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"alpha_closed", "enrolled_in_alpha": true }, "recorded_first_version": "v13", "tag": "FS000Z" }, { "name": "four_square_conjugate_global_compensation", "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": "FS0010" }, { "name": "four_square_conjugate_coordinate_square_transport", "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": "FS0011" }, { "name": "four_square_signed_conjugate_quaternion", "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": "FS0012" }, { "name": "four_square_conjugate_absolute_coordinates_total", 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"recorded_first_version": "v13", "tag": "FS0016" }, { "name": "four_square_cross_intersection", "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": "FS0017" }, { "name": "four_square_descent_nonzero_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": "v13", "tag": "FS0018" }, { "name": "four_square_descent_product_reassociate", "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": "FS0019" }, { "name": "four_square_descent_square_factor_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": "v13", "tag": "FS001A" }, { "name": "four_square_descent_square_factor_cancel", "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": "FS001B" }, { "name": "four_square_descent_scaled_norm_quotient", "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": "FS001C" }, { "name": "four_square_descent_quaternion_quotient", "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": "FS001D" }, { "name": "four_square_descent_strict_step_from_centered_quaternion", "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": "FS001E" }, { "name": "four_square_descent_modular_seed_multiplier_nonzero", "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": "FS001F" }, { "name": "four_square_descent_strict_multiplier_bounded", "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": "FS001G" }, { "name": "four_square_descent_prime_from_strict_step", "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": "FS001H" }, { "name": "four_square_descent_prime_from_modular_seed_and_step", "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": "FS001I" }, { "name": "four_square_descent_three_mod_four_primes_from_seed_and_step", "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": "FS001J" }, { "name": "four_square_lagrange_from_modular_seeds_and_strict_descent", "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": "FS001K" }, { "name": "four_square_descent_remainder_complement_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": "v13", "tag": "FS001L" }, { "name": "four_square_descent_centered_signed_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": "v13", "tag": "FS001M" }, { "name": "four_square_descent_centered_four_remainders_exist", "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": "FS001N" }, { "name": "four_square_descent_norm_bound_forces_smaller_multiplier", "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": "FS001O" }, { "name": "four_square_descent_matching_parity_sum_even", "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": "FS001P" }, { "name": "four_square_descent_matching_parity_absolute_even", "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": "FS001Q" }, { "name": "four_square_descent_double_pair_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": "FS001R" }, { "name": "four_square_descent_even_multiplier_paired_halving", "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": "FS001S" }, { "name": "four_square_descent_even_multiplier_matching_parity_halving", "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": "FS001T" }, { "name": "four_square_descent_odd_centered_magnitude_half_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": "v13", "tag": "FS001U" }, { "name": "four_square_descent_add_le_add", "recorded_authority": { 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"recorded_first_version": "v13", "tag": "FS001Y" }, { "name": "four_square_descent_zero_norm_coordinates", "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": "FS001Z" }, { "name": "four_square_descent_zero_centered_remainder_divides", "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": "FS0020" }, { "name": "four_square_descent_nonunit_proper_factor_not_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": "v13", "tag": "FS0021" }, { "name": "four_square_descent_divisible_coordinates_prime_factor", "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": "FS0022" }, { "name": "four_square_descent_bounded_centered_quotient_nonzero", "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": "FS0023" }, { "name": "four_square_descent_odd_centered_strict_step", "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": "FS0024" }, { "name": "four_square_euler_cross_swap", "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": "FS0025" }, { "name": "four_square_euler_mixed_ab", "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": "FS0026" }, { "name": "four_square_euler_mixed_ac", "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": "FS0027" }, { "name": "four_square_euler_mixed_ad", "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": "FS0028" }, { "name": "four_square_euler_mixed_bc", "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": "FS0029" }, { "name": "four_square_euler_mixed_bd", "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": "FS002A" }, { "name": "four_square_euler_mixed_cd", "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": "FS002B" }, { "name": "four_square_euler_all_mixed_cancel", "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": "FS002C" }, { "name": "four_square_euler_four_add_shuffle", "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": "FS002D" }, { "name": "four_square_euler_balance_aggregate", "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": "FS002E" }, { "name": "four_square_euler_compensation_cancel", "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": "FS002F" }, { "name": "four_square_euler_diagonal_block", "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": "FS002G" }, { "name": "four_square_euler_diagonal_expansion", "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": "FS002H" }, { "name": "four_square_euler_quaternion_conditional", "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": "FS002I" }, { "name": "four_square_euler_add_permute_six", "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": "FS002J" }, { "name": "four_square_euler_add_permute_nine", "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": "FS002K" }, { "name": "four_square_euler_add_permute_twelve", "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": "FS002L" }, { "name": "four_square_euler_add_permute_sixteen", "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": "FS002M" }, { "name": "four_square_euler_add_swap_last", "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": "FS002N" }, { "name": "four_square_euler_three_square_expansion", "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": "FS002O" }, { "name": "four_square_euler_cross_triple_expansion", "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": "FS002P" }, { "name": "four_square_euler_double_cross_swap", "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": "FS002Q" }, { "name": "four_square_euler_coordinate_single_decompose", "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": "FS002R" }, { "name": "four_square_euler_coordinate_triple_decompose", "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": "FS002S" }, { "name": "four_square_euler_diagonal_regroup", "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": "FS002T" }, { "name": "four_square_euler_left_decomposition", "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": "FS002U" }, { "name": "four_square_euler_cross_decomposition", "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": "FS002V" }, { "name": "four_square_euler_mixed_decomposition", "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": "FS002W" }, { "name": "four_square_euler_global_compensation", "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": "FS002X" }, { "name": "four_square_euler_quaternion", "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": "FS002Y" }, { "name": "four_square_euler_four_square_product_total", "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": "FS002Z" }, { "name": "four_square_euler_representations_closed_under_multiplication", "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": "FS0030" }, { "name": "four_square_prime_from_strict_descent", "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": "FS0031" }, { "name": "four_square_lagrange_from_strict_descent", "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": "FS0032" }, { "name": "four_square_descent_below_prime_multiplier_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": "v13", "tag": "FS0033" }, { "name": "four_square_prime_from_bounded_strict_descent_and_seed", "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": "FS0034" }, { "name": "four_square_prime_from_bounded_strict_descent", "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": "FS0035" }, { "name": "four_square_lagrange_from_bounded_strict_descent", "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": "FS0036" }, { "name": "four_square_zero_represented", "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": "FS0037" }, { "name": "four_square_one_represented", "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": "FS0038" }, { "name": "four_square_two_represented", "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": "FS0039" }, { "name": "four_square_three_represented", "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": "FS003A" }, { "name": "four_square_seven_represented", "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": "FS003B" }, { "name": "four_square_eleven_represented", "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": "FS003C" }, { "name": "four_square_two_square_embedding", "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": "FS003D" }, { "name": "four_square_prime_two_or_one_mod_four", "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": "FS003E" }, { "name": "four_square_prime_modular_seed_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": "FS003F" }, { "name": "four_square_prime_unit_seed_represented", "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": "FS003G" }, { "name": "four_square_prime_case_reduction", "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": "FS003H" }, { "name": "four_square_lagrange_bounded_from_primes", "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": "FS003I" }, { "name": "four_square_lagrange_from_all_primes", "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": "FS003J" }, { "name": "four_square_lagrange_from_three_mod_four_primes", "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": "FS003K" }, { "name": "four_square_lagrange_iff_three_mod_four_primes", "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": "FS003L" }, { "name": "four_square_prime_from_odd_signed_quaternion", "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": "FS003M" }, { "name": "four_square_lagrange_from_odd_signed_quaternion", "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": "FS003N" }, { "name": "four_square_prime_representation", "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": "FS003O" }, { "name": "four_square_lagrange", "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": "FS003P" }, { "name": "four_square_parity_square_mod_two_self", "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": "FS003Q" }, { "name": "four_square_parity_pair_mod_two_sum", "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": "FS003R" }, { "name": "four_square_parity_triple_mod_two_sum", "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": "FS003S" }, { "name": "four_square_parity_norm_mod_two_sum", "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": "FS003T" }, { "name": "four_square_parity_even_norm_coordinate_sum", "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": "FS003U" }, { "name": "four_square_parity_odd_blocks_crossed_selection", "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": "FS003V" }, { "name": "four_square_parity_even_coordinate_pair_selection", "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": "FS003W" }, { "name": "four_square_parity_even_norm_pair_selection", "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": "FS003X" }, { "name": "four_square_parity_swap_middle_coordinates", "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": "FS003Y" }, { "name": "four_square_parity_swap_outer_coordinates", "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": "FS003Z" }, { "name": "four_square_parity_even_multiplier_halving", "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": "FS0040" }, { "name": "four_square_parity_represented_double_halving", "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": "FS0041" }, { "name": "four_square_parity_represented_additive_double_halving", "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": "FS0042" }, { "name": "four_square_half_double_below_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": "v13", "tag": "FS0043" }, { "name": "four_square_two_half_ranges_overflow_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": "v13", "tag": "FS0044" }, { "name": "four_square_half_sum_below_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": "v13", "tag": "FS0045" }, { "name": "four_square_bounded_multiple_is_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": "v13", "tag": "FS0046" }, { "name": "four_square_ordered_square_difference_factor", "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": "FS0047" }, { "name": "four_square_ordered_square_congruence_factors", "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": "FS0048" }, { "name": "four_square_ordered_half_square_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": "FS0049" }, { "name": "four_square_prime_half_square_residues_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": "FS004A" }, { "name": "four_square_square_residue_prefix_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": "v13", "tag": "FS004B" }, { "name": "four_square_square_residue_prefix_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": "v13", "tag": "FS004C" }, { "name": "four_square_equal_square_remainders_are_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": "v13", "tag": "FS004D" }, { "name": "four_square_half_square_residue_prefix_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": "FS004E" }, { "name": "four_square_bounded_complement_prefix_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": "v13", "tag": "FS004F" }, { "name": "four_square_complement_gap_symmetry", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, 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