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| { | |
| "experiment": "DN1 \u2014 null distributions of three already-registered bars", | |
| "prereg": "docs/experiments/preregs/DN1_design_nulls.md", | |
| "status": "PRE-REGISTERED", | |
| "measures_nothing_new": true, | |
| "scope": "Calibrates thresholds, not measurements. Cannot overturn CV6, CV7 or R9; prices the bars they were judged against.", | |
| "n_sim": 1000000, | |
| "n_perm": 100000, | |
| "A1_design_null": { | |
| "definition": "R = range(group means) / sqrt(mean(per-group sample var)), G=5 groups of n=3", | |
| "distribution": "iid normal, scale-free in sigma and location-free in mu", | |
| "mean": 1.4558214009529349, | |
| "sd": 0.6683661758236041, | |
| "percentiles": { | |
| "p50": 1.3504426642962697, | |
| "p90": 2.3197482513624257, | |
| "p95": 2.685370632595311, | |
| "p99": 3.539988075003452, | |
| "p99.9": 4.87893156220862 | |
| }, | |
| "P_R_ge_10": 2e-06, | |
| "P_R_ge_10_exceedances_observed": 2, | |
| "note": "A one-sided exceedance of 0 in n_sim draws is reported as < 1/n_sim, not as 0. The bar is calibrated against this column." | |
| }, | |
| "C1_scale_freedom": { | |
| "required": "|p99(sigma=1) - p99(sigma=100)| <= 0.02", | |
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| "p99_sigma_100": 3.5461058294242056, | |
| "abs_diff": 0.006117754420753574, | |
| "fires": true, | |
| "falsification_witness": { | |
| "what": "same code with the denominator replaced by the constant 1.0", | |
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| "p99_sigma_100": 265.1280524472683, | |
| "abs_diff": 262.4712610013552, | |
| "control_would_fire": false, | |
| "note": "this must be False, or C1 cannot distinguish a scale-free statistic from any other" | |
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| "A2_permutation_null_410m": { | |
| "source": "results/d3_corpus_by_family_410m.json -> per_arm.<corpus>|s<seed>.<family>.z", | |
| "unit": "15 z values per family, permuted across 5 corpus labels, 3 per label", | |
| "by_family": { | |
| "multihop": { | |
| "observed_R": 25.361005428912275, | |
| "null_mean": 1.4354219513761668, | |
| "null_sd": 0.8281876972206043, | |
| "null_p50": 1.277465107028326, | |
| "null_p95": 2.515198551887543, | |
| "null_p99": 5.61098563909792, | |
| "null_max": 25.43264217979271, | |
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| "P_null_ge_bar": 0.00023, | |
| "n_null_ge_observed": 2, | |
| "p_observed_one_sided": 2.999970000299997e-05 | |
| }, | |
| "multilingual": { | |
| "observed_R": 19.426787847831193, | |
| "null_mean": 1.4472181163211184, | |
| "null_sd": 0.7043406387033073, | |
| "null_p50": 1.3324022652684364, | |
| "null_p95": 2.660570482190145, | |
| "null_p99": 3.8541903041621643, | |
| "null_max": 15.066763195787532, | |
| "n_null_ge_bar": 10, | |
| "P_null_ge_bar": 0.0001, | |
| "n_null_ge_observed": 0, | |
| "p_observed_one_sided": 9.99990000099999e-06 | |
| }, | |
| "order-ops": { | |
| "observed_R": 24.632511354365725, | |
| "null_mean": 1.4600481090175972, | |
| "null_sd": 0.724071411525985, | |
| "null_p50": 1.341316486899336, | |
| "null_p95": 2.7854524342316607, | |
| "null_p99": 3.4035854960502476, | |
| "null_max": 24.632511354365725, | |
| "n_null_ge_bar": 10, | |
| "P_null_ge_bar": 0.0001, | |
| "n_null_ge_observed": 1, | |
| "p_observed_one_sided": 1.999980000199998e-05 | |
| }, | |
| "poetry": { | |
| "observed_R": 42.686224720210525, | |
| "null_mean": 1.4207336216576643, | |
| "null_sd": 1.1226321014484546, | |
| "null_p50": 1.0953311671022932, | |
| "null_p95": 2.289972367428842, | |
| "null_p99": 8.799193358965976, | |
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| "n_null_ge_bar": 571, | |
| "P_null_ge_bar": 0.00571, | |
| "n_null_ge_observed": 1, | |
| "p_observed_one_sided": 1.999980000199998e-05 | |
| }, | |
| "typo": { | |
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| "null_mean": 1.4510950885052967, | |
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| "null_p50": 1.3394268870958137, | |
| "null_p95": 2.644590252011299, | |
| "null_p99": 4.196756766414129, | |
| "null_max": 11.924406661562124, | |
| "n_null_ge_bar": 11, | |
| "P_null_ge_bar": 0.00011, | |
| "n_null_ge_observed": 0, | |
| "p_observed_one_sided": 9.99990000099999e-06 | |
| } | |
| } | |
| }, | |
| "C2_pooled_sd_recomputes": { | |
| "required": "<= 1e-12 on all 5 families", | |
| "by_family": { | |
| "multihop": { | |
| "recomputed": 0.017453481001782855, | |
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| "recomputed": 0.019695881058294912, | |
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| "recomputed": 0.005578110253433368, | |
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| "max_abs_diff": 0.0, | |
| "fires": true | |
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| "C3_R_recomputes": { | |
| "required": "<= 1e-12 on all 5 families", | |
| "by_family": { | |
| "multihop": { | |
| "recomputed": 25.361005428912275, | |
| "stored": 25.36100542891225, | |
| "abs_diff": 2.4868995751603507e-14 | |
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| "multilingual": { | |
| "recomputed": 19.426787847831193, | |
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| "max_abs_diff": 2.4868995751603507e-14, | |
| "fires": true | |
| }, | |
| "C4_identity_in_support": { | |
| "required": "the unpermuted assignment reproduces the observed R exactly", | |
| "by_family": { | |
| "multihop": { | |
| "identity_R": 25.361005428912275, | |
| "observed_R": 25.361005428912275, | |
| "abs_diff": 0.0 | |
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| "identity_R": 19.426787847831193, | |
| "observed_R": 19.426787847831193, | |
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| "identity_R": 24.632511354365725, | |
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| "identity_R": 42.686224720210525, | |
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| "identity_R": 27.014210896207846, | |
| "observed_R": 27.014210896207846, | |
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| } | |
| }, | |
| "max_abs_diff": 0.0, | |
| "fires": true | |
| }, | |
| "C5_design_vs_permutation": { | |
| "required": "the two 99th percentiles agree to within a factor of 1.25", | |
| "p99_design": 3.539988075003452, | |
| "p99_permutation_worst_family": 8.799193358965976, | |
| "ratio": 2.485656214804451, | |
| "fires": false | |
| }, | |
| "B_tau_null_exact": { | |
| "n": 5, | |
| "n_orderings": 120, | |
| "bar": 0.6, | |
| "n_orderings_clearing_bar": 14, | |
| "P_single_family_tau_ge_bar": 0.11666666666666667, | |
| "distinct_tau_values": [ | |
| -1.0, | |
| -0.8, | |
| -0.6, | |
| -0.4, | |
| -0.2, | |
| 0.0, | |
| 0.2, | |
| 0.4, | |
| 0.6, | |
| 0.8, | |
| 1.0 | |
| ], | |
| "P_k_of_5_families_clear_under_independence": { | |
| "0": 0.5378028459362139, | |
| "1": 0.3551528227880658, | |
| "2": 0.09381395318930041, | |
| "3": 0.012390522119341565, | |
| "4": 0.0008182420267489713, | |
| "5": 2.1613940329218108e-05 | |
| }, | |
| "P_at_least_3_of_5_under_independence": 0.013230378086419754, | |
| "DEPENDENCE_CAVEAT": "the five families share the same five operators and one activation cache, so they are not independent; the independence figure is an UPPER bound on the evidence, not an estimate of it" | |
| }, | |
| "C_r9_count_null_exact": { | |
| "design": "8 corpora, 15 own-derangement draws each", | |
| "P_one_corpus_clears_all_draws_under_H0": 0.0625, | |
| "expected_count_under_H0": 0.5, | |
| "P_count_equals_zero_under_H0": 0.5967194738332182, | |
| "observed_count": 0, | |
| "reading": "a count of 0 is the modal outcome under the exact null, so the count alone carries almost no information; the direction does", | |
| "sign_test_on_direction": { | |
| "statistic": "number of corpora whose real z_vs_null is negative, min aggregation", | |
| "n_negative": 7, | |
| "n_total": 8, | |
| "z_by_corpus": { | |
| "Wikipedia_en": -1.6709216685460513, | |
| "USPTO_Backgrounds": -0.7050665067014444, | |
| "Pile-CC": -1.9874216306081265, | |
| "StackExchange": -0.09090121377251528, | |
| "Github": 0.593144297659444, | |
| "OOD_News_2024": -0.7490796022292463, | |
| "OOD_arXiv_2023": -0.0881460749226426, | |
| "OOD_CommonPile": -0.7064942600047919 | |
| }, | |
| "p_one_sided_exact_binomial": 0.03515625, | |
| "DEPENDENCE_CAVEAT": "the eight corpora share one activation cache and one 551-item battery; the sign test assumes independence and therefore understates the p-value" | |
| }, | |
| "positive_control": { | |
| "what": "persist on the same draws returns 8 of 8", | |
| "n_beating": 8, | |
| "why_it_matters": "the design CAN return the positive branch, so min's 0 of 8 is a failure of the statistic and not a lack of power in the null" | |
| } | |
| }, | |
| "controls_fired": { | |
| "C1_scale_freedom": true, | |
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| "C4_identity_in_support": true, | |
| "C5_design_vs_permutation": false | |
| }, | |
| "VERDICT": "UNCLEAR \u2014 a control did not fire: C5_design_vs_permutation", | |
| "provenance": { | |
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| "experiment": "DN1", | |
| "utc": "2026-08-31T23:19:44+00:00", | |
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