00 | 0.15 0.16 0.16 L163 crash recovery layer + API-change h 10.1 y 4.30 | 0.33 0.16 0.16 L012 store built by Opus 4.8, carried u h 11.0 y 1.40 | 0.24 0.21 0.21 L099 API-change sensor h 11.0 y 10.80 | 0.35 -0.02 -0.02 L147 claim learner h 13.1 y 9.30 | 0.38 0.05 0.05 L174 crash recovery (durable layer) h 15.1 y 6.70 | 0.38 0.12 0.12 L126 claim learner h 15.6 y 10.80 | 0.44 0.05 0.05 L124 claim learner h 16.7 y 11.90 | 0.46 0.05 0.05 L166 API-change sensor h 19.3 y 13.20 | 0.52 0.07 0.07 L057 handoff brief a5 (Haiku -> Opus 5. h 25.8 y 15.20 | 0.57 0.13 0.13 ============================================================================================================== B. GENERIC CEILING vs MATCHED FRACTION L166 Amazon cents (h from U7 counts): h 19.34, matched-fraction prediction 13.68, s 2.78 (matched fraction = clean - drifted = 29/212; phi = 29/41) law (Opus k) predicted lift 10.43 -> score 91.09 (obs - pred)/s 1.00 law (weak k) predicted lift 7.41 -> score 88.07 (obs - pred)/s 2.09 capped (Opus c) predicted lift 7.33 -> score 87.99 (obs - pred)/s 2.12 smooth cap (Opus c) predicted lift 9.67 -> score 90.33 (obs - pred)/s 1.28 constant (Opus c) predicted lift 5.71 -> score 86.37 (obs - pred)/s 2.70 constant (weak c) predicted lift 8.12 -> score 88.78 (obs - pred)/s 1.83 matched fraction (phi*h, p = 1) predicted lift 13.68 -> score 94.34 (obs - pred)/s -0.17 observed unanchored-change flags (ledger L166, 199/212): lift 13.21 observed full v3 notes (197/212): lift 12.26 L004 crash, lineage vs bare (87 tasks): h 8.00, matched-fraction prediction 5.75, s 2.64 (matched = told-bare - bare: failures the crash notice removes) law (Opus k) predicted lift 4.31 -> score 96.31 (obs - pred)/s 0.54 law (weak k) predicted lift 3.07 -> score 95.07 (obs - pred)/s 1.02 capped (Opus c) predicted lift 7.33 -> score 99.33 (obs - pred)/s -0.60 smooth cap (Opus c) predicted lift 5.86 -> score 97.86 (obs - pred)/s -0.04 constant (Opus c) predicted lift 5.71 -> score 97.71 (obs - pred)/s 0.02 constant (weak c) predicted lift 8.12 -> score 100.12 (obs - pred)/s -0.90 matched fraction (phi*h, p = 1) predicted lift 5.75 -> score 97.75 (obs - pred)/s 0.00 observed lineage 85/87: lift 5.75 L003 crash, lineage vs told bare (87 tasks): h 2.30, matched-fraction prediction 0.00, s 2.35 (told control already has the crash cause supplied) law (Opus k) predicted lift 1.24 -> score 98.94 (obs - pred)/s -0.53 law (weak k) predicted lift 0.88 -> score 98.58 (obs - pred)/s -0.38 capped (Opus c) predicted lift 2.30 -> score 100.00 (obs - pred)/s -0.98 smooth cap (Opus c) predicted lift 2.10 -> score 99.80 (obs - pred)/s -0.89 constant (Opus c) predicted lift 5.71 -> score 103.41 (obs - pred)/s -2.43 constant (weak c) predicted lift 8.12 -> score 105.82 (obs - pred)/s -3.46 matched fraction (phi*h, p = 1) predicted lift 0.00 -> score 97.70 (obs - pred)/s 0.00 observed lineage 85/87: lift 0.00 Likelihood ratio, matched fraction vs each model, over L166 + L004 + L003 (independent-normal approximation; L003 and L004 share the lineage arm, so they are not independent): vs law (Opus k) L166 alone 1.63 three rows 2.17 (model gets its Opus tau: 2.42) vs law (weak k) L166 alone 8.69 three rows 15.62 (model gets its Opus tau: 13.99) vs capped (Opus c) L166 alone 9.27 three rows 17.93 (model gets its Opus tau: 12.71) vs smooth cap (Opus c) L166 alone 2.22 three rows 3.31 (model gets its Opus tau: 4.18) vs constant (Opus c) L166 alone 37.90 three rows 727.65 (model gets its Opus tau: 42.41) vs constant (weak c) L166 alone 5.28 three rows 3145.50 (model gets its Opus tau: 53.92) Largest h among the 15 Opus rows: 25.8; among the 6 weaker rows: 36.9. ============================================================================================================== C. SELECTION: refit on weaker-row subsets, rescore the 15 Opus rows (own tau) drop L001 (haiku, h 33.4, y 8.90): k 0.433 tau 12.72; constant c 8.00; capped c 8.00 n=15 BF law vs zero 129.80 const 11.17 capped 7.21 smooth 3.93 | MAE law 2.99 const 5.14 capped 4.03 zero 6.32 drop L002 (haiku, h 19.9, y 6.50): k 0.392 tau 12.83; constant c 8.50; capped c 8.50 n=15 BF law vs zero 122.00 const 9.26 capped 5.56 smooth 2.95 | MAE law 3.25 const 5.24 capped 4.00 zero 6.32 drop L006 (haiku, h 36.9, y 29.23): k 0.206 tau 10.06; constant c 4.26; capped c 4.26 n=15 BF law vs zero 18.67 const 1.35 capped 1.13 smooth 1.09 | MAE law 4.54 const 4.92 capped 4.51 zero 6.32 drop L007 (haiku, h 27.6, y 17.24): k 0.333 tau 12.29; constant c 6.39; capped c 6.39 n=15 BF law vs zero 56.20 const 5.37 capped 4.02 smooth 2.97 | MAE law 3.63 const 4.86 capped 4.07 zero 6.32 drop L054 (opus-4.8, h 9.1, y 6.10) = Haiku-only fit (5 rows): k 0.380 tau 12.77; constant c 8.58; capped c 8.58 n=15 BF law vs zero 127.60 const 9.49 capped 5.63 smooth 3.27 | MAE law 3.33 const 5.26 capped 3.99 zero 6.32 drop L058 (haiku, h 21.4, y -17.90): k 0.486 tau 4.21; constant c 12.55; capped c 14.09 n=15 BF law vs zero 4985870.41 const 294149.74 capped 195.50 smooth 5.58 | MAE law 2.81 const 7.04 capped 4.24 zero 6.32 drop L001, scored on the 10 novel-family rows n=10 BF law vs zero 23.05 const 4.75 capped 3.51 smooth 2.38 | MAE law 3.73 const 5.47 capped 4.37 zero 6.29 drop L001, scored on the 6 strict-novel rows n= 6 BF law vs zero 10.17 const 1.86 capped 1.86 smooth 1.45 | MAE law 4.12 const 3.55 capped 3.55 zero 9.78 drop L002, scored on the 10 novel-family rows n=10 BF law vs zero 22.07 const 4.20 capped 2.96 smooth 1.97 | MAE law 3.90 const 5.47 capped 4.27 zero 6.29 drop L002, scored on the 6 strict-novel rows n= 6 BF law vs zero 9.38 const 1.56 capped 1.56 smooth 1.25 | MAE law 4.58 const 3.22 capped 3.22 zero 9.78 drop L006, scored on the 10 novel-family rows n=10 BF law vs zero 6.38 const 1.17 capped 1.03 smooth 0.99 | MAE law 4.78 const 5.47 capped 5.04 zero 6.29 drop L006, scored on the 6 strict-novel rows n= 6 BF law vs zero 4.49 const 0.79 capped 0.79 smooth 0.80 | MAE law 6.85 const 6.04 capped 6.04 zero 9.78 drop L007, scored on the 10 novel-family rows n=10 BF law vs zero 13.21 const 2.90 capped 2.38 smooth 1.94 | MAE law 4.14 const 5.47 capped 4.69 zero 6.29 drop L007, scored on the 6 strict-novel rows n= 6 BF law vs zero 6.91 const 1.42 capped 1.42 smooth 1.25 | MAE law 5.22 const 4.63 capped 4.63 zero 9.78 drop L054, scored on the 10 novel-family rows n=10 BF law vs zero 22.69 const 4.26 capped 2.98 smooth 2.10 | MAE law 3.95 const 5.47 capped 4.25 zero 6.29 drop L054, scored on the 6 strict-novel rows n= 6 BF law vs zero 9.38 const 1.54 capped 1.54 smooth 1.30 | MAE law 4.71 const 3.17 capped 3.17 zero 9.78 drop L058, scored on the 10 novel-family rows n=10 BF law vs zero 13960.04 const 2324.78 capped 18.11 smooth 2.16 | MAE law 3.53 const 6.95 capped 4.48 zero 6.29 drop L058, scored on the 6 strict-novel rows n= 6 BF law vs zero 648.20 const 5.97 capped 2.80 smooth 0.78 | MAE law 3.55 const 2.98 capped 2.90 zero 9.78 range over the 6 leave-one-out fits: BF vs zero 18.7-4985870.4, vs constant 1.35-294149.74, vs capped 1.13-195.50 all 22 weaker-row subsets of size 4-6: BF vs zero > 1 in 22, vs constant > 1 in 21, vs capped > 1 in 21; law MAE < constant MAE in 22, < capped MAE in 20 BF vs zero min/median/max 2.75 / 85.59 / 148323452.9; vs constant 0.93 / 9.38 / 9369211002389539836033889582059089821696.0; vs capped 0.90 / 5.57 / 728443874.4; k 0.069-0.621 weakest three subsets (by BF vs constant): ['L001', 'L002', 'L054', 'L058'] k 0.069 tau 9.58 BF zero 2.75 const 0.93 capped 0.90 MAE law 5.69 const 5.70 ['L002', 'L007', 'L054', 'L058'] k 0.162 tau 11.60 BF zero 5.38 const 1.08 capped 1.01 MAE law 4.88 const 5.18 ['L001', 'L002', 'L007', 'L054', 'L058'] k 0.206 tau 10.06 BF zero 18.67 const 1.35 capped 1.13 MAE law 4.54 const 4.92 weak fit WITHOUT the crash-recovery rows L006/L007 (L001 L002 L054 L058): k 0.069 tau 9.58; on the 15 Opus rows BF zero 2.75 const 0.93 capped 0.90; MAE law 5.69 const 5.70 capped 5.61 no-crash weak fit -> the 4 Opus crash-recovery rows n= 4 BF law vs zero 1.21 const 0.95 capped 0.95 smooth 0.95 | MAE law 3.66 const 3.52 capped 3.52 zero 4.19 ============================================================================================================== Z. h-PERMUTATION: weak-fitted law scored on the Opus rows with h shuffled among the 15 rows observed law lpd -51.945; permutations with lpd >= observed: 0/20000 -> p = 0.0000