{ "step": "C317", "status": "passed", "scope": "Same five source-qualified SP cases only; no census enlargement.", "input_sha256": { "PREVIOUS_DATA.json": "161fe982b41a30d69b9130bd247062e80e710bdb9a199d06ad88e11d68ce8b33", "C271_REGISTER.json": "54c510fb3c5860340276f64f9b1b40fef4a24e323ac52b0830193895ee91ae6a", "C287_DATA.json": "1f3fe8798fb89b1559247a1b209aabfa854d0ae5399b45623f4c398a36fa8ce0" }, "rows": [ { "i": 3, "j": 7, "gear": 1, "rail": "primary", "source_Flood_role": "Flood start", "coordinates_p_q_f_n": [ -5887, -5287, 3106, 3706 ], "crosswidths": [ [ 8993, 9593 ], [ 8393, 8993 ] ], "six_durations": [ 600, 8993, 9593, 8393, 8993, 600 ], "duration_incidence_rank": 3, "common_translation_dimension": 1, "exact_components": [ { "phase": "-1/4", "p_cumulative_OFF_Shem": "-23549/4", "q_cumulative_OFF_Flood": "-21149/4", "f_regular_SP_Flood": "12423/4", "n_regular_SP_Noah": "14823/4", "p_source_phase": "5888t BC", "q_source_phase": "5288t BC", "f_output_phase": "AD 3106t", "n_output_phase": "AD 3706t", "two_translations": [ "8993", "8993" ], "two_sides": [ "600", "600" ] }, { "phase": "1/4", "p_cumulative_OFF_Shem": "-23547/4", "q_cumulative_OFF_Flood": "-21147/4", "f_regular_SP_Flood": "12425/4", "n_regular_SP_Noah": "14825/4", "p_source_phase": "5887n BC", "q_source_phase": "5287n BC", "f_output_phase": "AD 3107n", "n_output_phase": "AD 3707n", "two_translations": [ "8993", "8993" ], "two_sides": [ "600", "600" ] } ], "C287_full_form_at_i": true, "C287_comparison": { "C287_S": -6345, "C287_R": 2648, "shared_q": -5287, "shared_n": 3706, "C287_minus_current_p_f": [ -458, -458 ], "same_side_width_old": 1058, "same_side_width_current": 600, "width_difference": 458, "C287_crosswidths": [ [ 8993, 10051 ], [ 7935, 8993 ] ], "current_crosswidths": [ [ 8993, 9593 ], [ 8393, 8993 ] ], "both_T8993_bridges_retained": true, "C287_source_role": "cumulative LXX_ON Shem at annual index i+2", "current_source_role": "cumulative LXX_OFF Shem at annual index i", "C287_regular_role": "regular MT Flood (inherited variant context)", "current_regular_role": "regular SP Flood (OFF/Terah0/full430)" } }, { "i": 4, "j": 6, "gear": 2, "rail": "companion", "source_Flood_role": "Flood close", "coordinates_p_q_f_n": [ -5886, -5286, 3107, 3707 ], "crosswidths": [ [ 8993, 9593 ], [ 8393, 8993 ] ], "six_durations": [ 600, 8993, 9593, 8393, 8993, 600 ], "duration_incidence_rank": 3, "common_translation_dimension": 1, "exact_components": [ { "phase": "-1/4", "p_cumulative_OFF_Shem": "-23545/4", "q_cumulative_OFF_Flood": "-21145/4", "f_regular_SP_Flood": "12427/4", "n_regular_SP_Noah": "14827/4", "p_source_phase": "5887t BC", "q_source_phase": "5287t BC", "f_output_phase": "AD 3107t", "n_output_phase": "AD 3707t", "two_translations": [ "8993", "8993" ], "two_sides": [ "600", "600" ] }, { "phase": "1/4", "p_cumulative_OFF_Shem": "-23543/4", "q_cumulative_OFF_Flood": "-21143/4", "f_regular_SP_Flood": "12429/4", "n_regular_SP_Noah": "14829/4", "p_source_phase": "5886n BC", "q_source_phase": "5286n BC", "f_output_phase": "AD 3108n", "n_output_phase": "AD 3708n", "two_translations": [ "8993", "8993" ], "two_sides": [ "600", "600" ] } ], "C287_full_form_at_i": true, "C287_comparison": { "C287_S": -6344, "C287_R": 2649, "shared_q": -5286, "shared_n": 3707, "C287_minus_current_p_f": [ -458, -458 ], "same_side_width_old": 1058, "same_side_width_current": 600, "width_difference": 458, "C287_crosswidths": [ [ 8993, 10051 ], [ 7935, 8993 ] ], "current_crosswidths": [ [ 8993, 9593 ], [ 8393, 8993 ] ], "both_T8993_bridges_retained": true, "C287_source_role": "cumulative LXX_ON Shem at annual index i+2", "current_source_role": "cumulative LXX_OFF Shem at annual index i", "C287_regular_role": "regular MT Flood (inherited variant context)", "current_regular_role": "regular SP Flood (OFF/Terah0/full430)" } }, { "i": 5, "j": 5, "gear": 2, "rail": "primary", "source_Flood_role": "Flood start", "coordinates_p_q_f_n": [ -5885, -5285, 3108, 3708 ], "crosswidths": [ [ 8993, 9593 ], [ 8393, 8993 ] ], "six_durations": [ 600, 8993, 9593, 8393, 8993, 600 ], "duration_incidence_rank": 3, "common_translation_dimension": 1, "exact_components": [ { "phase": "-1/4", "p_cumulative_OFF_Shem": "-23541/4", "q_cumulative_OFF_Flood": "-21141/4", "f_regular_SP_Flood": "12431/4", "n_regular_SP_Noah": "14831/4", "p_source_phase": "5886t BC", "q_source_phase": "5286t BC", "f_output_phase": "AD 3108t", "n_output_phase": "AD 3708t", "two_translations": [ "8993", "8993" ], "two_sides": [ "600", "600" ] }, { "phase": "1/4", "p_cumulative_OFF_Shem": "-23539/4", "q_cumulative_OFF_Flood": "-21139/4", "f_regular_SP_Flood": "12433/4", "n_regular_SP_Noah": "14833/4", "p_source_phase": "5885n BC", "q_source_phase": "5285n BC", "f_output_phase": "AD 3109n", "n_output_phase": "AD 3709n", "two_translations": [ "8993", "8993" ], "two_sides": [ "600", "600" ] } ], "C287_full_form_at_i": true, "C287_comparison": { "C287_S": -6343, "C287_R": 2650, "shared_q": -5285, "shared_n": 3708, "C287_minus_current_p_f": [ -458, -458 ], "same_side_width_old": 1058, "same_side_width_current": 600, "width_difference": 458, "C287_crosswidths": [ [ 8993, 10051 ], [ 7935, 8993 ] ], "current_crosswidths": [ [ 8993, 9593 ], [ 8393, 8993 ] ], "both_T8993_bridges_retained": true, "C287_source_role": "cumulative LXX_ON Shem at annual index i+2", "current_source_role": "cumulative LXX_OFF Shem at annual index i", "C287_regular_role": "regular MT Flood (inherited variant context)", "current_regular_role": "regular SP Flood (OFF/Terah0/full430)" } }, { "i": 6, "j": 4, "gear": 3, "rail": "companion", "source_Flood_role": "Flood close", "coordinates_p_q_f_n": [ -5884, -5284, 3109, 3709 ], "crosswidths": [ [ 8993, 9593 ], [ 8393, 8993 ] ], "six_durations": [ 600, 8993, 9593, 8393, 8993, 600 ], "duration_incidence_rank": 3, "common_translation_dimension": 1, "exact_components": [ { "phase": "-1/4", "p_cumulative_OFF_Shem": "-23537/4", "q_cumulative_OFF_Flood": "-21137/4", "f_regular_SP_Flood": "12435/4", "n_regular_SP_Noah": "14835/4", "p_source_phase": "5885t BC", "q_source_phase": "5285t BC", "f_output_phase": "AD 3109t", "n_output_phase": "AD 3709t", "two_translations": [ "8993", "8993" ], "two_sides": [ "600", "600" ] }, { "phase": "1/4", "p_cumulative_OFF_Shem": "-23535/4", "q_cumulative_OFF_Flood": "-21135/4", "f_regular_SP_Flood": "12437/4", "n_regular_SP_Noah": "14837/4", "p_source_phase": "5884n BC", "q_source_phase": "5284n BC", "f_output_phase": "AD 3110n", "n_output_phase": "AD 3710n", "two_translations": [ "8993", "8993" ], "two_sides": [ "600", "600" ] } ], "C287_full_form_at_i": false, "C287_comparison": null }, { "i": 7, "j": 3, "gear": 3, "rail": "primary", "source_Flood_role": "Flood start", "coordinates_p_q_f_n": [ -5883, -5283, 3110, 3710 ], "crosswidths": [ [ 8993, 9593 ], [ 8393, 8993 ] ], "six_durations": [ 600, 8993, 9593, 8393, 8993, 600 ], "duration_incidence_rank": 3, "common_translation_dimension": 1, "exact_components": [ { "phase": "-1/4", "p_cumulative_OFF_Shem": "-23533/4", "q_cumulative_OFF_Flood": "-21133/4", "f_regular_SP_Flood": "12439/4", "n_regular_SP_Noah": "14839/4", "p_source_phase": "5884t BC", "q_source_phase": "5284t BC", "f_output_phase": "AD 3110t", "n_output_phase": "AD 3710t", "two_translations": [ "8993", "8993" ], "two_sides": [ "600", "600" ] }, { "phase": "1/4", "p_cumulative_OFF_Shem": "-23531/4", "q_cumulative_OFF_Flood": "-21131/4", "f_regular_SP_Flood": "12441/4", "n_regular_SP_Noah": "14841/4", "p_source_phase": "5883n BC", "q_source_phase": "5283n BC", "f_output_phase": "AD 3111n", "n_output_phase": "AD 3711n", "two_translations": [ "8993", "8993" ], "two_sides": [ "600", "600" ] } ], "C287_full_form_at_i": false, "C287_comparison": null } ], "counts": { "source_rectangles": 5, "phase_rectangles": 10, "C287_complete_comparisons": 3, "C287_unavailable_at_same_i": 2 }, "crosswidth_matrix": [ [ 8993, 9593 ], [ 8393, 8993 ] ], "crosswidth_matrix_K_expressions": [ [ "17K", "17K+600" ], [ "17K\u2212600", "17K" ] ], "duration_algebra": { "vertex_order": [ "p", "q", "f", "n" ], "edge_order": [ [ 0, 1 ], [ 0, 2 ], [ 0, 3 ], [ 1, 2 ], [ 1, 3 ], [ 2, 3 ] ], "incidence_matrix": [ [ -1, 1, 0, 0 ], [ -1, 0, 1, 0 ], [ -1, 0, 0, 1 ], [ 0, -1, 1, 0 ], [ 0, -1, 0, 1 ], [ 0, 0, -1, 1 ] ], "rank": 3, "augmented_rank": 3, "fixed_duration_solution_translation_dimension": 1, "empirical_independence_claim": false }, "width_comparison": { "current": 600, "C287": 1058, "difference": 458, "difference_decomposition": "460\u22122; Cainan and annual-index roles remain distinct", "600_divisible_by_K": false }, "interpretation": "An admitted equal-17K rectangle with600-year sides exists in all five cases. It is not an all-K rectangle; six displayed durations have rank3 and preserve a common-translation freedom. At three admitted C287 indices, shifting its S and R corners by+458 gives the current p and f corners while q and n remain shared. This coordinate correspondence does not identify the changed source states or establish independent historical intent.", "suggested_next_bounded_question": "Audit the paired458-year corner displacement as separately sourced460-year cumulative Cainan insertion and2-year annual offset, and as the declared regular MT\u2192SP variant conversion; test whether those typed paths agree on precisely the three shared C287 cases.", "later_step_executed": false }