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LICENSE.md

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+# Licenses
+
+This collection repackages tasks from several sources. Each row's `license` column gives the license of its source:
+
+- MIT: RLVE-Gym, NPPC, EinsteinArena (platform and baselines)
+- CC-BY-4.0: MathConstraint; AlphaEvolve repository of problems (materials)
+- Apache-2.0: Reasoning Gym, FunSearch, AlphaEvolve repository of problems (code), Finch / Evolution Fine-Tuning (code)
+
+Please attribute the original authors when using the corresponding tasks.

README.md

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+---
+license: other
+license_name: mixed-permissive
+license_link: LICENSE.md
+tags:
+- math
+- reinforcement-learning
+- rl-environment
+- harbor
+size_categories:
+- 1K<n<10K
+---
+
+# MathConstructOptimize-Envs (Harbor)
+
+The 3,577 tasks of [`amphora/MathConstructOptimize-Envs`](https://huggingface.co/datasets/amphora/MathConstructOptimize-Envs) as runnable [Harbor](https://github.com/laude-institute/harbor) environments. Each task is one directory:
+
+```
+tasks/<task_id>/
+  task.toml              # metadata (subset, family, problem_key, tier, level, source, license, tags,
+                         #   direction/baseline/best_known for optimize), limits, network_mode = "no-network"
+  instruction.md         # the prompt; the agent writes its answer to /workdir/answer.json
+  environment/Dockerfile # python:3.11 slim + pinned numpy/scipy/sympy/networkx/pysat/z3/pulp/ortools
+  environment/instance.json
+  tests/test.sh          # runs tests/run.py + tests/check.py, writes /logs/verifier/reward.txt
+  solution/solve.sh      # oracle: a known valid answer
+```
+
+```bash
+uv tool install harbor
+huggingface-cli download amphora/MathConstructOptimize-Envs-harbor --repo-type dataset --local-dir mcoe
+harbor run -p mcoe/tasks -a oracle -n 16          # validate: every task scores > 0
+harbor run -p mcoe/tasks -a terminus-2 -m <model> -n 16
+```
+
+**Validation:**
+- The oracle agent passes on all 3,577 tasks (construct = 1.0, optimize ≥ 0.1), and a no-op agent scores 0.
+- An HTTP canary confirmed that `no-network` blocks internet access inside the task container. Research-level best constructions are public, so do not relax this for RL.
+- If you run many trials concurrently, raise Docker's default address pools. Each no-network task creates its own networks, and the defaults are exhausted at roughly 30 concurrent trials.
+
+See the main dataset card for the reward contract, tags, sources and the upstream verifier bugs we fixed.

families.csv

@@ -0,0 +1,143 @@
+family,subset,tier,domain,source,license,problem_key,n_tasks,tags
+ae_p10_kakeya_3d,optimize,research,geometry,AlphaEvolve-Repository-of-Problems/10-3d-kakeya,CC-BY-4.0,kakeya_needle_3d_prisms,1,exact_piecewise_integration;float_objective
+ae_p16_gagliardo_nirenberg,optimize,research,analysis,AlphaEvolve-Repository-of-Problems/16-gagliardo-nirenberg-special-case,CC-BY-4.0,nagy_gagliardo_nirenberg_sharp_constant,3,float_objective;known_optimum
+ae_p17_young_convolution,optimize,research,analysis,AlphaEvolve-Repository-of-Problems/17-young-convolution,CC-BY-4.0,young_convolution_sharp_constant,3,float_objective;known_optimum
+ae_p18_hardy_littlewood_maximal,optimize,research,analysis,AlphaEvolve-Repository-of-Problems/18-hardy-littlewood-maximal,CC-BY-4.0,centered_hardy_littlewood_weak11_constant_1d,1,exact_rational;known_optimum
+ae_p1_ff_kakeya,optimize,research,combinatorics,AlphaEvolve-Repository-of-Problems/1-finite-field-kakeya,CC-BY-4.0,finite_field_kakeya_min_size,10,exact_integer;finite_fields
+ae_p1_ff_nikodym,optimize,research,combinatorics,AlphaEvolve-Repository-of-Problems/1-finite-field-nikodym,CC-BY-4.0,finite_field_nikodym_min_size_d3,4,exact_integer;finite_fields
+ae_p24_de_bruijn_sharma,optimize,research,analysis,AlphaEvolve-Repository-of-Problems/24-de-bruijn-sharma,CC-BY-4.0,de_bruijn_sharma_x_intercept,4,float_objective;polynomials
+ae_p29_block_stacking,optimize,competition,analysis,AlphaEvolve-Repository-of-Problems/29-block-stacking,CC-BY-4.0,block_stacking_overhang_one_per_level,3,agentic_trivial;exact_rational;known_optimum
+ae_p30_arithmetic_kakeya,optimize,research,combinatorics,AlphaEvolve-Repository-of-Problems/30-arithmetic-kakeya,CC-BY-4.0,arithmetic_kakeya_entropy_sum_difference,2,additive_combinatorics;entropy;float_objective
+ae_p31_furstenberg_sarkozy,optimize,research,number_theory,AlphaEvolve-Repository-of-Problems/31-furstenberg-sarkozy,CC-BY-4.0,furstenberg_sarkozy_modular_exponent,2,additive_combinatorics;exact_integer
+ae_p32_spherical_designs,construct,research,discrete_geometry,AlphaEvolve-Repository-of-Problems/32-spherical-designs,CC-BY-4.0,spherical_t_design_s2,6,float_tolerance;numerical_design
+ae_p35_cubes_in_cube,optimize,research,discrete_geometry,AlphaEvolve-Repository-of-Problems/35-packing-in-a-dilate,CC-BY-4.0,unit_cubes_in_smallest_cube_n11,1,float_objective;packing
+ae_p37_turan_tetrahedron,optimize,research,combinatorics,AlphaEvolve-Repository-of-Problems/37-hypergraph-turan-tetrahedron,CC-BY-4.0,turan_density_K4_3,1,blow_up;extremal_hypergraph
+ae_p38_factorial_factors,construct,research,number_theory,AlphaEvolve-Repository-of-Problems/38-factoring-N-factorial,CC-BY-4.0,factorial_into_n_large_factors_A034258,60,agentic_trivial;exact_integer;ilp_friendly;np_search
+ae_p39_beat_the_average,optimize,research,probability,AlphaEvolve-Repository-of-Problems/39-beat-the-average,CC-BY-4.0,beat_the_average_X1X2X3_lt_2X4,1,discrete_measure;float_objective
+ae_p40_erdos_discrepancy,optimize,research,combinatorics,AlphaEvolve-Repository-of-Problems/40-erdos-discrepancy,CC-BY-4.0,erdos_discrepancy_C2_max_length,1,exact_integer;np_search;sat_friendly
+ae_p41_sphere_max_volume,optimize,research,discrete_geometry,AlphaEvolve-Repository-of-Problems/41-points-on-sphere-max-volume,CC-BY-4.0,max_volume_inscribed_polyhedron_n_vertices,7,float_objective
+ae_p42_sum_difference_i,optimize,research,combinatorics,AlphaEvolve-Repository-of-Problems/42-sum-difference-I,CC-BY-4.0,sum_difference_sumset_vs_diffset_exponent,1,additive_combinatorics;exact_integer
+ae_p43_sum_difference_ii,optimize,research,combinatorics,AlphaEvolve-Repository-of-Problems/43-sum-difference-II,CC-BY-4.0,sum_difference_diffset_vs_sumset_exponent,1,additive_combinatorics;exact_integer
+ae_p44_sum_difference_iii,optimize,research,combinatorics,AlphaEvolve-Repository-of-Problems/44-sum-difference-III,CC-BY-4.0,sum_difference_A_plus_B_vs_A_minus_B_exponent,1,additive_combinatorics;exact_integer
+ae_p45_sum_product_fp,optimize,research,combinatorics,AlphaEvolve-Repository-of-Problems/45-sum-product-finite-field,Apache-2.0,finite_field_sum_product_sqrt_p,3,additive_combinatorics;exact_integer
+ae_p52_erdos_squarefree,construct,research,number_theory,AlphaEvolve-Repository-of-Problems/52-erdos-squarefree,CC-BY-4.0,erdos_ab_plus_1_never_squarefree,50,exact_integer
+ae_p54_touching_cylinders,construct,research,discrete_geometry,AlphaEvolve-Repository-of-Problems/54-pairwise-touching-cylinders,CC-BY-4.0,mutually_touching_infinite_cylinders,2,float_tolerance;nonlinear_system
+ae_p58_happy_ending,construct,research,discrete_geometry,AlphaEvolve-Repository-of-Problems/58-erdos-szekeres-happy-ending,CC-BY-4.0,erdos_szekeres_no_convex_k_gon_2pow_k_minus_2,5,exact_integer;np_search
+ae_p59_isosceles_free_grid,optimize,research,discrete_geometry,AlphaEvolve-Repository-of-Problems/59-no-isosceles-grid,CC-BY-4.0,isosceles_free_grid_subset,2,exact_integer;np_search
+ae_p60_no5_on_sphere,optimize,research,discrete_geometry,AlphaEvolve-Repository-of-Problems/60-no-5-on-a-sphere,CC-BY-4.0,no_five_cospherical_grid_subset,6,exact_integer;np_search
+ae_p65_imo2025_p6_tiling,construct,competition,combinatorics,AlphaEvolve-Repository-of-Problems/65-imo-2025-p6,CC-BY-4.0,imo2025_p6_min_tiles,6,exact_integer
+ea_circle_packing_26,optimize,research,discrete_geometry,EinsteinArena/circle-packing,MIT,circle_packing_square_sum_radii_n26,1,exact_check;float_objective
+ea_circles_rectangle_21,optimize,research,discrete_geometry,EinsteinArena/circles-rectangle,MIT,circles_in_rectangle_perimeter4_sum_radii_n21,1,exact_check;float_objective
+ea_difference_bases,optimize,research,number_theory,EinsteinArena/difference-bases,MIT,difference_basis_ratio,1,exact_check
+ea_edges_vs_triangles,optimize,research,combinatorics,EinsteinArena/edges-vs-triangles,MIT,edges_vs_triangles_density_curve,1,float_objective
+ea_erdos_min_overlap,optimize,research,analysis,EinsteinArena/erdos-min-overlap,MIT,erdos_minimum_overlap_upper,1,float_objective
+ea_first_autocorrelation,optimize,research,analysis,EinsteinArena/first-autocorrelation-inequality,MIT,first_autocorrelation_inequality_upper,1,float_objective
+ea_flat_polynomials_70,optimize,research,analysis,EinsteinArena/flat-polynomials,MIT,flat_littlewood_polynomial_n70,1,float_objective
+ea_hadamard_det_51,optimize,research,combinatorics,EinsteinArena/hadamard-det-51,MIT,hadamard_maxdet_n51,1,ea_under_review;exact_check
+ea_heilbronn_triangle_11,optimize,research,discrete_geometry,EinsteinArena/heilbronn-triangles,MIT,heilbronn_triangle_n11,1,exact_check;float_objective
+ea_kakeya_needle_128,optimize,research,geometry,EinsteinArena/kakeya-needle-128,MIT,kakeya_needle_triangles_n128,1,ea_under_review;exact_check
+ea_kissing_number,optimize,research,discrete_geometry,"EinsteinArena/kissing-number-d11,-d11-605,-d12",MIT,kissing_number_overlap_loss,3,best_known_uncertain;exact_check
+ea_min_distance_ratio_16,optimize,research,discrete_geometry,EinsteinArena/min-distance-ratio-2d,MIT,max_min_distance_ratio_2d_n16,1,float_objective
+ea_no_three_in_line_75,optimize,research,discrete_geometry,EinsteinArena/no-three-in-line-75,MIT,no_three_in_line_n75,1,ea_under_review;exact_check
+ea_prime_number_theorem,optimize,research,number_theory,EinsteinArena/prime-number-theorem,MIT,pnt_chebyshev_certificate,1,float_objective;range_limited_certificate
+ea_ring_loading_15,optimize,research,combinatorics,EinsteinArena/ring-loading-15,MIT,ring_loading_m15,1,ea_under_review;exact_check
+ea_second_autocorrelation,optimize,research,analysis,EinsteinArena/second-autocorrelation-inequality,MIT,second_autocorrelation_inequality_lower,1,float_objective
+ea_shannon_c7_5,optimize,research,graph_theory,EinsteinArena/shannon-capacity-c7-5,MIT,independent_set_c7_strong_power5,1,ea_under_review;exact_check
+ea_sidon_45_set,optimize,research,number_theory,EinsteinArena/sidon-45-set,MIT,sidon_subsets_of_45_sets,1,ea_under_review;exact_check
+ea_snake_in_the_box_13,optimize,research,graph_theory,EinsteinArena/snake-in-the-box-13,MIT,snake_in_the_box_d13,1,ea_under_review;exact_check
+ea_sorting_network_16,optimize,research,combinatorics,EinsteinArena/sorting-network-16,MIT,sorting_network_size_n16,1,ea_under_review;exact_check
+ea_spencer_discrepancy,optimize,research,combinatorics,EinsteinArena/spencer-discrepancy,MIT,spencer_discrepancy_square_n_le20,1,ea_under_review;exact_check
+ea_tammes,optimize,research,discrete_geometry,EinsteinArena/tammes-problem,MIT,tammes_n50,1,float_objective
+ea_third_autocorrelation,optimize,research,analysis,EinsteinArena/third-autocorrelation-inequality,MIT,third_autocorrelation_inequality_upper,1,float_objective
+ea_thomson_282,optimize,research,discrete_geometry,EinsteinArena/thomson-problem,MIT,thomson_problem_n282,1,float_objective
+ea_two_deletion_code_16,optimize,research,coding_theory,EinsteinArena/two-deletion-code-16,MIT,two_deletion_code_n16,1,ea_under_review;exact_check
+ea_uncertainty_principle,optimize,research,analysis,EinsteinArena/uncertainty-principle,MIT,plus1_uncertainty_principle_upper,1,high_precision
+finch_3ap_diffs_40,optimize,research,combinatorics,Finch-EFT/skydiscover/erdos_1097_3ap_diffs_n40,Apache-2.0,erdos1097_3ap_differences_n40_m400,1,best_known_uncertain;exact_check;np_search
+finch_4subset_3dist_16,optimize,research,discrete_geometry,Finch-EFT/skydiscover/erdos_659_4subset_3dist_construction,Apache-2.0,erdos659_4sets_3dist_n16,1,best_known_uncertain;exact_check;np_search
+finch_flat_poly_32,optimize,research,analysis,Finch-EFT/skydiscover/erdos_flat_polynomials_n32,Apache-2.0,flat_littlewood_polynomial_n32,1,best_known_uncertain;float_objective;np_search
+finch_heilbronn_disk_12,optimize,research,discrete_geometry,Finch-EFT/skydiscover/erdos_507_heilbronn_disk_n12,Apache-2.0,heilbronn_disk_n12,1,best_known_uncertain;exact_check;float_objective
+finch_isosceles_free_grid_8,optimize,competition,discrete_geometry,Finch-EFT/skydiscover/erdos_isosceles_free_grid,Apache-2.0,isosceles_free_grid_subset,1,exact_check;exact_optimum_known;np_search
+finch_lcm_chain_10000,optimize,competition,number_theory,Finch-EFT/skydiscover/erdos_440_lcm_density,Apache-2.0,erdos440_lcm_consecutive_x10000,1,exact_check;exact_optimum_known
+finch_newman_200,optimize,research,number_theory,Finch-EFT/skydiscover/erdos_480_newman_density,Apache-2.0,erdos480_newman_finite_n200,1,best_known_uncertain;float_objective
+finch_no4_concyclic_12,optimize,research,discrete_geometry,Finch-EFT/skydiscover/erdos_654_no_four_concyclic_distances,Apache-2.0,erdos654_no4_concyclic_n12,1,best_known_uncertain;exact_check;np_search
+finch_sidon_pair_100,optimize,research,number_theory,Finch-EFT/skydiscover/erdos_43_sidon_pair,Apache-2.0,erdos43_sidon_pair_n100,1,best_known_uncertain;exact_check;np_search
+finch_sidon_set_121,optimize,competition,number_theory,Finch-EFT/skydiscover/erdos_difference_bases_N121,Apache-2.0,max_sidon_set_0_120,1,exact_check;exact_optimum_known
+finch_square_packing_12,optimize,research,discrete_geometry,Finch-EFT/skydiscover/erdos_106_square_packing,Apache-2.0,erdos106_squares_in_square_n12,1,exact_check
+finch_udg_girth_30,optimize,research,graph_theory,Finch-EFT/skydiscover/erdos_705_unit_distance_high_girth,Apache-2.0,erdos705_udg_chi4_girth_n30,1,best_known_uncertain;exact_check
+fs_admissible_set,optimize,research,combinatorics,FunSearch/admissible_set,Apache-2.0,admissible_set_constant_weight,2,integer_objective
+fs_cap_set,optimize,research,combinatorics,FunSearch/cap_set,Apache-2.0,cap_set_f3n,6,integer_objective
+fs_cycle_independent_set,optimize,research,graph_theory,FunSearch/cyclic_graphs,Apache-2.0,independent_set_strong_power_odd_cycle,7,integer_objective
+mc_all_interval,construct,competition,combinatorics,MathConstraint/all_interval,CC-BY-4.0,all_interval_series,40,agentic_trivial
+mc_antimagic_square,construct,competition,combinatorics,MathConstraint/antimagic_square,CC-BY-4.0,antimagic_square,6,np_search
+mc_bibd,construct,competition,combinatorics,MathConstraint/bibd,CC-BY-4.0,bibd,28,np_search
+mc_costas_array,construct,competition,combinatorics,MathConstraint/costas_array,CC-BY-4.0,costas_array,23,np_search
+mc_debruijn,construct,competition,combinatorics,MathConstraint/debruijn,CC-BY-4.0,de_bruijn_sequence,22,agentic_trivial
+mc_golomb,construct,competition,combinatorics,MathConstraint/golomb,CC-BY-4.0,golomb_ruler,18,np_search
+mc_graceful_graph,construct,competition,graph_theory,MathConstraint/graceful_graph,CC-BY-4.0,graceful_labeling,17,np_search
+mc_graph_k_coloring,construct,competition,graph_theory,MathConstraint/graph_k_coloring,CC-BY-4.0,graph_k_coloring,48,np_search
+mc_hadamard,construct,competition,combinatorics,MathConstraint/hadamard,CC-BY-4.0,legendre_pair,30,np_search
+mc_langford,construct,competition,combinatorics,MathConstraint/langford,CC-BY-4.0,langford_pairing,27,agentic_trivial;np_search
+mc_low_autocorrelation,construct,competition,combinatorics,MathConstraint/low_autocorrelation,CC-BY-4.0,low_autocorrelation_binary_sequence,31,np_search
+mc_magic_sequence,construct,competition,combinatorics,MathConstraint/magic_sequence,CC-BY-4.0,magic_sequence,30,agentic_trivial
+mc_max_clique,construct,competition,graph_theory,MathConstraint/max_clique,CC-BY-4.0,graph_clique,55,np_search
+mc_max_independent_set,construct,competition,graph_theory,MathConstraint/max_independent_set,CC-BY-4.0,graph_independent_set,60,np_search
+mc_non_transitive_dice,construct,competition,probability,MathConstraint/non_transitive_dice,CC-BY-4.0,intransitive_dice,15,agentic_trivial;np_search
+mc_number_partitioning,construct,competition,number_theory,MathConstraint/number_partitioning,CC-BY-4.0,equal_sum_partition_1_to_n,59,agentic_trivial
+mc_ortholatin,construct,competition,combinatorics,MathConstraint/ortholatin,CC-BY-4.0,orthogonal_latin_squares,21,np_search
+mc_pysms_chromatic_girth,construct,competition,graph_theory,MathConstraint/pysms_chromatic_girth,CC-BY-4.0,graph_existence_chromatic_girth,25,np_search
+mc_pysms_clique_coloring,construct,competition,graph_theory,MathConstraint/pysms_clique_coloring,CC-BY-4.0,graph_existence_clique_coloring,16,np_search
+mc_pysms_degree_bounds,construct,competition,graph_theory,MathConstraint/pysms_degree_bounds,CC-BY-4.0,graph_existence_degree_bounds,11,agentic_trivial;np_search
+mc_pysms_girth_degree,construct,competition,graph_theory,MathConstraint/pysms_girth_degree,CC-BY-4.0,graph_existence_girth_degree,18,np_search
+mc_pysms_graph_builder,construct,competition,graph_theory,MathConstraint/pysms_graph_builder,CC-BY-4.0,graph_existence_graph_builder,8,np_search
+mc_pysms_independent_connectivity,construct,competition,graph_theory,MathConstraint/pysms_independent_connectivity,CC-BY-4.0,graph_existence_independent_connectivity,15,np_search
+mc_pysms_min_connectivity,construct,competition,graph_theory,MathConstraint/pysms_min_connectivity,CC-BY-4.0,graph_existence_min_connectivity,12,agentic_trivial;np_search
+mc_pysms_min_degree,construct,competition,graph_theory,MathConstraint/pysms_min_degree,CC-BY-4.0,graph_existence_min_degree,12,agentic_trivial;np_search
+mc_pysms_min_girth,construct,competition,graph_theory,MathConstraint/pysms_min_girth,CC-BY-4.0,graph_existence_min_girth,13,agentic_trivial;np_search
+mc_pysms_mtf,construct,competition,graph_theory,MathConstraint/pysms_mtf,CC-BY-4.0,maximal_triangle_free_graph,12,agentic_trivial;np_search
+mc_pysms_num_edges_bounds,construct,competition,graph_theory,MathConstraint/pysms_num_edges_bounds,CC-BY-4.0,graph_existence_num_edges_bounds,12,agentic_trivial;np_search
+mc_quasigroup_idempotent,construct,competition,algebra,MathConstraint/quasigroup_idempotent,CC-BY-4.0,idempotent_qg3_quasigroup,12,np_search
+mc_ramsey,construct,competition,combinatorics,MathConstraint/ramsey,CC-BY-4.0,ramsey_two_colouring,54,np_search
+mc_social_golfers,construct,competition,combinatorics,MathConstraint/social_golfers,CC-BY-4.0,social_golfer,23,np_search
+mc_van_der_waerden,construct,competition,combinatorics,MathConstraint/van_der_waerden,CC-BY-4.0,van_der_waerden_colouring,42,np_search
+mc_vertex_cover,construct,competition,graph_theory,MathConstraint/vertex_cover,CC-BY-4.0,graph_vertex_cover,60,np_search
+nppc_bandwidth,construct,competition,graph_theory,NPPC/bandwidth,MIT,graph_bandwidth,60,agentic_trivial;np_search
+nppc_clique,construct,competition,graph_theory,NPPC/clique,MIT,graph_clique,60,agentic_trivial;np_search
+nppc_dominating_set,construct,competition,graph_theory,NPPC/dominating_set,MIT,graph_dominating_set,60,agentic_trivial;np_search
+nppc_independent_set,construct,competition,graph_theory,NPPC/independent_set,MIT,graph_independent_set,60,agentic_trivial;np_search
+nppc_quad_diophantine,construct,competition,number_theory,NPPC/quad_diop_equ,MIT,quadratic_diophantine_ax2_by_c,60,agentic_trivial;np_search
+nppc_quadratic_congruence,construct,competition,number_theory,NPPC/quadratic_congruence,MIT,quadratic_congruence_bounded,60,agentic_trivial;np_search
+nppc_three_coloring,construct,competition,graph_theory,NPPC/graph_three_colorability,MIT,graph_3_coloring,60,agentic_trivial;np_search
+nppc_vertex_cover,construct,competition,graph_theory,NPPC/vertex_cover,MIT,graph_vertex_cover,60,agentic_trivial;np_search
+rg_graph_color,construct,competition,graph_theory,ReasoningGym/graph_color,Apache-2.0,graph_k_coloring,60,agentic_trivial;np_search
+rg_intermediate_integration,construct,competition,analysis,ReasoningGym/intermediate_integration,Apache-2.0,symbolic_antiderivative,60,symbolic
+rg_simple_integration,construct,competition,analysis,ReasoningGym/simple_integration,Apache-2.0,symbolic_antiderivative_polynomial,60,symbolic
+rlve_antiderivative,construct,competition,analysis,RLVE-Gym/integral,MIT,symbolic_antiderivative,60,
+rlve_bezout_identity,construct,competition,number_theory,RLVE-Gym/bezout_identity,MIT,bezout_coefficients,60,agentic_trivial
+rlve_construct_hack_interval,construct,competition,number_theory,RLVE-Gym/construct_hack_interval,MIT,cf468c_hack_interval,60,
+rlve_crt,construct,competition,number_theory,RLVE-Gym/crt,MIT,generalized_crt,60,agentic_trivial
+rlve_distinct_subset_sum_permutation,construct,competition,combinatorics,RLVE-Gym/distinct_array_permutation,MIT,cf892d_gluttony,60,agentic_trivial
+rlve_even_degree_partition,construct,competition,graph_theory,RLVE-Gym/even_degree_graph_partitioning,MIT,gallai_even_partition,60,agentic_trivial
+rlve_graph_isomorphism,construct,competition,graph_theory,RLVE-Gym/graph_isomorphism,MIT,graph_isomorphism,60,agentic_trivial;np_search
+rlve_grid_parity_construction,construct,competition,algebra,RLVE-Gym/grid_parity_construction,MIT,lights_out_gf2,60,agentic_trivial
+rlve_imp_party,construct,competition,graph_theory,RLVE-Gym/imp_party,MIT,poi_party_clique_3n,60,agentic_trivial
+rlve_integer_linear_system,construct,competition,algebra,RLVE-Gym/gaussian_elimination,MIT,integer_linear_system,60,agentic_trivial
+rlve_largest_convex_polygon,construct,competition,discrete_geometry,RLVE-Gym/largest_convex_polygon,MIT,largest_convex_subset,60,agentic_trivial
+rlve_largest_rectangle,construct,competition,discrete_geometry,RLVE-Gym/largest_rectangle_among_points,MIT,largest_rectangle_in_point_set,60,agentic_trivial
+rlve_matrix_permutation_equivalence,construct,competition,combinatorics,RLVE-Gym/matrix_permutation_equivalence,MIT,binary_matrix_permutation_equivalence,60,agentic_trivial;np_search
+rlve_max_achromatic_coloring,construct,competition,graph_theory,RLVE-Gym/maximum_achromatic_number,MIT,achromatic_number,60,agentic_trivial;np_search
+rlve_maximum_clique,construct,competition,graph_theory,RLVE-Gym/maximum_clique,MIT,maximum_clique,60,agentic_trivial;np_search
+rlve_min_chromatic_number,construct,competition,graph_theory,RLVE-Gym/minimum_chromatic_number,MIT,graph_k_coloring_chromatic,60,agentic_trivial;np_search
+rlve_min_harmonious_coloring,construct,competition,graph_theory,RLVE-Gym/minimum_harmonious_chromatic_number,MIT,harmonious_chromatic_number,60,agentic_trivial;np_search
+rlve_pairwise_sums_recovery,construct,competition,combinatorics,RLVE-Gym/squ_squarks,MIT,poi_squarks_pairwise_sums,60,agentic_trivial
+rlve_pan_solar_panels,construct,competition,number_theory,RLVE-Gym/pan_solar_panels,MIT,poi_solar_panels_max_gcd,60,agentic_trivial
+rlve_polynomial_global_minimum,construct,competition,analysis,RLVE-Gym/polynomial_minimum,MIT,polynomial_global_minimum,60,agentic_trivial
+rlve_polynomial_integer_roots,construct,competition,algebra,RLVE-Gym/polynomial_factorization,MIT,integer_root_factorization,60,agentic_trivial;unique_answer
+rlve_polynomial_interpolation,construct,competition,algebra,RLVE-Gym/polynomial_interpolation,MIT,lagrange_interpolation_integer,60,agentic_trivial;unique_answer
+rlve_prefix_product_permutation,construct,competition,number_theory,RLVE-Gym/prefix_product_mod_distinct_permutation,MIT,cf487c_prefix_product_sequence,60,
+rlve_prefix_sum_permutation,construct,competition,number_theory,RLVE-Gym/prefix_sum_mod_distinct_permutation,MIT,prefix_sum_mod_distinct_permutation,60,
+rlve_prime_graph_coloring,construct,competition,graph_theory,RLVE-Gym/prime_graph_minimum_chromatic_number,MIT,prime_distance_graph_coloring,60,agentic_trivial
+rlve_recursive_sequence_sum,construct,competition,number_theory,RLVE-Gym/recursive_sequence_sum_construction,MIT,linear_recurrence_subset_sum,60,agentic_trivial
+rlve_round_robin_scores,construct,competition,combinatorics,RLVE-Gym/round_robin,MIT,tournament_score_realisation_3_1_0,60,agentic_trivial
+rlve_shortest_path_count,construct,competition,combinatorics,RLVE-Gym/shortest_path_count_construction,MIT,cf388b_shortest_path_count,60,
+rlve_smallest_enclosing_circle,construct,competition,geometry,RLVE-Gym/smallest_circle,MIT,minimum_enclosing_circle,60,agentic_trivial
+rlve_subgraph_isomorphism,construct,competition,graph_theory,RLVE-Gym/subgraph_isomorphism,MIT,induced_subgraph_isomorphism,60,agentic_trivial;np_search

tasks/construct-mc-low-autocorrelation-l5-s2/instruction.md

@@ -0,0 +1,7 @@
+For a sequence seq[0..39] with entries in {-1, +1}, define the aperiodic autocorrelations C_k = sum_{i=0}^{40-k-1} seq[i]*seq[i+k] for k = 1..39 and the energy E = sum_k C_k^2.
+
+Find a sequence of length 40 with E <= 108.
+
+Answer format: {"seq": [s_0, s_1, ..., s_39]} with every s_i equal to -1 or 1
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-mc-low-autocorrelation-l5-s2/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-low-autocorrelation-l5-s2"
+version = "0.2.0"
+description = "construct/mc_low_autocorrelation"
+authors = []
+keywords = ["rlmath", "construct", "mc_low_autocorrelation"]
+
+[metadata]
+subset = "construct"
+family = "mc_low_autocorrelation"
+problem_key = "low_autocorrelation_binary_sequence"
+domain = "combinatorics"
+tier = "competition"
+level = "5"
+source = "MathConstraint/low_autocorrelation"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-mc-number-partitioning-l2-s2/instruction.md

@@ -0,0 +1,7 @@
+Partition the integers 1, 2, ..., 15 into 3 disjoint subsets (numbered 0..2) that all have the same sum 40 (the total is 120).
+
+Find such a partition.
+
+Answer format: {"x": [x_1, ..., x_15]}: a list of 15 integers in 0..2, where the i-th entry (0-indexed) is the subset containing the integer i+1
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-mc-number-partitioning-l2-s2/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-number-partitioning-l2-s2"
+version = "0.2.0"
+description = "construct/mc_number_partitioning"
+authors = []
+keywords = ["rlmath", "construct", "mc_number_partitioning"]
+
+[metadata]
+subset = "construct"
+family = "mc_number_partitioning"
+problem_key = "equal_sum_partition_1_to_n"
+domain = "number_theory"
+tier = "competition"
+level = "2"
+source = "MathConstraint/number_partitioning"
+source_license = "CC-BY-4.0"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-mc-pysms-chromatic-girth-l4-s3/instruction.md

@@ -0,0 +1,8 @@
+Construct a simple undirected graph on the 20 vertices 0..19 such that:
+  - the graph has at least 21 edges
+  - the chromatic number is at most 3: the vertices can be coloured with colours 0..2 so that adjacent vertices get different colours (you must also give such a colouring)
+  - the girth is at least 7: the graph has no cycle of length less than 7 (a graph without cycles qualifies)
+
+Answer format: {"edges": [[u, v], ...], "coloring": [c_0, ..., c_19]} where each edge is a pair of distinct vertices in 0..19, listed once; coloring[i] is the colour (0..2) of vertex i
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-mc-pysms-chromatic-girth-l4-s3/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-pysms-chromatic-girth-l4-s3"
+version = "0.2.0"
+description = "construct/mc_pysms_chromatic_girth"
+authors = []
+keywords = ["rlmath", "construct", "mc_pysms_chromatic_girth"]
+
+[metadata]
+subset = "construct"
+family = "mc_pysms_chromatic_girth"
+problem_key = "graph_existence_chromatic_girth"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "MathConstraint/pysms_chromatic_girth"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-mc-van-der-waerden-l2-s4/instruction.md

@@ -0,0 +1,7 @@
+Colour the integers 1, 2, ..., 24 with 2 colours (numbered 0..1) so that there is no monochromatic arithmetic progression of length 4: no a >= 1, d >= 1 with a + 3*d <= 24 such that a, a+d, ..., a+3*d all have the same colour.
+
+Find such a colouring.
+
+Answer format: {"colors": [c_1, ..., c_24]}: 24 integers in 0..1; the i-th entry (0-indexed) is the colour of the integer i+1
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-mc-van-der-waerden-l2-s4/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-mc-van-der-waerden-l2-s4"
+version = "0.2.0"
+description = "construct/mc_van_der_waerden"
+authors = []
+keywords = ["rlmath", "construct", "mc_van_der_waerden"]
+
+[metadata]
+subset = "construct"
+family = "mc_van_der_waerden"
+problem_key = "van_der_waerden_colouring"
+domain = "combinatorics"
+tier = "competition"
+level = "2"
+source = "MathConstraint/van_der_waerden"
+source_license = "CC-BY-4.0"
+tags = ["np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-nppc-3col-l3-s3/instruction.md

@@ -0,0 +1,8 @@
+Graph with 30 vertices labelled 0..29 and edge list
+[[0, 1], [0, 9], [0, 10], [0, 14], [1, 7], [1, 8], [1, 12], [1, 16], [1, 25], [1, 26], [2, 19], [2, 25], [3, 12], [3, 27], [4, 10], [4, 12], [4, 21], [5, 21], [5, 22], [6, 17], [6, 23], [6, 29], [7, 9], [7, 23], [7, 26], [8, 26], [10, 17], [11, 12], [11, 18], [11, 27], [12, 22], [12, 24], [12, 25], [13, 16], [13, 19], [13, 25], [13, 28], [14, 17], [14, 20], [14, 21], [14, 25], [15, 16], [15, 18], [15, 26], [16, 21], [16, 22], [17, 25], [18, 20], [18, 24], [18, 25], [18, 29], [19, 24], [21, 24], [21, 26], [21, 27], [22, 23], [22, 26], [23, 28], [25, 26], [25, 29]]
+
+Give a proper colouring with colours 0, 1, 2: adjacent vertices must get different colours.
+
+Answer format: {"coloring": [c_0, ..., c_29]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-nppc-dominating-set-l4-s8/instruction.md

@@ -0,0 +1,8 @@
+Undirected graph with 100 vertices labelled 0..99 and 1651 edges:
+[[0, 1], [0, 2], [0, 3], [0, 7], [0, 13], [0, 16], [0, 17], [0, 18], [0, 20], [0, 26], [0, 27], [0, 34], [0, 39], [0, 43], [0, 44], [0, 47], [0, 49], [0, 51], [0, 53], [0, 54], [0, 57], [0, 59], [0, 60], [0, 61], [0, 62], [0, 72], [0, 73], [0, 75], [0, 80], [0, 82], [0, 84], [0, 86], [0, 87], [0, 89], [0, 91], [0, 94], [0, 99], [1, 4], [1, 6], [1, 11], [1, 12], [1, 14], [1, 16], [1, 17], [1, 18], [1, 20], [1, 22], [1, 27], [1, 29], [1, 34], [1, 37], [1, 38], [1, 39], [1, 42], [1, 43], [1, 44], [1, 49], [1, 51], [1, 53], [1, 54], [1, 58], [1, 59], [1, 61], [1, 62], [1, 63], [1, 65], [1, 66], [1, 68], [1, 70], [1, 71], [1, 72], [1, 73], [1, 78], [1, 80], [1, 81], [1, 92], [1, 93], [1, 94], [2, 3], [2, 6], [2, 7], [2, 20], [2, 24], [2, 25], [2, 30], [2, 31], [2, 32], [2, 34], [2, 35], [2, 37], [2, 41], [2, 43], [2, 44], [2, 47], [2, 50], [2, 55], [2, 56], [2, 57], [2, 62], [2, 63], [2, 64], [2, 65], [2, 66], [2, 67], [2, 72], [2, 79], [2, 81], [2, 82], [2, 88], [2, 91], [2, 92], [2, 93], [3, 5], [3, 6], [3, 8], [3, 9], [3, 11], [3, 13], [3, 14], [3, 15], [3, 16], [3, 17], [3, 23], [3, 24], [3, 26], [3, 27], [3, 29], [3, 35], [3, 38], [3, 39], [3, 48], [3, 51], [3, 52], [3, 55], [3, 56], [3, 60], [3, 61], [3, 62], [3, 63], [3, 64], [3, 65], [3, 66], [3, 67], [3, 68], [3, 70], [3, 74], [3, 75], [3, 76], [3, 77], [3, 78], [3, 79], [3, 82], [3, 84], [3, 85], [3, 87], [3, 90], [3, 98], [4, 11], [4, 16], [4, 17], [4, 18], [4, 20], [4, 22], [4, 23], [4, 24], [4, 34], [4, 36], [4, 39], [4, 44], [4, 46], [4, 47], [4, 49], [4, 57], [4, 60], [4, 61], [4, 62], [4, 63], [4, 65], [4, 69], [4, 72], [4, 74], [4, 83], [4, 86], [4, 94], [4, 96], [5, 9], [5, 10], [5, 17], [5, 22], [5, 25], [5, 30], [5, 31], [5, 32], [5, 34], [5, 35], [5, 37], [5, 39], [5, 40], [5, 49], [5, 51], [5, 54], [5, 63], [5, 66], [5, 67], [5, 69], [5, 70], [5, 71], [5, 74], [5, 76], [5, 83], [5, 85], [5, 86], [5, 88], [5, 91], [5, 93], [5, 97], [5, 98], [5, 99], [6, 9], [6, 13], [6, 16], [6, 20], [6, 23], [6, 24], [6, 25], [6, 26], [6, 28], [6, 29], [6, 32], [6, 38], [6, 46], [6, 52], [6, 58], [6, 61], [6, 62], [6, 63], [6, 64], [6, 67], [6, 68], [6, 70], [6, 77], [6, 79], [6, 80], [6, 82], [6, 84], [6, 87], [6, 88], [6, 90], [6, 95], [6, 96], [7, 9], [7, 10], [7, 14], [7, 15], [7, 16], [7, 20], [7, 23], [7, 28], [7, 29], [7, 31], [7, 36], [7, 37], [7, 39], [7, 43], [7, 45], [7, 46], [7, 47], [7, 48], [7, 49], [7, 50], [7, 51], [7, 52], [7, 53], [7, 54], [7, 55], [7, 60], [7, 62], [7, 63], [7, 64], [7, 65], [7, 68], [7, 72], [7, 74], [7, 75], [7, 79], [7, 80], [7, 81], [7, 82], [7, 89], [7, 92], [7, 94], [7, 99], [8, 11], [8, 14], [8, 17], [8, 20], [8, 23], [8, 24], [8, 26], [8, 27], [8, 31], [8, 32], [8, 40], [8, 42], [8, 44], [8, 45], [8, 47], [8, 48], [8, 52], [8, 58], [8, 59], [8, 61], [8, 64], [8, 67], [8, 73], [8, 75], [8, 77], [8, 80], [8, 82], [8, 88], [8, 90], [8, 97], [8, 98], [9, 13], [9, 20], [9, 24], [9, 25], [9, 35], [9, 36], [9, 37], [9, 38], [9, 43], [9, 47], [9, 48], [9, 61], [9, 62], [9, 63], [9, 65], [9, 67], [9, 69], [9, 70], [9, 76], [9, 81], [9, 83], [9, 85], [9, 86], [9, 87], [9, 89], [9, 90], [9, 96], [10, 12], [10, 16], [10, 17], [10, 18], [10, 19], [10, 21], [10, 22], [10, 29], [10, 33], [10, 35], [10, 36], [10, 38], [10, 46], [10, 57], [10, 58], [10, 61], [10, 63], [10, 66], [10, 75], [10, 92], [10, 93], [10, 98], [11, 13], [11, 15], [11, 16], [11, 22], [11, 30], [11, 32], [11, 34], [11, 37], [11, 38], [11, 40], [11, 41], [11, 46], [11, 48], [11, 49], [11, 57], [11, 74], [11, 75], [11, 76], [11, 87], [11, 96], [11, 98], [11, 99], [12, 16], [12, 18], [12, 19], [12, 21], [12, 22], [12, 23], [12, 31], [12, 32], [12, 36], [12, 39], [12, 41], [12, 47], [12, 52], [12, 61], [12, 63], [12, 64], [12, 68], [12, 71], [12, 86], [12, 93], [12, 95], [12, 97], [13, 14], [13, 15], [13, 16], [13, 20], [13, 25], [13, 27], [13, 28], [13, 29], [13, 31], [13, 34], [13, 36], [13, 37], [13, 38], [13, 39], [13, 40], [13, 44], [13, 47], [13, 51], [13, 61], [13, 62], [13, 64], [13, 65], [13, 66], [13, 76], [13, 77], [13, 80], [13, 86], [13, 97], [13, 98], [14, 19], [14, 23], [14, 25], [14, 32], [14, 34], [14, 40], [14, 46], [14, 51], [14, 52], [14, 55], [14, 56], [14, 58], [14, 66], [14, 76], [14, 83], [14, 87], [14, 91], [14, 97], [14, 98], [14, 99], [15, 22], [15, 29], [15, 30], [15, 37], [15, 43], [15, 44], [15, 45], [15, 47], [15, 48], [15, 49], [15, 50], [15, 53], [15, 60], [15, 64], [15, 66], [15, 68], [15, 69], [15, 71], [15, 73], [15, 74], [15, 77], [15, 78], [15, 86], [15, 88], [15, 96], [16, 17], [16, 19], [16, 20], [16, 21], [16, 22], [16, 27], [16, 29], [16, 31], [16, 34], [16, 38], [16, 42], [16, 44], [16, 47], [16, 54], [16, 56], [16, 57], [16, 58], [16, 67], [16, 72], [16, 73], [16, 76], [16, 77], [16, 84], [16, 86], [16, 90], [16, 92], [16, 94], [16, 99], [17, 21], [17, 22], [17, 23], [17, 24], [17, 32], [17, 33], [17, 36], [17, 38], [17, 39], [17, 46], [17, 47], [17, 49], [17, 50], [17, 53], [17, 57], [17, 58], [17, 60], [17, 63], 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[91, 93], [91, 96], [92, 93], [92, 94], [92, 97], [92, 99], [93, 96], [93, 98], [94, 97], [95, 96], [95, 97], [95, 98], [97, 98], [97, 99], [98, 99]]
+
+Find a dominating set of size at most 20: a set D of distinct vertices such that every vertex is in D or adjacent to a vertex of D.
+
+Answer format: {"dominating_set": [v_1, v_2, ...]} (distinct integers in 0..99, at most 20 of them).
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-nppc-dominating-set-l4-s8/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-nppc-dominating-set-l4-s8"
+version = "0.2.0"
+description = "construct/nppc_dominating_set"
+authors = []
+keywords = ["rlmath", "construct", "nppc_dominating_set"]
+
+[metadata]
+subset = "construct"
+family = "nppc_dominating_set"
+problem_key = "graph_dominating_set"
+domain = "graph_theory"
+tier = "competition"
+level = "4"
+source = "NPPC/dominating_set"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rg-graph-color-l1-s1/instruction.md

@@ -0,0 +1,9 @@
+Colour the vertices of this graph so that no two adjacent vertices have the same colour.
+
+Vertices: [0, 1, 2, 3, 4, 5]
+Edges: [[0, 2], [0, 4], [0, 5], [1, 5], [2, 3]]
+Possible colours: [1, 2, 3, 4]
+
+Answer format: {"coloring": [c_0, c_1, ..., c_5]} where c_i in 1..4 is the colour of vertex i
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rg-graph-color-l1-s1/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-graph-color-l1-s1"
+version = "0.2.0"
+description = "construct/rg_graph_color"
+authors = []
+keywords = ["rlmath", "construct", "rg_graph_color"]
+
+[metadata]
+subset = "construct"
+family = "rg_graph_color"
+problem_key = "graph_k_coloring"
+domain = "graph_theory"
+tier = "competition"
+level = "1"
+source = "ReasoningGym/graph_color"
+source_license = "Apache-2.0"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rg-simple-integration-l5-s8/instruction.md

@@ -0,0 +1,11 @@
+Find an antiderivative F(X) of
+
+    f(X) = -9*X**8/5 + 4*X**7 - 7*X**6 + 24*X**3 + 2/3
+
+i.e. any F with dF/dX = f(X).
+
+Write the antiderivative as a single expression in the variable X using Python/SymPy syntax: + - * / and ** for powers (always write * for multiplication), parentheses, the constants E and pi, and the functions sin, cos, tan, asin, acos, atan, sinh, cosh, tanh, exp, log (natural logarithm), sqrt, Abs. An additive constant such as + C is optional.
+
+Answer format: {"antiderivative": "<expression>"}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rg-simple-integration-l5-s8/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rg-simple-integration-l5-s8"
+version = "0.2.0"
+description = "construct/rg_simple_integration"
+authors = []
+keywords = ["rlmath", "construct", "rg_simple_integration"]
+
+[metadata]
+subset = "construct"
+family = "rg_simple_integration"
+problem_key = "symbolic_antiderivative_polynomial"
+domain = "analysis"
+tier = "competition"
+level = "5"
+source = "ReasoningGym/simple_integration"
+source_license = "Apache-2.0"
+tags = ["symbolic"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-antiderivative-l4-s1/instruction.md

@@ -0,0 +1,11 @@
+Find an antiderivative F(x) of
+
+f(x) = 36*x + 6
+
+(sympy syntax; log is the natural logarithm), i.e. any expression with F'(x) = f(x). Any constant of integration and any equivalent form is accepted.
+
+Write F as a string in sympy syntax using only: the variable x, integer literals, + - * / ** and parentheses, and the functions sin cos tan asin acos atan sinh cosh tanh exp log sqrt and constants E, pi (no decimals, no other names; always write * explicitly).
+
+Answer format: {"F": "<expression>"}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-antiderivative-l4-s1/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-antiderivative-l4-s1"
+version = "0.2.0"
+description = "construct/rlve_antiderivative"
+authors = []
+keywords = ["rlmath", "construct", "rlve_antiderivative"]
+
+[metadata]
+subset = "construct"
+family = "rlve_antiderivative"
+problem_key = "symbolic_antiderivative"
+domain = "analysis"
+tier = "competition"
+level = "4"
+source = "RLVE-Gym/integral"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-bezout-identity-l1-s4/instruction.md

@@ -0,0 +1,10 @@
+You are given 2 nonzero integers A = [-7, -7] (A[0], ..., A[1]).
+
+Find integers X[0], ..., X[1] (any sign, any size) such that
+S = A[0]*X[0] + ... + A[1]*X[1] = 7.
+
+(7 is the smallest positive value S can take.)
+
+Answer format: {"X": [X_0, ..., X_1]}  (a JSON list of 2 integers)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-bezout-identity-l1-s4/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-bezout-identity-l1-s4"
+version = "0.2.0"
+description = "construct/rlve_bezout_identity"
+authors = []
+keywords = ["rlmath", "construct", "rlve_bezout_identity"]
+
+[metadata]
+subset = "construct"
+family = "rlve_bezout_identity"
+problem_key = "bezout_coefficients"
+domain = "number_theory"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/bezout_identity"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-crt-l6-s0/instruction.md

@@ -0,0 +1,13 @@
+Find any non-negative integer x satisfying all of the following 8 congruences (the moduli need not be pairwise coprime; the system is consistent):
+x ≡ 15623008382971 (mod 16799074560376)
+x ≡ 33146323976667 (mod 100070206328936)
+x ≡ 12295310146698 (mod 24184244031781)
+x ≡ 3420224519430 (mod 129796305786173)
+x ≡ 17265682835099 (mod 38650282490168)
+x ≡ 64214877424117 (mod 69001652881486)
+x ≡ 478289381863 (mod 13273824092374)
+x ≡ 15474596783279 (mod 117741933522324)
+
+Answer format: {"x": <non-negative integer>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-crt-l6-s0/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-crt-l6-s0"
+version = "0.2.0"
+description = "construct/rlve_crt"
+authors = []
+keywords = ["rlmath", "construct", "rlve_crt"]
+
+[metadata]
+subset = "construct"
+family = "rlve_crt"
+problem_key = "generalized_crt"
+domain = "number_theory"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/crt"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-distinct-subset-sum-permutation-l3-s8/instruction.md

@@ -0,0 +1,7 @@
+You are given an array A of 10 distinct integers: A = [6, 0, 13, 7, 4, 14, 17, 5, 15, 11] (positions 1..10).
+
+Output an array B that is a permutation of A such that for every non-empty proper subset S of positions (S a subset of {1, ..., 10}, 0 < |S| < 10) the sums of A and of B over the positions in S are different.
+
+Answer format: {"B": [B_1, ..., B_10]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-distinct-subset-sum-permutation-l3-s8/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-distinct-subset-sum-permutation-l3-s8"
+version = "0.2.0"
+description = "construct/rlve_distinct_subset_sum_permutation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_distinct_subset_sum_permutation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_distinct_subset_sum_permutation"
+problem_key = "cf892d_gluttony"
+domain = "combinatorics"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/distinct_array_permutation"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-even-degree-partition-l2-s6/instruction.md

@@ -0,0 +1,8 @@
+An undirected simple graph has 8 vertices labelled 0..7 and edge list
+[[0, 2], [0, 5], [1, 3], [1, 4], [1, 5], [1, 7], [3, 4], [3, 5], [4, 5], [4, 6], [5, 7], [6, 7]]
+
+Assign every vertex to group 1 or group 2 so that, for every vertex v, the number of neighbours of v lying in the same group as v is even (zero counts as even). One of the groups may be empty.
+
+Answer format: {"groups": [g_0, ..., g_7]}  with each g_i in {1, 2}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-even-degree-partition-l2-s6/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-even-degree-partition-l2-s6"
+version = "0.2.0"
+description = "construct/rlve_even_degree_partition"
+authors = []
+keywords = ["rlmath", "construct", "rlve_even_degree_partition"]
+
+[metadata]
+subset = "construct"
+family = "rlve_even_degree_partition"
+problem_key = "gallai_even_partition"
+domain = "graph_theory"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/even_degree_graph_partitioning"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-even-degree-partition-l6-s9/instruction.md

@@ -0,0 +1,8 @@
+An undirected simple graph has 40 vertices labelled 0..39 and edge list
+[[0, 2], [0, 3], [0, 5], [0, 6], [0, 10], [0, 11], [0, 12], [0, 13], [0, 14], [0, 15], [0, 16], [0, 17], [0, 19], [0, 20], [0, 21], [0, 22], [0, 23], [0, 24], [0, 25], [0, 26], [0, 27], [0, 28], [0, 30], [0, 31], [0, 32], [0, 33], [0, 34], [0, 35], [0, 36], [0, 37], [0, 39], [1, 3], [1, 8], [1, 10], [1, 22], [1, 29], [1, 35], [2, 4], [2, 9], [2, 11], [2, 13], [2, 14], [2, 15], [2, 16], [2, 18], [2, 19], [2, 21], [2, 24], [2, 27], [2, 28], [2, 29], [2, 30], [2, 32], [2, 34], [2, 35], [2, 38], [2, 39], [3, 5], [3, 6], [3, 7], [3, 9], [3, 13], [3, 15], [3, 16], [3, 17], [3, 18], [3, 19], [3, 21], [3, 26], [3, 27], [3, 28], [3, 29], [3, 31], [3, 35], [3, 36], [3, 37], [3, 38], [4, 6], [4, 8], [4, 9], [4, 12], [4, 13], [4, 14], [4, 15], [4, 16], [4, 17], [4, 18], [4, 19], [4, 20], [4, 21], [4, 22], [4, 23], [4, 24], [4, 25], [4, 28], [4, 30], [4, 31], [4, 32], [4, 34], [4, 35], [4, 36], [4, 37], [5, 7], [5, 8], [5, 9], [5, 10], [5, 11], [5, 15], [5, 16], [5, 17], [5, 18], [5, 19], [5, 22], [5, 23], [5, 24], [5, 26], [5, 28], [5, 29], [5, 31], [5, 32], [5, 33], [5, 34], [5, 35], [5, 36], [6, 8], [6, 10], [6, 15], [6, 16], [6, 18], [6, 19], [6, 20], [6, 22], [6, 28], [6, 29], [6, 31], [6, 35], [6, 37], [6, 38], [6, 39], [7, 10], [7, 12], [7, 14], [7, 15], [7, 16], [7, 17], [7, 21], [7, 25], [7, 26], [7, 27], [7, 28], [7, 29], [7, 32], [7, 36], [7, 39], [8, 9], [8, 15], [8, 16], [8, 20], [8, 21], [8, 22], [8, 25], [8, 27], [8, 28], [8, 29], [8, 33], [8, 36], [8, 37], [8, 38], [9, 13], [9, 15], [9, 21], [9, 25], [9, 26], [9, 27], [9, 28], [9, 29], [9, 34], [9, 36], [9, 37], [9, 38], [9, 39], [10, 15], [10, 16], [10, 24], [10, 26], [10, 27], [10, 29], [10, 32], [10, 33], [10, 35], [10, 36], [10, 38], [11, 12], [11, 14], [11, 15], [11, 21], [11, 22], [11, 23], [11, 25], [11, 26], [11, 27], [11, 31], [11, 34], [11, 36], [11, 37], [12, 13], [12, 14], [12, 15], [12, 16], [12, 17], [12, 19], [12, 21], [12, 22], [12, 27], [12, 28], [12, 33], [12, 34], [12, 35], [12, 37], [13, 14], [13, 15], [13, 17], [13, 18], [13, 19], [13, 21], [13, 28], [13, 31], [13, 33], [13, 34], [13, 37], [14, 15], [14, 16], [14, 19], [14, 23], [14, 24], [14, 26], [14, 28], [14, 31], [14, 32], [14, 35], [14, 36], [14, 39], [15, 17], [15, 18], [15, 19], [15, 20], [15, 21], [15, 22], [15, 23], [15, 24], [15, 27], [15, 30], [15, 32], [15, 33], [15, 34], [15, 36], [15, 39], [16, 18], [16, 20], [16, 21], [16, 22], [16, 28], [16, 30], [16, 33], [16, 34], [16, 35], [16, 36], [16, 37], [17, 21], [17, 22], [17, 23], [17, 27], [17, 28], [17, 29], [17, 30], [17, 31], [17, 32], [17, 33], [17, 34], [17, 35], [17, 36], [17, 38], [18, 21], [18, 22], [18, 25], [18, 26], [18, 27], [18, 28], [18, 30], [18, 31], [18, 34], [18, 37], [19, 21], [19, 26], [19, 28], [19, 29], [19, 31], [19, 32], [19, 35], [19, 37], [19, 39], [20, 22], [20, 23], [20, 28], [20, 31], [20, 33], [20, 35], [20, 37], [20, 38], [20, 39], [21, 22], [21, 24], [21, 25], [21, 26], [21, 28], [21, 30], [21, 32], [21, 34], [21, 35], [21, 39], [22, 23], [22, 27], [22, 29], [22, 30], [22, 31], [22, 33], [22, 34], [22, 36], [22, 37], [22, 38], [23, 24], [23, 29], [23, 31], [23, 32], [23, 33], [23, 36], [23, 37], [24, 26], [24, 27], [24, 28], [24, 29], [24, 30], [24, 32], [24, 34], [24, 38], [25, 27], [25, 28], [25, 29], [25, 39], [26, 27], [26, 28], [26, 30], [26, 31], [26, 32], [26, 34], [26, 35], [27, 28], [27, 29], [27, 30], [27, 31], [27, 36], [27, 37], [28, 29], [28, 30], [28, 32], [28, 34], [28, 36], [28, 38], [29, 34], [29, 37], [30, 34], [30, 37], [31, 34], [31, 37], [32, 34], [32, 36], [32, 37], [32, 38], [32, 39], [33, 35], [33, 36], [33, 37], [34, 38], [35, 36], [35, 37], [36, 39]]
+
+Assign every vertex to group 1 or group 2 so that, for every vertex v, the number of neighbours of v lying in the same group as v is even (zero counts as even). One of the groups may be empty.
+
+Answer format: {"groups": [g_0, ..., g_39]}  with each g_i in {1, 2}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-even-degree-partition-l6-s9/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-even-degree-partition-l6-s9"
+version = "0.2.0"
+description = "construct/rlve_even_degree_partition"
+authors = []
+keywords = ["rlmath", "construct", "rlve_even_degree_partition"]
+
+[metadata]
+subset = "construct"
+family = "rlve_even_degree_partition"
+problem_key = "gallai_even_partition"
+domain = "graph_theory"
+tier = "competition"
+level = "6"
+source = "RLVE-Gym/even_degree_graph_partitioning"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-largest-convex-polygon-l2-s3/instruction.md

@@ -0,0 +1,16 @@
+You are given 9 points in the plane, indexed 0..8 (distinct, no three collinear):
+0: (1, 1)
+1: (9, 6)
+2: (0, 9)
+3: (4, 2)
+4: (5, 7)
+5: (9, 8)
+6: (5, 3)
+7: (6, 3)
+8: (7, 8)
+
+The largest subset of these points in convex position has exactly 7 points. Find 7 distinct points that are the vertices of a convex polygon (every chosen point is a vertex of the convex hull of the chosen points).
+
+Answer format: {"indices": [i_1, ..., i_7]}  (any order)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-largest-convex-polygon-l2-s3/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-largest-convex-polygon-l2-s3"
+version = "0.2.0"
+description = "construct/rlve_largest_convex_polygon"
+authors = []
+keywords = ["rlmath", "construct", "rlve_largest_convex_polygon"]
+
+[metadata]
+subset = "construct"
+family = "rlve_largest_convex_polygon"
+problem_key = "largest_convex_subset"
+domain = "discrete_geometry"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/largest_convex_polygon"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-min-harmonious-coloring-l3-s1/instruction.md

@@ -0,0 +1,8 @@
+An undirected simple graph has 10 vertices labelled 0..9 and edge list
+[[2, 5], [3, 4], [3, 7], [4, 5], [4, 9], [5, 8]]
+
+A harmonious colouring assigns colours so that (1) adjacent vertices get different colours and (2) for every unordered pair of distinct colours {x, y} there is at most one edge whose endpoints are coloured x and y. The minimum number of colours in a harmonious colouring of this graph is 4. Give a harmonious colouring using only colours 0..3.
+
+Answer format: {"colors": [c_0, ..., c_9]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-min-harmonious-coloring-l3-s1/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-min-harmonious-coloring-l3-s1"
+version = "0.2.0"
+description = "construct/rlve_min_harmonious_coloring"
+authors = []
+keywords = ["rlmath", "construct", "rlve_min_harmonious_coloring"]
+
+[metadata]
+subset = "construct"
+family = "rlve_min_harmonious_coloring"
+problem_key = "harmonious_chromatic_number"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/minimum_harmonious_chromatic_number"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-pairwise-sums-recovery-l1-s6/instruction.md

@@ -0,0 +1,6 @@
+Find 3 distinct positive integers whose 3 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
+11, 8, 7
+
+Answer format: {"numbers": [x_1, ..., x_3]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-pairwise-sums-recovery-l1-s6/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-pairwise-sums-recovery-l1-s6"
+version = "0.2.0"
+description = "construct/rlve_pairwise_sums_recovery"
+authors = []
+keywords = ["rlmath", "construct", "rlve_pairwise_sums_recovery"]
+
+[metadata]
+subset = "construct"
+family = "rlve_pairwise_sums_recovery"
+problem_key = "poi_squarks_pairwise_sums"
+domain = "combinatorics"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/squ_squarks"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-pairwise-sums-recovery-l5-s9/instruction.md

@@ -0,0 +1,6 @@
+Find 18 distinct positive integers whose 153 pairwise sums (over all unordered pairs), taken as a multiset, are exactly:
+32, 19, 51, 32, 43, 30, 42, 28, 49, 21, 47, 53, 43, 49, 47, 31, 22, 41, 49, 15, 19, 22, 47, 65, 55, 39, 29, 28, 59, 50, 35, 60, 15, 48, 62, 14, 48, 25, 13, 44, 66, 31, 31, 42, 64, 45, 64, 36, 34, 35, 29, 57, 30, 41, 37, 38, 32, 25, 41, 51, 18, 52, 9, 36, 48, 26, 25, 26, 38, 63, 59, 58, 20, 29, 40, 44, 63, 37, 54, 24, 37, 50, 7, 31, 12, 35, 58, 42, 34, 38, 44, 40, 50, 41, 33, 27, 43, 54, 42, 34, 36, 10, 33, 8, 31, 44, 35, 38, 16, 52, 22, 47, 40, 40, 37, 35, 51, 25, 29, 23, 51, 24, 53, 28, 41, 34, 57, 47, 30, 38, 45, 14, 57, 70, 61, 45, 44, 36, 3, 17, 46, 57, 56, 53, 37, 23, 55, 19, 27, 56, 30, 21, 50
+
+Answer format: {"numbers": [x_1, ..., x_18]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-pairwise-sums-recovery-l5-s9/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-pairwise-sums-recovery-l5-s9"
+version = "0.2.0"
+description = "construct/rlve_pairwise_sums_recovery"
+authors = []
+keywords = ["rlmath", "construct", "rlve_pairwise_sums_recovery"]
+
+[metadata]
+subset = "construct"
+family = "rlve_pairwise_sums_recovery"
+problem_key = "poi_squarks_pairwise_sums"
+domain = "combinatorics"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/squ_squarks"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-polynomial-global-minimum-l5-s1/instruction.md

@@ -0,0 +1,7 @@
+Let f(x) = (1029)*x^0 + (-5118)*x^1 + (11549)*x^2 + (-15348)*x^3 + (13457)*x^4 + (-8058)*x^5 + (3361)*x^6 + (-960)*x^7 + (182)*x^8 + (-20)*x^9 + (1)*x^10.
+
+Find a real number x0 at which f attains its global minimum over the reals. Your answer is accepted if f(x0) <= min f + 1e-9 * max(1, |min f|) (f(x0) is evaluated exactly from the decimal/binary value you submit).
+
+Answer format: {"x0": <number>}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-polynomial-global-minimum-l5-s1/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-global-minimum-l5-s1"
+version = "0.2.0"
+description = "construct/rlve_polynomial_global_minimum"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_global_minimum"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_global_minimum"
+problem_key = "polynomial_global_minimum"
+domain = "analysis"
+tier = "competition"
+level = "5"
+source = "RLVE-Gym/polynomial_minimum"
+source_license = "MIT"
+tags = ["agentic_trivial"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-polynomial-integer-roots-l2-s4/instruction.md

@@ -0,0 +1,7 @@
+The degree-5 polynomial
+P(x) = (12)*x^1 + (31)*x^2 + (27)*x^3 + (9)*x^4 + (1)*x^5
+can be written as (x - a_1)(x - a_2)...(x - a_5) with integers a_1, ..., a_5 (not necessarily distinct). Find such integers.
+
+Answer format: {"roots": [a_1, ..., a_5]}  (any order, with multiplicity)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-polynomial-integer-roots-l2-s4/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-integer-roots-l2-s4"
+version = "0.2.0"
+description = "construct/rlve_polynomial_integer_roots"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_integer_roots"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_integer_roots"
+problem_key = "integer_root_factorization"
+domain = "algebra"
+tier = "competition"
+level = "2"
+source = "RLVE-Gym/polynomial_factorization"
+source_license = "MIT"
+tags = ["agentic_trivial", "unique_answer"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-polynomial-interpolation-l1-s5/instruction.md

@@ -0,0 +1,10 @@
+A polynomial f(x) = a_0 + a_1 x + ... + a_2 x^2 of degree 2 with integer coefficients satisfies
+f(1) = -5
+f(0) = -5
+f(-1) = -1
+
+Find a_0, ..., a_2.
+
+Answer format: {"coeffs": [a_0, a_1, ..., a_2]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-polynomial-interpolation-l1-s5/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-polynomial-interpolation-l1-s5"
+version = "0.2.0"
+description = "construct/rlve_polynomial_interpolation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_polynomial_interpolation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_polynomial_interpolation"
+problem_key = "lagrange_interpolation_integer"
+domain = "algebra"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/polynomial_interpolation"
+source_license = "MIT"
+tags = ["agentic_trivial", "unique_answer"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-prefix-product-permutation-l1-s0/instruction.md

@@ -0,0 +1,5 @@
+Find a permutation p_1, ..., p_3 of the integers 1, 2, ..., 3 such that the 3 prefix products p_1, p_1*p_2, ..., p_1*p_2*...*p_3 are pairwise distinct modulo 3.
+
+Answer format: {"perm": [p_1, ..., p_3]}
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-prefix-product-permutation-l1-s0/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-prefix-product-permutation-l1-s0"
+version = "0.2.0"
+description = "construct/rlve_prefix_product_permutation"
+authors = []
+keywords = ["rlmath", "construct", "rlve_prefix_product_permutation"]
+
+[metadata]
+subset = "construct"
+family = "rlve_prefix_product_permutation"
+problem_key = "cf487c_prefix_product_sequence"
+domain = "number_theory"
+tier = "competition"
+level = "1"
+source = "RLVE-Gym/prefix_product_mod_distinct_permutation"
+source_license = "MIT"
+tags = []
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/construct-rlve-subgraph-isomorphism-l3-s3/instruction.md

@@ -0,0 +1,10 @@
+G1 is an undirected simple graph on vertices 0..6 with edges
+[[1, 4], [1, 2], [2, 6]]
+G2 is an undirected simple graph on vertices 0..11 with edges
+[[2, 7], [1, 11], [0, 5], [4, 6], [1, 3], [1, 10], [2, 8], [5, 7], [8, 11], [0, 2], [6, 11], [6, 10], [7, 9], [3, 5], [5, 11], [7, 8]]
+
+Find an injective map p from the vertices of G1 to the vertices of G2 such that for every pair u != v of G1 vertices, (u, v) is an edge of G1 if and only if (p(u), p(v)) is an edge of G2 (i.e. G1 is isomorphic to the subgraph of G2 induced by the image of p).
+
+Answer format: {"p": [p(0), ..., p(6)]}  (distinct integers in 0..11)
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/construct-rlve-subgraph-isomorphism-l3-s3/task.toml

@@ -0,0 +1,40 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/construct-rlve-subgraph-isomorphism-l3-s3"
+version = "0.2.0"
+description = "construct/rlve_subgraph_isomorphism"
+authors = []
+keywords = ["rlmath", "construct", "rlve_subgraph_isomorphism"]
+
+[metadata]
+subset = "construct"
+family = "rlve_subgraph_isomorphism"
+problem_key = "induced_subgraph_isomorphism"
+domain = "graph_theory"
+tier = "competition"
+level = "3"
+source = "RLVE-Gym/subgraph_isomorphism"
+source_license = "MIT"
+tags = ["agentic_trivial", "np_search"]
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]

tasks/optimize-ea-no-three-in-line-n75/instruction.md

@@ -0,0 +1,22 @@
+## Problem
+
+Choose as many distinct points as possible from the $75\times75$ integer grid $\{0,1,\ldots,74\}^2$
+such that no three chosen points lie on one straight line. Lines of every slope count, not only rows,
+columns and diagonals. **Maximize the number of points.**
+
+Every row contains at most two chosen points, so $D(75)\le150$. As of September 2026, 150-point
+configurations are known for every grid size up to 76 except 75; the best public construction for 75
+has 148 points.
+
+## Verification
+
+Collinearity is tested exactly with integer arithmetic for every triple of submitted points.
+
+## Answer format
+
+`{"points": [[x_1, y_1], [x_2, y_2], ...]}` with between 1 and 150 distinct integer pairs,
+0 <= x, y <= 74. The score is the number of points.
+
+Reward: 0 for an invalid answer; otherwise 0.1 plus up to 0.9 for progress from a trivial baseline toward the best known value.
+
+Write your final answer as JSON to `/workdir/answer.json`. The instance data is also in `/workdir/instance.json`. Only `/workdir/answer.json` is graded. There is no internet access.

tasks/optimize-ea-no-three-in-line-n75/task.toml

@@ -0,0 +1,43 @@
+schema_version = "1.4"
+artifacts = []
+
+[task]
+name = "rlmath/optimize-ea-no-three-in-line-n75"
+version = "0.2.0"
+description = "optimize/ea_no_three_in_line_75"
+authors = []
+keywords = ["rlmath", "optimize", "ea_no_three_in_line_75"]
+
+[metadata]
+subset = "optimize"
+family = "ea_no_three_in_line_75"
+problem_key = "no_three_in_line_n75"
+domain = "discrete_geometry"
+tier = "research"
+level = "research"
+source = "EinsteinArena/no-three-in-line-75"
+source_license = "MIT"
+tags = ["ea_under_review", "exact_check"]
+direction = "maximize"
+baseline = 73.0
+best_known = 148
+
+[verifier]
+timeout_sec = 300.0
+
+[verifier.env]
+
+[agent]
+timeout_sec = 900.0
+
+[environment]
+network_mode = "no-network"
+build_timeout_sec = 600.0
+os = "linux"
+cpus = 2
+memory_mb = 4096
+mcp_servers = []
+
+[environment.env]
+
+[solution.env]