{ "catalog_sha256_by_recorded_version": { "v29": "2db42c10aa3196dda6a2fff73db02a86906091826a880abf4b38227f5f34f0b0" }, "per_theorem": [ { "name": "totient_coprime_decidable", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0001" }, { "name": "totient_unit_bit_choice_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0002" }, { "name": "totient_unit_bit_choice_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0003" }, { "name": "totient_unit_prefix_empty", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0004" }, { "name": "totient_unit_prefix_drop_last", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0005" }, { "name": "totient_unit_prefix_entry", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0006" }, { "name": "totient_unit_prefix_extend", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0007" }, { "name": "totient_unit_prefix_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0008" }, { "name": "totient_unit_prefix_all_bits", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0009" }, { "name": "totient_unit_prefix_equal_entry", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP000A" }, { "name": "totient_unit_count_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP000B" }, { "name": "totient_unit_count_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP000C" }, { "name": "totient_unit_count_bounded", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP000D" }, { "name": "totient_unit_count_zero_length", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP000E" }, { "name": "totient_unit_count_succ_decompose", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP000F" }, { "name": "totient_unit_count_succ_intro", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0010" }, { "name": "totient_unit_choice_mod_one", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0011" }, { "name": "totient_unit_count_mod_one", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0012" }, { "name": "totient_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0013" }, { "name": "totient_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0014" }, { "name": "totient_bounded", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0015" }, { "name": "totient_zero_excluded", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0016" }, { "name": "totient_one", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0017" }, { "name": "totient_one_value", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0018" }, { "name": "totient_exists_unique", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0019" }, { "name": "totient_unit_count_length_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP001A" }, { "name": "totient_unit_count_value_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP001B" }, { "name": "totient_unit_count_zero_value", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP001C" }, { "name": "totient_unit_choices_equal_of_equivalence", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP001D" }, { "name": "totient_unit_count_interval_balance", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP001E" }, { "name": "totient_coprime_periodic", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP001F" }, { "name": "totient_unit_count_period_block", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0020" }, { "name": "totient_unit_count_periods", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0021" }, { "name": "totient_unit_count_pointwise_equal", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0022" }, { "name": "totient_unit_count_modulus_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0023" }, { "name": "totient_value_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0024" }, { "name": "totient_modulus_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0025" }, { "name": "totient_divisor_reflexive", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0026" }, { "name": "totient_coprime_divisor_right", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0027" }, { "name": "totient_coprime_product_iff", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0028" }, { "name": "totient_prime_coprime_iff_nondivisor", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0029" }, { "name": "totient_coprime_repeated_factor", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP002A" }, { "name": "totient_coprime_cancel_unit_factor", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP002B" }, { "name": "totient_prime_multiple_is_not_unit", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP002C" }, { "name": "totient_nonzero_prime_block_offset_not_divisible", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP002D" }, { "name": "totient_prime_block_positive_offset_units", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP002E" }, { "name": "totient_unit_count_repeated_prime_factor", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP002F" }, { "name": "totient_unit_choice_transport", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0030" }, { "name": "totient_prime_block_end", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0031" }, { "name": "totient_count_defect_step", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0032" }, { "name": "totient_new_prime_block_count_balance", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0033" }, { "name": "totient_new_prime_multiple_blocks_balance", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0034" }, { "name": "totient_unit_count_new_prime_balance", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0035" }, { "name": "totient_unit_count_new_prime_factor", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0036" }, { "name": "totient_repeated_prime_factor", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0037" }, { "name": "totient_new_prime_factor", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0038" }, { "name": "totient_prime_value", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0039" }, { "name": "totient_prime_power_successor_value", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP003A" }, { "name": "totient_prime_power_value", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP003B" }, { "name": "totient_coprime_divisor_left", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP003C" }, { "name": "totient_coprime_multiplication_prime_step", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP003D" }, { "name": "totient_coprime_multiplicative_from_prime_list", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP003E" }, { "name": "totient_coprime_multiplicative", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP003F" }, { "name": "totient_euler_factor_exists", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0040" }, { "name": "totient_euler_factor_correct", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0041" }, { "name": "totient_euler_factor_functional", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0042" }, { "name": "totient_prime_entries_decoded_power", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0043" }, { "name": "totient_prime_entries_selected_power", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0044" }, { "name": "totient_prime_support_powers_pairwise_coprime", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": "TP0045" }, { "name": "totient_pairwise_coprime_product_fold", "recorded_authority": { "admitted_to_alpha": true, "admitted_to_stable": false, "alpha_checked_use": true, "alpha_evidence": "alpha_closed", "checked_use": true, "enrolled_in_alpha": true, "stable_member": false }, "recorded_first_version": "v29", "tag": 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