{ "title": "Supplementary Table S2", "description": "Complete calculated matrix of three selected source zones at six unchanged local endpoints (18 paths), plus four unchanged regional comparator paths. Nine local paths are principal and nine supplementary. The three-source matrix is not an exhaustive test of possible sources.", "model_version": "Original cost model; complete source matrix", "definitions": { "straight_line_km": "Great-circle separation of the same source and site endpoints, calculated with the haversine formula using a radius of 6371 km. This is a geographical reference distance, not a reconstructed journey.", "path_to_straight_line_ratio": "Total analytical path length divided by great-circle separation of the original endpoints. The ratio reflects the terrain model, raster grid and movement rules together; it does not isolate the effect of terrain weights.", "composite_cost_index": "The composite cost index combines slope-dependent walking speed with the stated terrain adjustments. It is calculated on the cell grid before the map line is simplified and is a relative comparison measure, not an estimate of journey duration.", "cost_relative_to_harb_central_100": "100 × scenario cost index / 117.8229537558447. Göllü Dağ/Kömürcü–Harbetsuvan is set to 100. A value of 57.0 means 57% of the reference cost under the same assumptions, not 57% of its journey duration.", "percentage_contrasts": "All current reductions use unrounded total_path_length_km, including both endpoint connectors. Rounded displayed values should not be used to recompute them.", "grid_path_length_km": "Sum of the horizontal distances of all elementary steps actually costed, including intermediate cells in longer moves; uses the same row distances and diagonal-distance rule as the original model.", "source_connector_km": "Great-circle distance between the exact source coordinate and its grid-cell centre. Included in total length, even below 0.01 km, but not in movement cost.", "target_connector_km": "Great-circle distance between the target grid-cell centre and the exact site coordinate. Included in total length, even below 0.01 km, but not in movement cost.", "endpoint_connectors_km": "source_connector_km + target_connector_km; geometrical connectors are not costed or optimised.", "total_path_length_km": "grid_path_length_km + source_connector_km + target_connector_km. This is the reported analytical distance. It is a horizontal model distance, not measured distance travelled over the ground.", "archived_display_length_km": "Historical measurement of the simplified map line with the original endpoint handling. Retained for comparison, not used for current distance percentages.", "display_rounding": "Components and totals are rounded independently, so displayed components may not sum exactly. Percentages use unrounded totals.", "analysis_role": "Principal: three sources at Harbetsuvan, Karahan and Göbekli. Supplementary: three sources at Sefer, Taşlı and Hamzan. Regional comparator: four retained scenarios at Jerf and Körtik.", "endpoint_status": "Original model endpoint or illustrative. Does not replace the separate archaeological coordinate-verification record.", "figure_2_displayed": "Whether the scenario belongs to the 14-path display subset retained in Figure 2.", "simplified_display_length_km": "Length of the simplified display polyline; never used for reported analytical percentages." }, "scope_note": "Taşlı and Hamzan use illustrative, unverified local endpoints and are excluded from the principal analysis. Regional comparator paths are unchanged. Figure 2 displays the original 14-path subset for legibility; the interactive map and this table include all 22 calculated paths.", "endpoint_check": "For Harbetsuvan, Karahan, Göbekli and Sefer, verified locations remain in the original model cells. Substituting their terminal connectors changes total lengths by less than 0.06% and six principal contrasts by less than 0.02 percentage points. The Karahan–Nemrut contrast rounds to 30.7% rather than 30.8% under that substitution. All reported principal values retain the original endpoints.", "sensitivity_note": "Each of the six original sensitivity variants was applied to all nine principal paths (54 runs). Total lengths change by −3.08% to +4.72%; both eastern alternatives remain shorter than Göllü Dağ/Kömürcü at all three destinations. The 3 × 3 and 5 × 5 neighbourhoods produce identical expanded paths for all nine cases and are not independent tests of geographical robustness. Source-endpoint placement and the illustrative Taşlı and Hamzan locations remain untested. Supplementary local and regional comparator paths were not added to the principal sensitivity suite.", "rows": [ { "route_key": "harb-central", "analysis_role": "principal", "endpoint_status": "original model endpoint", "figure_2_displayed": true, "source": "Göllü Dağ/Kömürcü", "target": "Harbetsuvan Tepesi", "source_latitude": 38.2546612, "source_longitude": 34.5446033, "target_latitude": 37.048676, "target_longitude": 39.252434, "grid_path_length_km": 487.5703982342601, "source_connector_km": 1.0861847470841555, "target_connector_km": 0.2945386573131009, "total_path_length_km": 488.95112163865736, "straight_line_km": 435.55732299793476, "endpoint_connectors_km": 1.3807234043972563, "path_to_straight_line_ratio": 1.1225873055542124, "length_excess_percent": 12.258730555421238, "composite_cost_index": 117.8229537558447, "cost_relative_to_harb_central_100": 100.0, "archived_display_length_km": 484.83477598729513, "simplified_display_length_km": 484.83477598729513 }, { "route_key": "harb-bingol", "analysis_role": "principal", "endpoint_status": "original model endpoint", "figure_2_displayed": true, "source": "Bingöl/Solhan", "target": "Harbetsuvan Tepesi", "source_latitude": 38.9659351, "source_longitude": 41.0518147, "target_latitude": 37.048676, "target_longitude": 39.252434, "grid_path_length_km": 292.20830844237685, "source_connector_km": 0.41893014501509745, "target_connector_km": 0.2945386573131009, "total_path_length_km": 292.9217772447051, "straight_line_km": 265.1344396367945, "endpoint_connectors_km": 0.7134688023281983, "path_to_straight_line_ratio": 1.1048047083056287, "length_excess_percent": 10.480470830562872, "composite_cost_index": 67.20555383569288, "cost_relative_to_harb_central_100": 57.03944069757214, "archived_display_length_km": 290.20635498535836, "simplified_display_length_km": 290.20635498535836 }, { "route_key": "harb-nemrut", "analysis_role": "principal", "endpoint_status": "original model endpoint", "figure_2_displayed": true, 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128.17929991832818, "endpoint_connectors_km": 0.960364622247672, "path_to_straight_line_ratio": 1.1686279880385337, "length_excess_percent": 16.862798803853373, "composite_cost_index": 38.77555743956191, "cost_relative_to_harb_central_100": 32.910019825095766, "archived_display_length_km": 147.7496778698442, "simplified_display_length_km": 147.7496778698442 }, { "route_key": "kortik-nemrut", "analysis_role": "regional comparator", "endpoint_status": "original model endpoint", "figure_2_displayed": true, "source": "Nemrut Dağ", "target": "Körtik Tepe", "source_latitude": 38.6546955, "source_longitude": 42.2554405, "target_latitude": 37.8144228, "target_longitude": 40.9838383, "grid_path_length_km": 163.68100369794342, "source_connector_km": 0.9618604043993497, "target_connector_km": 0.5414344772325745, "total_path_length_km": 165.18429857957534, "straight_line_km": 145.1355116986765, "endpoint_connectors_km": 1.5032948816319243, "path_to_straight_line_ratio": 1.138138396635299, "length_excess_percent": 13.813839663529892, "composite_cost_index": 45.69917000106093, "cost_relative_to_harb_central_100": 38.786304827970746, "archived_display_length_km": 164.16346657239467, "simplified_display_length_km": 164.16346657239467 } ], "contrasts": [ { "reference_route": "harb-central", "candidate_route": "harb-bingol", "total_path_reduction_percent": 40.091807896254515, "printed_one_decimal_percent": 40.1, "grid_only_reduction_percent": 40.06848867351024 }, { "reference_route": "harb-central", "candidate_route": "harb-nemrut", "total_path_reduction_percent": 27.96386335801081, "printed_one_decimal_percent": 28.0, "grid_only_reduction_percent": 28.01755391519414 }, { "reference_route": "karahan-central", "candidate_route": "karahan-bingol", "total_path_reduction_percent": 42.83949411722085, "printed_one_decimal_percent": 42.8, "grid_only_reduction_percent": 42.867709461394135 }, { "reference_route": "karahan-central", "candidate_route": "karahan-nemrut", "total_path_reduction_percent": 30.758546123856746, "printed_one_decimal_percent": 30.8, "grid_only_reduction_percent": 30.84998516596159 }, { "reference_route": "gobekli-central", "candidate_route": "gobekli-bingol", "total_path_reduction_percent": 37.597577366958326, "printed_one_decimal_percent": 37.6, "grid_only_reduction_percent": 37.56396289450106 }, { "reference_route": "gobekli-central", "candidate_route": "gobekli-nemrut", "total_path_reduction_percent": 15.808134062485035, "printed_one_decimal_percent": 15.8, "grid_only_reduction_percent": 15.827986720589282 } ], "source_files": [ "data/complete_matrix/complete_matrix_inputs.json", "data/complete_matrix/primary_complete_paths.json", "data/complete_matrix/distance_metrics_all_76.json", "data/complete_matrix/verified_coordinate_check.json" ], "metric_version": "full_costed_path", "comparison_count_note": "22 base paths: nine principal, nine supplementary local, four regional comparators. Six principal eastern–central contrasts, using Göllü Dağ/Kömürcü as the same-site reference. Six sensitivity variants give 54 runs." }