{ "n_items": 720, "n_judged": 720, "decoy_random": { "n": 120, "yes": 0, "rate": 0.0 }, "decoy_namespace": { "n": 120, "yes": 3, "rate": 0.025 }, "groups": [ { "gid": "control/duality_ceil_floor", "source": "positive_control", "space": "-", "n_judged": 12, "n_related": 12, "rate": 1.0, "lift_over_namespace_decoys": 0.975, "p_value": 1.3037785298202383e-14, "mean_confidence": 0.9358333333333334, "top_relations": [ [ "ceiling replaced by floor", 8 ], [ "ceiling division replaced by floor division", 1 ], [ "ceilroot replaced by floorroot", 1 ], [ "ceil replaced with floor throughout", 1 ] ], "examples": [ [ "Int.ceil_add_int", "Int.floor_add_int", "ceiling replaced by floor" ], [ "Int.ceil_sub_ofNat", "Int.floor_sub_ofNat", "ceiling replaced by floor" ], [ "Nat.ceil_add_nat", "Nat.floor_add_nat", "ceiling replaced by floor" ], [ "ceilDiv_zero", "floorDiv_zero", "ceiling division replaced by floor division" ] ], "stats": {} }, { "gid": "control/duality_sup_inf", "source": "positive_control", "space": "-", "n_judged": 12, "n_related": 12, "rate": 1.0, "lift_over_namespace_decoys": 0.975, "p_value": 1.3037785298202383e-14, "mean_confidence": 0.9375, "top_relations": [ [ "sup replaced by inf", 3 ], [ "sup replaced by inf with corresponding notation changes", 1 ], [ "sup replaced by inf with union replaced by intersection", 1 ], [ "sup replaced by inf with type classes swapped", 1 ] ], "examples": [ [ "Finset.image_sup_product", "Finset.image_inf_product", "sup replaced by inf with corresponding notation changes" ], [ "Filter.HasBasis.sup", "Filter.HasBasis.inf", "sup replaced by inf with union replaced by intersection" ], [ "ContinuousAt.sup", "ContinuousAt.inf", "sup replaced by inf" ], [ "GaloisInsertion.l_sup_u", "GaloisInsertion.l_inf_u", "sup replaced by inf" ] ], "stats": {} }, { "gid": "vocab/e5_mistral/k80/c38", "source": "vocab_diversity", "space": "e5_mistral", "n_judged": 12, "n_related": 12, "rate": 1.0, "lift_over_namespace_decoys": 0.975, "p_value": 1.3037785298202383e-14, "mean_confidence": 0.8833333333333333, "top_relations": [ [ "ici replaced by ioi", 3 ], [ "iic replaced by iio", 1 ], [ "ico replaced by ioo", 1 ], [ "icc/ici replaced by ioo/ioi", 1 ] ], "examples": [ [ "Fin.isAddFreimanIso_Iic", "Fin.isAddFreimanIso_Iio", "Iic replaced by Iio" ], [ "ENNReal.iInter_Ici_coe_nat", "ENNReal.iInter_Ioi_coe_nat", "Ici replaced by Ioi" ], [ "Finset.Icc_subset_Ico_iff", "Finset.Icc_subset_Ioo_iff", "Ico replaced by Ioo" ], [ "ENNReal.iUnion_Icc_coe_nat", "ENNReal.iUnion_Ioo_coe_nat", "Icc/Ici replaced by Ioo/Ioi" ] ], "stats": { "n": 189, "coherence": 0.512052059173584, "graph_lift": 0.17582420552979217, "dominance": 0.3548387096774194, "distinct_swaps": 16 } }, { "gid": "vocab/e5_mistral/k80/c10", "source": "vocab_diversity", "space": "e5_mistral", "n_judged": 12, "n_related": 12, "rate": 1.0, "lift_over_namespace_decoys": 0.975, "p_value": 1.3037785298202383e-14, "mean_confidence": 0.875, "top_relations": [ [ "subalgebra replaced by subring", 3 ], [ "same distributive property for different algebraic structures", 1 ], [ "alghom replaced by ringhom (analogous homomorphism types)", 1 ], [ "subalgebra replaced by subsemiring (analogous structures)", 1 ] ], "examples": [ [ "Algebra.map_sup", "Subring.map_sup", "same distributive property for different algebraic structures" ], [ "AlgEquiv.toAlgHom_unop", "AlgHom.toRingHom_unop", "AlgHom replaced by RingHom (analogous homomorphism types)" ], [ "Algebra.comap_top", "Subsemiring.comap_top", "Subalgebra replaced by Subsemiring (analogous structures)" ], [ "GradedAlgebra.mem_support_iff", "GradedRing.mem_support_iff", "GradedAlgebra.proj replaced by GradedRing.proj" ] ], "stats": { "n": 123, "coherence": 0.5410376191139221, "graph_lift": 0.11993727633703899, "dominance": 0.29310344827586204, "distinct_swaps": 19 } }, { "gid": "hunt/e5_mistral/k200/c57", "source": "relation_hunt", "space": "e5_mistral", "n_judged": 12, "n_related": 11, "rate": 0.9166666666666666, "lift_over_namespace_decoys": 0.8916666666666666, "p_value": 1.2333744892099455e-12, "mean_confidence": 0.9125, "top_relations": [ [ "ceiling replaced by floor", 6 ], [ "ceiling replaced with floor", 3 ], [ "ceiling replaced by floor and inequality swapped", 1 ], [ "ceiling division replaced with floor division", 1 ] ], "examples": [ [ "Nat.ceilRoot_def", "Nat.floorRoot_def", "ceiling replaced by floor" ], [ "le_smul_ceilDiv", "smul_floorDiv_le", "ceiling replaced by floor and inequality swapped" ], [ "Nat.ceil_le_ceil", "Nat.floor_le_floor", "ceiling replaced by floor" ], [ "Nat.measurable_ceil", "Nat.measurable_floor", "ceiling replaced by floor" ] ], "stats": { "n": 55, "coherence": 0.7784521579742432, "graph_lift": 0.27404505581246563, "transfer_lift": 0.509090909090909, "distinct@1": 0.9272727272727272 } }, { "gid": "control/min_to_max", "source": "positive_control", "space": "-", "n_judged": 12, "n_related": 11, "rate": 0.9166666666666666, "lift_over_namespace_decoys": 0.8916666666666666, "p_value": 1.2333744892099455e-12, "mean_confidence": 0.9291666666666667, "top_relations": [ [ "min replaced by max", 8 ], [ "< replaced by > with min replaced by max", 1 ], [ "min replaced by max, or replaced by and", 1 ], [ "min replaced with max", 1 ] ], "examples": [ [ "Filter.tendsto_nhds_min_right", "Filter.tendsto_nhds_max_right", "< replaced by > with min replaced by max" ], [ "LocallyLipschitz.const_min", "LocallyLipschitz.const_max", "min replaced by max" ], [ "Fin.min_val", "Fin.max_val", "min replaced by max" ], [ "abs_min_sub_min_le_max", "abs_max_sub_max_le_max", "min replaced by max" ] ], "stats": {} }, { "gid": "control/duality_max_min", "source": "positive_control", "space": "-", "n_judged": 12, "n_related": 11, "rate": 0.9166666666666666, "lift_over_namespace_decoys": 0.8916666666666666, "p_value": 1.2333744892099455e-12, "mean_confidence": 0.9166666666666666, "top_relations": [ [ "max replaced by min", 8 ], [ "max replaced by min with order reversal", 1 ], [ "max replaced by min, or/exists replaced by and/forall", 1 ], [ "max and min replaced with each other", 1 ] ], "examples": [ [ "ofDual_max", "ofDual_min", "max replaced by min with order reversal" ], [ "WithBot.coe_max", "WithBot.coe_min", "max replaced by min" ], [ "Monotone.map_finset_max'", "Monotone.map_finset_min'", "max replaced by min" ], [ "Finset.lt_fold_max", "Finset.lt_fold_min", "max replaced by min, or/exists replaced by and/forall" ] ], "stats": {} }, { "gid": "hunt/e5_mistral/k200/c82", "source": "relation_hunt", "space": "e5_mistral", "n_judged": 12, "n_related": 11, "rate": 0.9166666666666666, "lift_over_namespace_decoys": 0.8916666666666666, "p_value": 1.2333744892099455e-12, "mean_confidence": 0.9041666666666667, "top_relations": [ [ "ici replaced by iic", 2 ], [ "ici replaced by iic (order direction reversed)", 2 ], [ "ici replaced by iic and ioi replaced by iio", 1 ], [ "ici/ioi replaced by iic/iio", 1 ] ], "examples": [ [ "nhdsSet_Ici", "nhdsSet_Iic", "Ici replaced by Iic and Ioi replaced by Iio" ], [ "borel_eq_generateFrom_Ici", "borel_eq_generateFrom_Iic", "Ici replaced by Iic" ], [ "Set.Ici_diff_Ioi_same", "Set.Iic_diff_Iio_same", "Ici/Ioi replaced by Iic/Iio" ], [ "Set.preimage_const_sub_Ici", "Set.preimage_const_sub_Iic", "Ici replaced by Iic (order direction reversed)" ] ], "stats": { "n": 100, "coherence": 0.46619662642478943, "graph_lift": 0.2492977869886681, "transfer_lift": 0.18000000000000005, "distinct@1": 0.93 } }, { "gid": "nonlex/e5_mistral/r10k200/c140", "source": "nonlexical_fast", "space": "e5_mistral", "n_judged": 12, "n_related": 11, "rate": 0.9166666666666666, "lift_over_namespace_decoys": 0.8916666666666666, "p_value": 1.2333744892099455e-12, "mean_confidence": 0.8833333333333333, "top_relations": [ [ "ceiling replaced by floor", 7 ], [ "int replaced by nat with ceil replaced by floor", 1 ], [ "ceiling vs floor, position in inequality reversed", 1 ], [ "ceiling replaced by round", 1 ] ], "examples": [ [ "Int.ceil_int", "Nat.floor_nat", "int replaced by nat with ceil replaced by floor" ], [ "Int.ceil_sub_int", "Int.floor_sub_nat", "ceiling replaced by floor" ], [ "Int.ceil_one", "Nat.floor_one", "ceiling replaced by floor" ], [ "Int.ceil_sub_ofNat", "Nat.floor_sub_nat", "ceiling replaced by floor" ] ], "stats": { "n": 52, "coherence": 0.49916520714759827, "graph_lift": 0.08794924205185403, "median_lex": 0.18198555707931519, "distinct_swaps": 23 } }, { "gid": "hunt/e5_large_stmt/k80/c44", "source": "relation_hunt", "space": "e5_large_stmt", "n_judged": 12, "n_related": 11, "rate": 0.9166666666666666, "lift_over_namespace_decoys": 0.8916666666666666, "p_value": 1.2333744892099455e-12, "mean_confidence": 0.85, "top_relations": [ [ "ici replaced by iic", 4 ], [ "order direction \u2265 reversed to \u2264, intervals swapped", 1 ], [ "neighborhood direction \u2265 replaced by \u2264", 1 ], [ "ici replaced by iic (direction reversed)", 1 ] ], "examples": [ [ "EReal.preimage_coe_Ici", "EReal.preimage_coe_Iic", "Ici replaced by Iic" ], [ "nhdsWithin_Ici_eq'", "nhdsWithin_Iic_eq'", "order direction \u2265 reversed to \u2264, intervals swapped" ], [ "Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Ici", "Set.compl_section_ordSeparatingSet_mem_nhdsWithin_Iic", "neighborhood direction \u2265 replaced by \u2264" ], [ "Set.range_IciExtend", "Set.range_IicExtend", "Ici replaced by Iic (direction reversed)" ] ], "stats": { "n": 186, "coherence": 0.4930684268474579, "graph_lift": 0.16954756489927064, "transfer_lift": 0.4916666666666667, "distinct@1": 0.8083333333333333 } }, { "gid": "control/duality_upper_lower", "source": "positive_control", "space": "-", "n_judged": 12, "n_related": 10, "rate": 0.8333333333333334, "lift_over_namespace_decoys": 0.8083333333333333, "p_value": 5.780469740626146e-11, "mean_confidence": 0.9, "top_relations": [ [ "upper replaced by lower with ici replaced by iic", 1 ], [ "uppersemicontinuous replaced by lowersemicontinuous", 1 ], [ "lowerbounds replaced by upperbounds in second argument", 1 ], [ "upperclosure and isupperset swapped for lowerclosure and islowerset", 1 ] ], "examples": [ [ "upperBounds_insert", "lowerBounds_insert", "upper replaced by lower with Ici replaced by Iic" ], [ "Continuous.comp_upperSemicontinuousOn_antitone", "Continuous.comp_lowerSemicontinuousOn_antitone", "UpperSemicontinuous replaced by LowerSemicontinuous" ], [ "image2_upperBounds_lowerBounds_subset_lowerBounds_image2", "image2_lowerBounds_lowerBounds_subset_lowerBounds_image2", "lowerBounds replaced by upperBounds in second argument" ], [ "upperClosure_min", "lowerClosure_min", "upperClosure and IsUpperSet swapped for lowerClosure and IsLowerSet" ] ], "stats": {} }, { "gid": "vocab/e5_large/k200/c90", "source": "vocab_diversity", "space": "e5_large", "n_judged": 12, "n_related": 10, "rate": 0.8333333333333334, "lift_over_namespace_decoys": 0.8083333333333333, "p_value": 5.780469740626146e-11, "mean_confidence": 0.875, "top_relations": [ [ "addsubgroup replaced by addsubmonoid", 2 ], [ "int replaced by nat", 1 ], [ "scaling direction and sides swapped", 1 ], [ "base ring \u2124 replaced by \u2115", 1 ] ], "examples": [ [ "AddConstMapClass.map_add_int'", "AddConstMapClass.map_add_nat'", "int replaced by nat" ], [ "AddSubgroup.pointwise_smul_le_iff\u2080", "AddSubmonoid.le_pointwise_smul_iff\u2080", "scaling direction and sides swapped" ], [ "ArithmeticFunction.intCoe_apply", "ArithmeticFunction.natCoe_apply", "base ring \u2124 replaced by \u2115" ], [ "AddSubgroup.smul_mem_pointwise_smul", "AddSubmonoid.smul_mem_pointwise_smul", "AddSubgroup replaced by AddSubmonoid" ] ], "stats": { "n": 49, "coherence": 0.5644168853759766, "graph_lift": null, "dominance": 0.3541666666666667, "distinct_swaps": 12 } }, { "gid": "hunt/e5_large/k200/c99", "source": "relation_hunt", "space": "e5_large", "n_judged": 12, "n_related": 10, "rate": 0.8333333333333334, "lift_over_namespace_decoys": 0.8083333333333333, "p_value": 5.780469740626146e-11, "mean_confidence": 0.8708333333333332, "top_relations": [ [ "nonunitalsubsemiring replaced by subsemigroup", 2 ], [ "parameter name r replaced by m", 1 ], [ "subfield replaced by subsemigroup", 1 ], [ "nonunitalsubsemiring replaced by submonoid (analogous structures)", 1 ] ], "examples": [ [ "NonUnitalSubsemiring.centralizer_eq_top_iff_subset", "Subsemigroup.centralizer_eq_top_iff_subset", "parameter name R replaced by M" ], [ "Subfield.coe_iSup_of_directed", "Subsemigroup.coe_iSup_of_directed", "Subfield replaced by Subsemigroup" ], [ "NonUnitalSubsemiring.mem_sSup_of_directedOn", "Submonoid.mem_sSup_of_directedOn", "NonUnitalSubsemiring replaced by Submonoid (analogous structures)" ], [ "NonUnitalSubsemiring.centralizer_eq_top_iff_subset", "Submonoid.centralizer_eq_top_iff_subset", "equivalent statements" ] ], "stats": { "n": 222, "coherence": 0.4575135409832001, "graph_lift": 0.25494000813336914, "transfer_lift": 0.4083333333333333, "distinct@1": 0.5166666666666667 } }, { "gid": "hunt/e5_large_stmt/k200/c104", "source": "relation_hunt", "space": "e5_large_stmt", "n_judged": 12, "n_related": 9, "rate": 0.75, "lift_over_namespace_decoys": 0.725, "p_value": 1.7839553197470642e-09, "mean_confidence": 0.8666666666666667, "top_relations": [ [ "icc replaced by ioc", 3 ], [ "interval types changed", 2 ], [ "interval types substituted: icc\u2194ioc, ici\u2194ioi", 1 ], [ "ico/icc replaced by ioo/ioc (order direction swap)", 1 ] ], "examples": [ [ "Finset.Icc_subset_Ici_self", "Finset.Ioc_subset_Ioi_self", "interval types substituted: Icc\u2194Ioc, Ici\u2194Ioi" ], [ "integrableOn_Icc_iff_integrableOn_Ioo", "integrableOn_Ioc_iff_integrableOn_Ioo'", "Icc replaced by Ioc" ], [ "Set.Icc_inter_Icc", "Set.Ioc_inter_Ioc", "Icc replaced by Ioc" ], [ "Finset.Ico_insert_right", "Finset.Ioo_insert_right", "Ico/Icc replaced by Ioo/Ioc (order direction swap)" ] ], "stats": { "n": 121, "coherence": 0.5186368823051453, "graph_lift": 0.21867233992331703, "transfer_lift": 0.39166666666666666, "distinct@1": 0.525 } }, { "gid": "hunt/e5_mistral/k200/c133", "source": "relation_hunt", "space": "e5_mistral", "n_judged": 12, "n_related": 9, "rate": 0.75, "lift_over_namespace_decoys": 0.725, "p_value": 1.7839553197470642e-09, "mean_confidence": 0.875, "top_relations": [ [ "icc replaced by iic", 5 ], [ "same preimage structure for interval types", 1 ], [ "icc/projicc replaced by iic/projiic", 1 ], [ "icc/iic interval types", 1 ] ], "examples": [ [ "Set.range_projIcc", "Set.range_projIic", "Icc replaced by Iic" ], [ "Set.preimage_sub_const_Icc", "Set.preimage_sub_const_Iic", "same preimage structure for interval types" ], [ "Set.IccExtend_of_mem", "Set.IicExtend_of_mem", "Icc replaced by Iic" ], [ "WithBot.preimage_coe_Icc", "WithBot.preimage_coe_Iic", "Icc replaced by Iic" ] ], "stats": { "n": 38, "coherence": 0.503445029258728, "graph_lift": 0.19551267316243587, "transfer_lift": 0.3947368421052632, "distinct@1": 0.8947368421052632 } }, { "gid": "vocab/e5_mistral/k200/c40", "source": "vocab_diversity", "space": "e5_mistral", "n_judged": 12, "n_related": 9, "rate": 0.75, "lift_over_namespace_decoys": 0.725, "p_value": 1.7839553197470642e-09, "mean_confidence": 0.9166666666666666, "top_relations": [ [ "cos replaced by cosh", 3 ], [ "tan replaced with tanh", 2 ], [ "sin replaced with sinh", 2 ], [ "sin replaced by sinh", 1 ] ], "examples": [ [ "Complex.contDiff_cos", "Complex.contDiff_cosh", "cos replaced by cosh" ], [ "Complex.ofReal_cos", "Complex.ofReal_cosh", "cos replaced by cosh" ], [ "Complex.cos_neg", "Complex.cosh_neg", "cos replaced by cosh" ], [ "Complex.sin_ofReal_re", "Complex.sinh_ofReal_re", "sin replaced by sinh" ] ], "stats": { "n": 66, "coherence": 0.5668074488639832, "graph_lift": 0.04707021284497556, "dominance": 0.3125, "distinct_swaps": 13 } }, { "gid": "vocab/e5_large/k200/c160", "source": "vocab_diversity", "space": "e5_large", "n_judged": 12, "n_related": 8, "rate": 0.6666666666666666, "lift_over_namespace_decoys": 0.6416666666666666, "p_value": 4.0622344322415126e-08, "mean_confidence": 0.8916666666666666, "top_relations": [ [ "cos replaced by cosh", 5 ], [ "sin replaced by sinh, cos replaced by cosh", 2 ], [ "cos replaced by cosh, sin replaced by sinh", 1 ] ], "examples": [ [ "Complex.hasDerivAt_sin", "Real.hasDerivAt_sinh", "sin replaced by sinh, cos replaced by cosh" ], [ "Complex.cos_sq'", "Complex.sinh_sq", "sin replaced by sinh, cos replaced by cosh" ], [ "Complex.hasDerivAt_cos", "Complex.hasDerivAt_cosh", "cos replaced by cosh, sin replaced by sinh" ], [ "Complex.cos_conj", "Complex.cosh_conj", "cos replaced by cosh" ] ], "stats": { "n": 79, "coherence": 0.5856923460960388, "graph_lift": 0.04442170686629733, "dominance": 0.2987012987012987, "distinct_swaps": 17 } }, { "gid": "vocab/e5_large/k200/c106", "source": "vocab_diversity", "space": "e5_large", "n_judged": 12, "n_related": 8, "rate": 0.6666666666666666, "lift_over_namespace_decoys": 0.6416666666666666, "p_value": 4.0622344322415126e-08, "mean_confidence": 0.8458333333333333, "top_relations": [ [ "order reversed: parameters and conditions swapped", 2 ], [ "comparison direction reversed: r < f x becomes f x < r", 1 ], [ "order relations reversed (\u2265\u2194\u2264, >\u2194<)", 1 ], [ "inequality direction swapped (r \u2264 f x \u2194 f x \u2264 r)", 1 ] ], "examples": [ [ "Finset.uIcc_of_ge", "Set.uIcc_of_le", "order reversed: parameters and conditions swapped" ], [ "Finset.uIcc_of_ge", "Finset.uIcc_of_le", "order reversed: parameters and conditions swapped" ], [ "MonotoneOn.convex_gt", "MonotoneOn.convex_lt", "comparison direction reversed: r < f x becomes f x < r" ], [ "List.Sorted.gt_of_ge", "List.Sorted.lt_of_le", "order relations reversed (\u2265\u2194\u2264, >\u2194<)" ] ], "stats": { "n": 55, "coherence": 0.5660575032234192, "graph_lift": 0.180368676563267, "dominance": 0.3018867924528302, "distinct_swaps": 14 } }, { "gid": "control/duality_top_bot", "source": "positive_control", "space": "-", "n_judged": 12, "n_related": 8, "rate": 0.6666666666666666, "lift_over_namespace_decoys": 0.6416666666666666, "p_value": 4.0622344322415126e-08, "mean_confidence": 0.8916666666666666, "top_relations": [ [ "top replaced by bot", 4 ], [ "top replaced by bottom", 3 ], [ "ordertop replaced by orderbot", 1 ] ], "examples": [ [ "Filter.limsInf_top", "Filter.limsInf_bot", "top replaced by bot" ], [ "Subsemiring.op_top", "Subsemiring.op_bot", "top replaced by bottom" ], [ "Subgroup.relindex_top_right", "Subgroup.relindex_bot_right", "top replaced by bottom" ], [ "eq_top_mono", "eq_bot_mono", "top replaced by bottom" ] ], "stats": {} }, { "gid": "nonlex/e5_mistral/r10k80/c63", "source": "nonlexical_fast", "space": "e5_mistral", "n_judged": 12, "n_related": 7, "rate": 0.5833333333333334, "lift_over_namespace_decoys": 0.5583333333333333, "p_value": 7.24177990769373e-07, "mean_confidence": 0.875, "top_relations": [ [ "ceiling replaced by floor", 2 ], [ "ceiling division replaced by floor division", 1 ], [ "bddabove replaced by bddbelow with inequality swap", 1 ], [ "sup replaced by inf, left multiplication order adjusted", 1 ] ], "examples": [ [ "Finsupp.ceilDiv_apply", "Pi.floorDiv_def", "ceiling division replaced by floor division" ], [ "BddAbove.smul_of_nonneg", "bddBelow_smul_iff_of_pos", "BddAbove replaced by BddBelow with inequality swap" ], [ "ENNReal.mul_iSup", "NNReal.iInf_mul", "sup replaced by inf, left multiplication order adjusted" ], [ "Int.ceil_one", "Nat.floor_one", "ceiling replaced by floor" ] ], "stats": { "n": 71, "coherence": 0.21178923547267914, "graph_lift": 0.0952544305151375, "median_lex": 0.12725786864757538, "distinct_swaps": 46 } }, { "gid": "control/le_to_lt", "source": "positive_control", "space": "-", "n_judged": 12, "n_related": 7, "rate": 0.5833333333333334, "lift_over_namespace_decoys": 0.5583333333333333, "p_value": 7.24177990769373e-07, "mean_confidence": 0.8624999999999999, "top_relations": [ [ "\u2264 replaced by <", 4 ], [ "\u2264 replaced with <", 2 ], [ "\u2264 replaced by < (weak to strict inequality)", 1 ] ], "examples": [ [ "Cardinal.toPartENat_le_natCast_iff", "Cardinal.toPartENat_lt_natCast_iff", "\u2264 replaced by <" ], [ "Set.finite_le_nat", "Set.finite_lt_nat", "\u2264 replaced by <" ], [ "sup_le_of_le_sdiff_right", "sup_lt_of_lt_sdiff_right", "\u2264 replaced by < (weak to strict inequality)" ], [ "PrimeSpectrum.asIdeal_le_asIdeal", "PrimeSpectrum.asIdeal_lt_asIdeal", "\u2264 replaced by <" ] ], "stats": {} }, { "gid": "vocab/e5_mistral/k200/c189", "source": "vocab_diversity", "space": "e5_mistral", "n_judged": 12, "n_related": 7, "rate": 0.5833333333333334, "lift_over_namespace_decoys": 0.5583333333333333, "p_value": 7.24177990769373e-07, "mean_confidence": 0.875, "top_relations": [ [ "column replaced by row", 1 ], [ "row sums replaced by column sums", 1 ], [ "row/column indices swapped", 1 ], [ "col replaced by row", 1 ] ], "examples": [ [ "Matrix.det_updateColumn_add", "Matrix.det_updateRow_add", "column replaced by row" ], [ "Matrix.det_ne_zero_of_sum_col_pos", "Matrix.det_ne_zero_of_sum_row_pos", "row sums replaced by column sums" ], [ "Matrix.SpecialLinearGroup.isCoprime_col", "Matrix.SpecialLinearGroup.isCoprime_row", "row/column indices swapped" ], [ "Matrix.col_inj", "Matrix.row_inj", "col replaced by row" ] ], "stats": { "n": 70, "coherence": 0.5688158869743347, "graph_lift": 0.1326934049145962, "dominance": 0.36363636363636365, "distinct_swaps": 15 } }, { "gid": "hunt/e5_large_stmt/k200/c55", "source": "relation_hunt", "space": "e5_large_stmt", "n_judged": 12, "n_related": 7, "rate": 0.5833333333333334, "lift_over_namespace_decoys": 0.5583333333333333, "p_value": 7.24177990769373e-07, "mean_confidence": 0.8791666666666668, "top_relations": [ [ "iic replaced by iio", 2 ], [ "iic replaced by ioi", 1 ], [ "iic replaced by ioi and ici replaced by iio", 1 ], [ "iic replaced by ioi with inequality direction reversed", 1 ] ], "examples": [ [ "Set.preimage_add_const_Iic", "Set.preimage_add_const_Ioi", "Iic replaced by Ioi" ], [ "Set.preimage_neg_Iic", "Set.preimage_neg_Ioi", "Iic replaced by Ioi and Ici replaced by Iio" ], [ "pi_Iic_mem_nhds", "pi_Ioi_mem_nhds", "Iic replaced by Ioi with inequality direction reversed" ], [ "isLowerSet_iff_Iic_subset", "isLowerSet_iff_Iio_subset", "Iic replaced by Iio" ] ], "stats": { "n": 315, "coherence": 0.4483938217163086, "graph_lift": 0.1974108339079491, "transfer_lift": 0.20833333333333331, "distinct@1": 0.7416666666666667 } }, { "gid": "control/add_to_mul", "source": "positive_control", "space": "-", "n_judged": 12, "n_related": 7, "rate": 0.5833333333333334, "lift_over_namespace_decoys": 0.5583333333333333, "p_value": 7.24177990769373e-07, "mean_confidence": 0.8999999999999999, "top_relations": [ [ "addition replaced by multiplication", 6 ], [ "addition replaced by multiplication in second component", 1 ] ], "examples": [ [ "Polynomial.map_add", "Polynomial.map_mul", "addition replaced by multiplication" ], [ "Rat.add_num_den'", "Rat.mul_num_den'", "addition replaced by multiplication" ], [ "PerfectClosure.add_aux_left", "PerfectClosure.mul_aux_left", "addition replaced by multiplication in second component" ], [ "Cardinal.continuum_add_self", "Cardinal.continuum_mul_self", "addition replaced by multiplication" ] ], "stats": {} }, { "gid": "hunt/e5_large_stmt/k200/c133", "source": "relation_hunt", "space": "e5_large_stmt", "n_judged": 12, "n_related": 7, "rate": 0.5833333333333334, "lift_over_namespace_decoys": 0.5583333333333333, "p_value": 7.24177990769373e-07, "mean_confidence": 0.8416666666666667, "top_relations": [ [ "icc replaced by ico", 1 ], [ "interval boundaries adjusted (ico\u2192ioi, icc\u2192ici)", 1 ], [ "icc replaced by uicc (unordered interval)", 1 ], [ "icc replaced by ioo (norm_cast with different interval)", 1 ] ], "examples": [ [ "Set.iUnion_Icc_right", "Set.iUnion_Ico_right", "Icc replaced by Ico" ], [ "Finset.mul_prod_Ico_eq_prod_Icc", "Finset.mul_prod_Ioi_eq_prod_Ici", "interval boundaries adjusted (Ico\u2192Ioi, Icc\u2192Ici)" ], [ "Set.image_update_Icc_right", "Set.image_update_uIcc_right", "Icc replaced by uIcc (unordered interval)" ], [ "Finset.coe_Icc", "Finset.coe_Ioo", "Icc replaced by Ioo (norm_cast with different interval)" ] ], "stats": { "n": 504, "coherence": 0.45497384667396545, "graph_lift": 0.19861925176803047, "transfer_lift": 0.23333333333333334, "distinct@1": 0.8166666666666667 } }, { "gid": "hunt/e5_large/k200/c35", "source": "relation_hunt", "space": "e5_large", "n_judged": 12, "n_related": 6, "rate": 0.5, "lift_over_namespace_decoys": 0.475, "p_value": 1.0453453358531073e-05, "mean_confidence": 0.8375, "top_relations": [ [ "ioc replaced by ioo", 4 ], [ "ioc replaced by ioo (same as 229 with different attributes)", 1 ], [ "succ replaced by pred, ioc replaced by ioo", 1 ] ], "examples": [ [ "csInf_Ioc", "csInf_Ioo", "Ioc replaced by Ioo" ], [ "Set.Ioc_subset_Ioc_left", "Set.Ioo_subset_Ioo_left", "Ioc replaced by Ioo" ], [ "Finset.Ioc_subset_Ioc_left", "Set.Ioo_subset_Ioo_left", "Ioc replaced by Ioo (same as 229 with different attributes)" ], [ "Order.Ioc_succ_right", "Order.Ioo_pred_right_eq_insert", "succ replaced by pred, Ioc replaced by Ioo" ] ], "stats": { "n": 181, "coherence": 0.5747559666633606, "graph_lift": 0.20782685236056878, "transfer_lift": 0.2916666666666667, "distinct@1": 0.6333333333333333 } }, { "gid": "hunt/deepseek_prover/k200/c8", "source": "relation_hunt", "space": "deepseek_prover", "n_judged": 12, "n_related": 6, "rate": 0.5, "lift_over_namespace_decoys": 0.475, "p_value": 1.0453453358531073e-05, "mean_confidence": 0.8583333333333334, "top_relations": [ [ "pure replaced by singleton set", 1 ], [ "hom replaced by inv", 1 ], [ "pair notation unified", 1 ], [ "bottom replaced by top", 1 ] ], "examples": [ [ "Filter.isUnit_iff_singleton", "Finset.isUnit_iff_singleton", "pure replaced by singleton set" ], [ "CategoryTheory.Bicategory.unitors_equal", "CategoryTheory.MonoidalCategory.unitors_inv_equal", "hom replaced by inv" ], [ "LinearPMap.mem_graph_iff", "LinearPMap.mem_graph_iff'", "pair notation unified" ], [ "IntermediateField.finInsepDegree_bot'", "IntermediateField.finInsepDegree_top", "bottom replaced by top" ] ], "stats": { "n": 85, "coherence": 0.5222575068473816, "graph_lift": 0.046789214483922856, "transfer_lift": 0.6, "distinct@1": 0.8941176470588236 } }, { "gid": "hunt/deepseek_prover/k200/c58", "source": "relation_hunt", "space": "deepseek_prover", "n_judged": 12, "n_related": 6, "rate": 0.5, "lift_over_namespace_decoys": 0.475, "p_value": 1.0453453358531073e-05, "mean_confidence": 0.875, "top_relations": [ [ "isclosed replaced by iscompact", 1 ], [ "\u2205 replaced by univ, \u2203 replaced by \u2200", 1 ], [ "empty set \u2194 universal set, bottom \u2194 top", 1 ], [ "unique replaced by subsingleton", 1 ] ], "examples": [ [ "isClosed_set_pi", "isCompact_univ_pi", "IsClosed replaced by IsCompact" ], [ "Set.mem_dite_empty_right", "Set.mem_dite_univ_left", "\u2205 replaced by univ, \u2203 replaced by \u2200" ], [ "Sublattice.coe_eq_empty", "Sublattice.coe_eq_univ", "empty set \u2194 universal set, bottom \u2194 top" ], [ "Finset.nonempty_iff_eq_singleton_default", "Set.Nonempty.eq_univ", "Unique replaced by Subsingleton" ] ], "stats": { "n": 124, "coherence": 0.2544347941875458, "graph_lift": 0.042662292206166574, "transfer_lift": 0.2666666666666666, "distinct@1": 0.8666666666666667 } }, { "gid": "hunt/e5_large/k200/c159", "source": "relation_hunt", "space": "e5_large", "n_judged": 12, "n_related": 5, "rate": 0.4166666666666667, "lift_over_namespace_decoys": 0.39166666666666666, "p_value": 0.00012442496480945386, "mean_confidence": 0.7999999999999999, "top_relations": [ [ "empty replaced by univ with bot replaced by top", 1 ], [ "closeds/\u2205/\u22a5 duality with opens/univ/\u22a4", 1 ], [ "empty set replaced by zero", 1 ], [ "empty set replaced by universal set", 1 ] ], "examples": [ [ "LieSubmodule.span_empty", "Submodule.span_univ", "empty replaced by univ with bot replaced by top" ], [ "TopologicalSpace.Closeds.coe_eq_empty", "TopologicalSpace.Opens.coe_eq_univ", "Closeds/\u2205/\u22a5 duality with Opens/univ/\u22a4" ], [ "Ideal.span_empty", "Ideal.span_zero", "empty set replaced by zero" ], [ "Finset.piecewise_empty", "Set.piecewise_univ", "empty set replaced by universal set" ] ], "stats": { "n": 133, "coherence": 0.5774680376052856, "graph_lift": 0.2623270791233814, "transfer_lift": 0.44999999999999996, "distinct@1": 0.7 } }, { "gid": "hunt/e5_mistral/k200/c90", "source": "relation_hunt", "space": "e5_mistral", "n_judged": 12, "n_related": 5, "rate": 0.4166666666666667, "lift_over_namespace_decoys": 0.39166666666666666, "p_value": 0.00012442496480945386, "mean_confidence": 0.8416666666666667, "top_relations": [ [ "i\u2081 replaced by i\u2082", 1 ], [ "biproduct replaced by biprod", 1 ], [ "fork replaced by pullbackcone", 1 ], [ "terminal y replaced by x, fst replaced by snd", 1 ] ], "examples": [ [ "CategoryTheory.Limits.pullback_diagonal_map_snd_fst_fst", "CategoryTheory.Limits.pullback_diagonal_map_snd_snd_fst", "i\u2081 replaced by i\u2082" ], [ "CategoryTheory.Limits.biproduct.lift_\u03c0", "HomologicalComplex.biprod_lift_snd_f", "biproduct replaced by biprod" ], [ "CategoryTheory.Limits.Fork.IsLimit.lift_\u03b9'", "CategoryTheory.Limits.PullbackCone.IsLimit.lift_snd", "Fork replaced by PullbackCone" ], [ "CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_fst", "CategoryTheory.Limits.BinaryFan.isLimit_iff_isIso_snd", "terminal Y replaced by X, fst replaced by snd" ] ], "stats": { "n": 1419, "coherence": 0.3038126230239868, "graph_lift": 0.19684339710632298, "transfer_lift": 0.275, "distinct@1": 0.8916666666666667 } }, { "gid": "hunt/e5_large/k200/c174", "source": "relation_hunt", "space": "e5_large", "n_judged": 12, "n_related": 5, "rate": 0.4166666666666667, "lift_over_namespace_decoys": 0.39166666666666666, "p_value": 0.00012442496480945386, "mean_confidence": 0.85, "top_relations": [ [ "iic replaced by ioi", 2 ], [ "monotoneon replaced by antitoneon in hypothesis", 1 ], [ "interval direction reversed", 1 ], [ "iio replaced by ioi with iic replaced by ici", 1 ] ], "examples": [ [ "Set.preimage_subtype_val_Iic", "Set.preimage_subtype_val_Ioi", "Iic replaced by Ioi" ], [ "AntitoneOn.Iic", "MonotoneOn.Ioi", "MonotoneOn replaced by AntitoneOn in hypothesis" ], [ "MeasureTheory.integral_Iic_of_hasDerivAt_of_tendsto'", "MeasureTheory.integral_Ioi_of_hasDerivAt_of_tendsto", "interval direction reversed" ], [ "Finset.map_subtype_embedding_Iic", "Finset.map_subtype_embedding_Ioi", "Iic replaced by Ioi" ] ], "stats": { "n": 149, "coherence": 0.6002615094184875, "graph_lift": 0.23558867202783138, "transfer_lift": 0.4083333333333333, "distinct@1": 0.7833333333333333 } }, { "gid": "vocab/e5_large/k200/c5", "source": "vocab_diversity", "space": "e5_large", "n_judged": 12, "n_related": 4, "rate": 0.3333333333333333, "lift_over_namespace_decoys": 0.3083333333333333, "p_value": 0.0012285239819902682, "mean_confidence": 0.8416666666666667, "top_relations": [ [ "cos replaced by tan", 3 ], [ "different trig functions with same conjugation pattern", 1 ] ], "examples": [ [ "Complex.cos_conj", "Complex.tanh_conj", "different trig functions with same conjugation pattern" ], [ "Complex.ofReal_cos", "Complex.ofReal_tan", "cos replaced by tan" ], [ "Complex.cos_ne_zero_iff", "Real.tan_ne_zero_iff", "cos replaced by tan" ], [ "Complex.cos_conj", "Complex.tan_conj", "cos replaced by tan" ] ], "stats": { "n": 156, "coherence": 0.5614461898803711, "graph_lift": 0.16090820765677222, "dominance": 0.3146853146853147, "distinct_swaps": 25 } }, { "gid": "hunt/deepseek_prover/k80/c31", "source": "relation_hunt", "space": "deepseek_prover", "n_judged": 12, "n_related": 3, "rate": 0.25, "lift_over_namespace_decoys": 0.225, "p_value": 0.009991214594536415, "mean_confidence": 0.8666666666666667, "top_relations": [ [ "icc replaced by ioc", 1 ], [ "icc/ico replaced by ioc/ioo (order direction swap)", 1 ], [ "iio replaced by ioi (direction reversed)", 1 ] ], "examples": [ [ "Finset.Icc_subset_Icc_iff", "Set.Ioc_subset_Ioc_iff", "Icc replaced by Ioc" ], [ "Finset.Icc_diff_Ico_self", "Finset.Ioc_diff_Ioo_self", "Icc/Ico replaced by Ioc/Ioo (order direction swap)" ], [ "Cardinal.mk_Iio_real", "Cardinal.mk_Ioi_real", "Iio replaced by Ioi (direction reversed)" ] ], "stats": { "n": 2151, "coherence": 0.12485537678003311, "graph_lift": 0.1186556721567188, "transfer_lift": 0.08333333333333334, "distinct@1": 0.925 } }, { "gid": "nonlex/e5_mistral/r10k30/c25", "source": "nonlexical_fast", "space": "e5_mistral", "n_judged": 12, "n_related": 3, "rate": 0.25, "lift_over_namespace_decoys": 0.225, "p_value": 0.009991214594536415, "mean_confidence": 0.8333333333333334, "top_relations": [ [ "antitone replaced by strictanti, \u2264 replaced by <", 1 ], [ "antitone\u2192monotone swapped with strictanti\u2192strictmono", 1 ], [ "antitoneon replaced by strictmonoon", 1 ] ], "examples": [ [ "Antitone.imp", "StrictAnti.imp", "Antitone replaced by StrictAnti, \u2264 replaced by <" ], [ "Antitone.const_mul_of_nonpos", "StrictAnti.mul_const_of_neg", "Antitone\u2192Monotone swapped with StrictAnti\u2192StrictMono" ], [ "AntitoneOn.union_right", "StrictMonoOn.union", "AntitoneOn replaced by StrictMonoOn" ] ], "stats": { "n": 172, "coherence": 0.2897212505340576, "graph_lift": 0.09536147267837035, "median_lex": 0.22269758582115173, "distinct_swaps": 39 } }, { "gid": "hunt/deepseek_prover/k30/c29", "source": "relation_hunt", "space": "deepseek_prover", "n_judged": 12, "n_related": 3, "rate": 0.25, "lift_over_namespace_decoys": 0.225, "p_value": 0.009991214594536415, "mean_confidence": 0.8708333333333332, "top_relations": [ [ "equivalent formulations of perpendicular bisector", 1 ], [ "woppside replaced by wsameside", 1 ], [ "index order reversed in biconditional", 1 ] ], "examples": [ [ "AffineSubspace.mem_perpBisector_iff_dist_eq'", "AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero", "equivalent formulations of perpendicular bisector" ], [ "AffineSubspace.wOppSide_iff_exists_right", "AffineSubspace.wSameSide_iff_exists_right", "WOppSide replaced by WSameSide" ], [ "AddCommGroup.ModEq.sub_iff_left", "AddCommGroup.ModEq.sub_iff_right", "index order reversed in biconditional" ] ], "stats": { "n": 8127, "coherence": 0.14691230654716492, "graph_lift": 0.03621773431762938, "transfer_lift": 0.09166666666666665, "distinct@1": 0.9833333333333333 } }, { "gid": "nonlex/e5_mistral/r10k200/c62", "source": "nonlexical_fast", "space": "e5_mistral", "n_judged": 12, "n_related": 3, "rate": 0.25, "lift_over_namespace_decoys": 0.225, "p_value": 0.009991214594536415, "mean_confidence": 0.8250000000000001, "top_relations": [ [ "same structure for scalar multiplication and boundedness", 1 ], [ "boundedness preserved under negation", 1 ], [ "bddabove replaced by bddbelow", 1 ] ], "examples": [ [ "Filter.BoundedAtFilter.smul", "MeasureTheory.OuterMeasure.smul_boundedBy", "same structure for scalar multiplication and boundedness" ], [ "Filter.BoundedAtFilter.neg", "IsBoundedLinearMap.neg", "boundedness preserved under negation" ], [ "BddAbove.isBoundedUnder", "BddBelow.range_mono", "BddAbove replaced by BddBelow" ] ], "stats": { "n": 150, "coherence": 0.19500663876533508, "graph_lift": 0.11223979511874785, "median_lex": 0.21566936373710632, "distinct_swaps": 47 } }, { "gid": "nonlex/e5_large/r10k80/c73", "source": "nonlexical_fast", "space": "e5_large", "n_judged": 12, "n_related": 3, "rate": 0.25, "lift_over_namespace_decoys": 0.225, "p_value": 0.009991214594536415, "mean_confidence": 0.8624999999999999, "top_relations": [ [ "isbounded replaced by iswf", 2 ], [ "isbounded replaced by islindelof (bounded vs lindelof)", 1 ] ], "examples": [ [ "Bornology.isBounded_insert", "Set.isWF_insert", "IsBounded replaced by IsWF" ], [ "Bornology.IsBounded.union", "Set.IsWF.union", "IsBounded replaced by IsWF" ], [ "Bornology.IsBounded.union", "IsLindelof.union", "IsBounded replaced by IsLindelof (bounded vs Lindelof)" ] ], "stats": { "n": 123, "coherence": 0.1655602604150772, "graph_lift": 0.07894286409945979, "median_lex": 0.20491136610507965, "distinct_swaps": 34 } }, { "gid": "nonlex/e5_large/r3k30/c26", "source": "nonlexical_fast", "space": "e5_large", "n_judged": 12, "n_related": 2, "rate": 0.16666666666666666, "lift_over_namespace_decoys": 0.14166666666666666, "p_value": 0.06519616545357713, "mean_confidence": 0.8708333333333332, "top_relations": [ [ "same disjointness property for different structures", 1 ], [ "liftrel replaced by lex (same monotonicity pattern)", 1 ] ], "examples": [ [ "CommMonoid.primaryComponent.disjoint", "IsPGroup.disjoint_of_ne", "same disjointness property for different structures" ], [ "Computation.LiftRel.imp", "List.Lex.imp", "LiftRel replaced by Lex (same monotonicity pattern)" ] ], "stats": { "n": 82, "coherence": 0.05138542503118515, "graph_lift": 0.11794941722821115, "median_lex": 0.21676383912563324, "distinct_swaps": 30 } }, { "gid": "nonlex/e5_large/r10k200/c138", "source": "nonlexical_fast", "space": "e5_large", "n_judged": 12, "n_related": 1, "rate": 0.08333333333333333, "lift_over_namespace_decoys": 0.05833333333333333, "p_value": 0.32014266578441974, "mean_confidence": 0.8583333333333334, "top_relations": [ [ "composition equaling identity (same structure, different objects)", 1 ] ], "examples": [ [ "CategoryTheory.Arrow.hom_inv_id_left", "CategoryTheory.Functor.leftDerivedZeroIsoSelf_hom_inv_id", "composition equaling identity (same structure, different objects)" ] ], "stats": { "n": 75, "coherence": 0.14681537449359894, "graph_lift": 0.07345572671577068, "median_lex": 0.19087257981300354, "distinct_swaps": 19 } }, { "gid": "nonlex/e5_large/r10k200/c83", "source": "nonlexical_fast", "space": "e5_large", "n_judged": 12, "n_related": 0, "rate": 0.0, "lift_over_namespace_decoys": -0.025, "p_value": 1.0, "mean_confidence": 0.8958333333333334, "top_relations": [], "examples": [], "stats": { "n": 49, "coherence": 0.2340729832649231, "graph_lift": 0.09501730764691682, "median_lex": 0.25144708156585693, "distinct_swaps": 26 } } ] }