{ "catalog_sha256_by_recorded_version": { "v13": "cad57a21657e2df09f01174069efcfed194d87b68c0b4042b234df5759583e5a", "v15": "0123e5938f43cf67833751e2a6102d6598ac24c9be6db9a0d353ec3f55e5f32c", "v19": "f1c3d3fba013ca3a5b62a4103dd00bd5b7e39b1f785ed9023099704ad033004b", "v23": "818da349674b1ef33c17fa85b2e9a0a6653370046d88e7814300297f7bc7f4d2" }, "per_theorem": [ { "name": "even_square_is_four_multiple", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0000" }, { "name": "odd_square_is_four_multiple_plus_one", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0001" }, { "name": "square_mod_four_zero_or_one", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0002" }, { "name": "sum_two_squares_mod_four_cases", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0003" }, { "name": "sum_two_squares_not_four_mod_three", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0004" }, { "name": "prime_mod_four_one_minus_one_square_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0005" }, { "name": "prime_mod_four_one_bounded_minus_one_square_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0006" }, { "name": "predecessor_square_congruence_yields_divisible_norm", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0007" }, { "name": "prime_mod_four_one_divisible_two_square_norm_exists", "recorded_authority": { "admitted_to_alpha": false, "admitted_to_stable": false, "alpha_checked_use": false, "alpha_evidence": null, "enrolled_in_alpha": false }, "recorded_first_version": "not_recorded", "tag": "TS0008" }, { "name": "prime_mod_four_one_bounded_divisible_two_square_norm_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0009" }, { "name": "positive_multiple_below_twice_equals_base", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000A" }, { "name": "bounded_divisible_two_square_norm_equals_prime", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000B" }, { "name": "prime_is_not_natural_square", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000C" }, { "name": "natural_square_monotone_expanded", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000D" }, { "name": "prime_floor_square_strictly_below_prime", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000E" }, { "name": "prime_floor_bounded_coordinate_square_strict", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000F" }, { "name": "two_strict_values_sum_below_double", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000G" }, { "name": "prime_floor_bounded_two_square_norm_below_double", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000H" }, { "name": "floor_square_successor_grid_strictly_exceeds_input", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000I" }, { "name": "floor_square_oversized_grid_exists", "recorded_authority": { "admitted_to_alpha": false, "admitted_to_stable": false, "alpha_checked_use": false, "alpha_evidence": null, "enrolled_in_alpha": false }, "recorded_first_version": "not_recorded", "tag": "TS000J" }, { "name": "prime_floor_bounded_divisible_norm_represents_prime", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000K" }, { "name": "finite_bounded_into_oversized_not_injective", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS000L" }, { "name": "floor_square_oversized_bounded_grid_not_injective", "recorded_authority": { "admitted_to_alpha": false, "admitted_to_stable": false, "alpha_checked_use": false, "alpha_evidence": null, "enrolled_in_alpha": false }, "recorded_first_version": "not_recorded", "tag": "TS000M" }, { "name": "finite_bounded_into_collision_from_constructive_decision", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS000N" }, { "name": "finite_prefix_collision_succ", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS000O" }, { "name": "finite_prefix_last_occurrence_collision", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS000P" }, { "name": "finite_prefix_injective_extend_fresh", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS000Q" }, { "name": "finite_prefix_collision_or_injective", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS000R" }, { "name": "finite_bounded_into_oversized_collision", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS000S" }, { "name": "floor_square_oversized_bounded_grid_collision", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000T" }, { "name": "affine_grid_point_remainder_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000U" }, { "name": "beta_affine_residue_grid_extend", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000V" }, { "name": "beta_affine_residue_grid_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000W" }, { "name": "beta_affine_residue_grid_bounded", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000X" }, { "name": "prime_floor_affine_residue_grid_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000Y" }, { "name": "prime_floor_affine_residue_grid_collision", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS000Z" }, { "name": "equal_affine_remainders_balanced", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0010" }, { "name": "balanced_zero_congruence_implies_multiple", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS0011" }, { "name": "multiple_implies_balanced_zero_congruence", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS0012" }, { "name": "negative_one_scaled_square_identity", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0013" }, { "name": "negative_one_scaled_square_congruent_zero", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0014" }, { "name": "balanced_linear_congruence_implies_squared_congruence", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0015" }, { "name": "balanced_zero_sum_implies_squared_congruence", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS0016" }, { "name": "negative_one_congruent_square_norm_multiple", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0017" }, { "name": "negative_one_linear_congruence_norm_multiple", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0018" }, { "name": "negative_one_opposite_linear_congruence_norm_multiple", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0019" }, { "name": "natural_absolute_difference_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001A" }, { "name": "bounded_natural_absolute_difference", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001B" }, { "name": "affine_collision_difference_linear_or_opposite", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001C" }, { "name": "affine_collision_absolute_difference_norm_multiple", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001D" }, { "name": "flat_square_index_row_not_at_least_width", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001E" }, { "name": "flat_square_index_row_below_width", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001F" }, { "name": "absolute_difference_zero_forces_coordinate_equality", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001G" }, { "name": "nonzero_coordinate_pair_has_positive_square_norm", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001H" }, { "name": "distinct_flat_indices_have_positive_difference_norm", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001I" }, { "name": "strict_successor_coordinate_bound_is_weak_bound", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001J" }, { "name": "shared_beta_collision_remainders_equal", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001K" }, { "name": "equal_remainder_affine_values_balanced_congruent", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001L" }, { "name": "prime_floor_decoded_affine_collision_represents_prime", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001M" }, { "name": "prime_floor_affine_grid_collision_represents_prime", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001N" }, { "name": "prime_mod_four_one_is_sum_of_two_squares", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001O" }, { "name": "two_square_add_swap_nested", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS001P" }, { "name": "two_square_sum_square_expands", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS001Q" }, { "name": "two_square_absolute_difference_square_balance", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS001R" }, { "name": "two_square_cross_product_interchange", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS001S" }, { "name": "two_square_product_expands", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS001T" }, { "name": "two_square_product_norm_blocks", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS001U" }, { "name": "two_square_sum_square_blocks", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS001V" }, { "name": "brahmagupta_fibonacci_two_square_identity", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "TS001W" }, { "name": "two_square_representation_multiplicatively_closed", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001X" }, { "name": "zero_one_and_two_have_two_square_representations", "recorded_authority": { "admitted_to_alpha": false, "admitted_to_stable": false, "alpha_checked_use": false, "alpha_evidence": null, "enrolled_in_alpha": false }, "recorded_first_version": "not_recorded", "tag": "TS001Y" }, { "name": "every_natural_square_is_sum_of_two_squares", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS001Z" }, { "name": "prime_is_two_or_odd", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v15", "tag": "TS0020" }, { "name": "prime_mod_four_trichotomy", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", 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