### Table A. Key results per candidate (ascent start = named gate; distances along the valley-floor path)

| route | col (map m / DEM m) | Island -> gate km (stades 177.6 / 185) | gate -> col km (climb m) | km/day over 9 d | col -> plain km | km/day over 4 d (3 d) | gate -> plain km (stades 177.6 / 185) | km/day over 13 marching d | steepest 500 m on descent (% , km from col) | plain visible from col (% azimuths) |
|---|---|---|---|---|---|---|---|---|---|---|
| R1 Isere - Arc (Maurienne) - Col du Mont-Cenis | du Mont-Cenis 2083 / 2088 | Aiguebelle 158 (888 / 853) | 87 (+1825) | 9.7 | 32 | 8.0 (10.7) | 119 (670 / 643) | 9.2 | 53% at 13.0 km | no (0.0%) |
| R2 Isere - Arc - Ambin/Savine - Col Clapier - Val Clarea | Clapier 2482 / 2478 | Aiguebelle 158 (888 / 853) | 86 (+2209) | 9.5 | 25 | 6.2 (8.3) | 110 (622 / 597) | 8.5 | 50% at 1.0 km | yes (0.6%) |
| R2b Isere - Arc - Ambin - Col du Petit Mont-Cenis - Mont-Cenis plateau | du Petit Mont-Cenis 2183 / 2180 | Aiguebelle 158 (888 / 853) | 80 (+1842) | 8.8 | 34 | 8.6 (11.5) | 114 (642 / 616) | 8.8 | 54% at 15.2 km | no (0.0%) |
| R3 Isere - Tarentaise - Col du Petit-Saint-Bernard - Aosta - Ivrea | du Petit-Saint-Bernard 2188 / 2190 | Albertville 169 (950 / 912) | 64 (+1937) | 7.1 | 72 | 17.9 (23.9) | 135 (762 / 731) | 10.4 | 29% at 12.2 km | no (0.0%) |
| R4 Durance (direct from Avignon) - Briancon - Col de Montgenevre - Susa | de Montgenevre 1854 / 1851 | Sisteron 161 (908 / 872) | 132 (+1722) | 14.7 | 51 | 12.8 (17.1) | 184 (1033 / 992) | 14.1 | 23% at 5.0 km | no (0.0%) |
| R4c Rhone - Drome - Col de Cabre - Gap - Durance - Col de Montgenevre (Livy/de Beer approach) | de Montgenevre 1854 / 1852 | Crest 91 (512 / 492) | 222 (+2894) | 24.7 | 51 | 12.8 (17.1) | 274 (1540 / 1478) | 21.0 | 25% at 5.0 km | no (0.0%) |
| R5 Durance (direct) - Guil - Col de la Traversette - Po (Saluzzo) | de la Traversette 2947 / 2913 | Sisteron 161 (908 / 872) | 139 (+2687) | 15.4 | 28 | 7.0 (9.3) | 167 (939 / 901) | 12.8 | 51% at 0.5 km | yes (17.3%) |
| R5g Rhone - Drome - Col de Grimone - Gap - Durance - Guil - Traversette (de Beer 1955) | de la Traversette 2947 / 2924 | Crest 91 (512 / 492) | 237 (+3980) | 26.4 | 28 | 7.1 (9.4) | 266 (1495 / 1435) | 20.4 | 51% at 0.0 km | yes (17.3%) |
| R5c Rhone - Drome - Col de Cabre - Gap - Durance - Guil - Traversette | de la Traversette 2947 / 2883 | Crest 91 (512 / 492) | 228 (+3823) | 25.4 | 28 | 7.1 (9.4) | 257 (1446 / 1388) | 19.8 | 50% at 0.8 km | yes (17.3%) |
| R6 Durance (direct) - Ubaye - Col de Larche - Stura - Cuneo | de Larche 1991 / 2002 | Sisteron 161 (908 / 872) | 114 (+1601) | 12.6 | 79 | 19.8 (26.3) | 192 (1084 / 1041) | 14.8 | 23% at 4.0 km | no (0.0%) |
| R6v Durance (direct) - Guillestre - Col de Vars - Ubaye - Col de Larche - Cuneo | de Larche 1991 / 2002 | Sisteron 161 (908 / 872) | 143 (+2603) | 15.9 | 79 | 19.8 (26.3) | 222 (1251 / 1201) | 17.1 | 23% at 4.0 km | no (0.0%) |
| R7 Rhone - Lyon - Geneva - Valais - Col du Grand-Saint-Bernard - Aosta - Ivrea | du Grand-Saint-Bernard 2469 / 2495 | Martigny 379 (2135 / 2050) | 37 (+1954) | 4.1 | 52 | 12.9 (17.2) | 88 (498 / 478) | 6.8 | 54% at 1.8 km | no (0.0%) |

### Table B. Sensitivity to the definition of the 'beginning of the ascent'

| route | definition | start (m, km from Island) | b: Island->start km (stades 177.6) | c: start->col km, zigzag-corrected km, km/day/9d | e: start->plain km (stades 177.6), km/day/13d |
|---|---|---|---|---|---|
| R1 | gate:Aiguebelle | 326 m, 158 km | 158 (888) | 87, 88, 9.7 | 119 (670), 9.2 |
| R1 | flat10 | 1281 m, 236 km | 236 (1326) | 9, 10, 1.1 | 41 (232), 3.2 |
| R1 | z500 | 501 m, 187 km | 187 (1052) | 58, 59, 6.5 | 90 (507), 6.9 |
| R2 | gate:Aiguebelle | 326 m, 158 km | 158 (888) | 86, 86, 9.5 | 110 (622), 8.5 |
| R2 | flat10 | 459 m, 182 km | 182 (1028) | 61, 61, 6.8 | 86 (483), 6.6 |
| R2 | z500 | 501 m, 187 km | 187 (1052) | 56, 57, 6.3 | 82 (459), 6.3 |
| R2b | gate:Aiguebelle | 326 m, 158 km | 158 (888) | 80, 80, 8.9 | 114 (642), 8.8 |
| R2b | flat10 | 459 m, 182 km | 182 (1028) | 55, 56, 6.2 | 89 (503), 6.9 |
| R2b | z500 | 501 m, 187 km | 187 (1052) | 50, 51, 5.7 | 85 (479), 6.5 |
| R3 | gate:Albertville | 346 m, 169 km | 169 (950) | 64, 64, 7.1 | 135 (762), 10.4 |
| R3 | flat10 | 697 m, 210 km | 210 (1182) | 22, 23, 2.5 | 94 (529), 7.2 |
| R3 | z500 | 504 m, 193 km | 193 (1088) | 39, 40, 4.4 | 111 (624), 8.5 |
| R4 | gate:Sisteron | 494 m, 161 km | 161 (908) | 132, 133, 14.7 | 184 (1033), 14.1 |
| R4 | flat10 | 939 m, 267 km | 267 (1505) | 26, 27, 2.9 | 78 (436), 6.0 |
| R4 | z500 | 517 m, 146 km | 146 (819) | 148, 148, 16.5 | 199 (1122), 15.3 |
| R4c | gate:Crest | 199 m, 91 km | 91 (512) | 222, 223, 24.7 | 274 (1540), 21.0 |
| R4c | flat10 | 939 m, 287 km | 287 (1616) | 26, 26, 2.9 | 78 (436), 6.0 |
| R4c | z500 | 500 m, 140 km | 140 (790) | 173, 173, 19.3 | 224 (1263), 17.2 |
| R5 | gate:Sisteron | 494 m, 161 km | 161 (908) | 139, 139, 15.5 | 167 (939), 12.8 |
| R5 | flat10 | 875 m, 248 km | 248 (1394) | 52, 53, 5.9 | 80 (453), 6.2 |
| R5 | z500 | 517 m, 146 km | 146 (819) | 154, 155, 17.2 | 182 (1028), 14.0 |
| R5g | gate:Crest | 199 m, 91 km | 91 (512) | 237, 238, 26.5 | 266 (1495), 20.4 |
| R5g | flat10 | 870 m, 277 km | 277 (1558) | 52, 52, 5.8 | 80 (449), 6.1 |
| R5g | z500 | 509 m, 135 km | 135 (760) | 193, 194, 21.6 | 222 (1247), 17.0 |
| R5c | gate:Crest | 199 m, 91 km | 91 (512) | 228, 229, 25.5 | 257 (1446), 19.8 |
| R5c | flat10 | 871 m, 268 km | 268 (1509) | 52, 52, 5.8 | 80 (449), 6.1 |
| R5c | z500 | 500 m, 140 km | 140 (790) | 179, 180, 20.0 | 208 (1168), 16.0 |
| R6 | gate:Sisteron | 494 m, 161 km | 161 (908) | 114, 114, 12.6 | 192 (1084), 14.8 |
| R6 | flat10 | 822 m, 225 km | 225 (1267) | 50, 50, 5.5 | 129 (725), 9.9 |
| R6 | z500 | 517 m, 146 km | 146 (819) | 129, 129, 14.4 | 208 (1173), 16.0 |
| R6v | gate:Sisteron | 494 m, 161 km | 161 (908) | 143, 143, 15.9 | 222 (1251), 17.1 |
| R6v | flat10 | 1306 m, 292 km | 292 (1643) | 13, 13, 1.4 | 92 (517), 7.1 |
| R6v | z500 | 517 m, 146 km | 146 (819) | 159, 159, 17.7 | 238 (1340), 18.3 |
| R7 | gate:Martigny | 474 m, 379 km | 379 (2135) | 37, 37, 4.1 | 88 (498), 6.8 |
| R7 | flat10 | 496 m, 381 km | 381 (2145) | 35, 35, 3.9 | 87 (488), 6.7 |
| R7 | z500 | 556 m, 180 km | 180 (1014) | 236, 236, 26.3 | 288 (1620), 22.1 |

### Table C. Rhone crossing -> 'Island' (Polybius 3.49.5: four days' march)

| leg | km along valley | km straight | stades (177.6 / 185) | km/day over 4 days | band 12-25 |
|---|---|---|---|---|---|
| Fourques/Arles -> Island (ii) Aygues | 57 | 50 | 321 / 308 | 14.2 | in band |
| Beaucaire-Tarascon -> Island (ii) Aygues | 42 | 35 | 239 / 229 | 10.6 | slow |
| Roquemaure -> Island (ii) Aygues | 9 | 9 | 49 / 47 | 2.2 | slow |
| Fourques/Arles -> Island (i) Isere | 159 | 147 | 894 / 858 | 39.7 | fast |
| Beaucaire-Tarascon -> Island (i) Isere | 144 | 132 | 812 / 780 | 36.1 | fast |
| Roquemaure -> Island (i) Isere | 111 | 105 | 623 / 598 | 27.6 | fast |
| Beaucaire-Tarascon -> Drome confluence (Loriol) | 117 | 106 | 657 / 631 | 29.2 | fast |

### Table D. Where 800 stades from the Island falls (Polybius 3.50.1) and the straight-line ('crow') distances

| route | 800 st @177.6 m = 142.1 km falls at | 800 st @185 m = 148.0 km falls at | Island->gate straight km | gate->col straight km | col->plain straight km | gate->plain straight km |
|---|---|---|---|---|---|---|
| R1 | 45.532N 6.124E (274 m; nearest waypoint Montmelian at 136 km) | 45.555N 6.191E (nearest Aiguebelle at 158 km) | 129 | 56 | 29 | 85 |
| R2 | 45.532N 6.124E (274 m; nearest waypoint Montmelian at 136 km) | 45.555N 6.191E (nearest Aiguebelle at 158 km) | 129 | 64 | 24 | 85 |
| R2b | 45.532N 6.124E (274 m; nearest waypoint Montmelian at 136 km) | 45.555N 6.191E (nearest Aiguebelle at 158 km) | 129 | 57 | 29 | 85 |
| R3 | 45.532N 6.123E (273 m; nearest waypoint Montmelian at 136 km) | 45.560N 6.190E (nearest Montmelian at 136 km) | 143 | 38 | 61 | 99 |
| R4 | 44.031N 5.946E (395 m; nearest waypoint Sisteron at 161 km) | 44.082N 5.950E (nearest Sisteron at 161 km) | 97 | 102 | 45 | 144 |
| R4c | 44.634N 5.435E (520 m; nearest waypoint Luc-en-Diois at 144 km) | 44.590N 5.473E (nearest Luc-en-Diois at 144 km) | 72 | 136 | 45 | 179 |
| R5 | 44.031N 5.946E (395 m; nearest waypoint Sisteron at 161 km) | 44.082N 5.950E (nearest Sisteron at 161 km) | 97 | 106 | 25 | 123 |
| R5g | 44.691N 5.500E (571 m; nearest waypoint Die at 127 km) | 44.673N 5.559E (nearest Col de Grimone at 157 km) | 72 | 161 | 25 | 186 |
| R5c | 44.634N 5.435E (520 m; nearest waypoint Luc-en-Diois at 144 km) | 44.590N 5.473E (nearest Luc-en-Diois at 144 km) | 72 | 161 | 25 | 186 |
| R6 | 44.031N 5.946E (395 m; nearest waypoint Sisteron at 161 km) | 44.082N 5.950E (nearest Sisteron at 161 km) | 97 | 80 | 57 | 137 |
| R6v | 44.031N 5.946E (395 m; nearest waypoint Sisteron at 161 km) | 44.082N 5.950E (nearest Sisteron at 161 km) | 97 | 80 | 57 | 137 |
| R7 | 45.563N 5.399E (305 m; nearest waypoint Bourgoin-Jallieu at 132 km) | 45.561N 5.473E (nearest Bourgoin-Jallieu at 132 km) | 213 | 27 | 42 | 63 |

### Table E. Cumulative distance from the Island at named points (km; stades at 177.6 m in brackets)

- **R1**: Grenoble 91.3 (514); Montmelian 135.9 (765); Aiguebelle 157.8 (888); Saint-Jean-de-Maurienne 190.4 (1072); Modane 219.9 (1238); Lanslebourg 241.4 (1359); Col du Mont-Cenis 244.8 (1378); Susa 263.0 (1481); Turin 315.4 (1776)
- **R2**: Modane 219.9 (1238); Bramans 229.3 (1291); Le Planay (Bramans) 234.6 (1321); Lac Savine 242.2 (1364); Col Clapier 243.3 (1370); Giaglione 251.7 (1417); Susa 254.4 (1433); Turin 306.8 (1728)
- **R3**: Montmelian 135.9 (765); Albertville 168.7 (950); Moutiers 194.4 (1095); Bourg-Saint-Maurice 220.5 (1241); Col du Petit-Saint-Bernard 232.1 (1307); Aosta 274.7 (1547); Ivrea 340.9 (1919); Turin 391.4 (2204)
- **R4**: Avignon 20.7 (117); Cavaillon 43.8 (246); Manosque 115.1 (648); Sisteron 161.2 (908); Tallard 195.1 (1099); Embrun 236.4 (1331); Guillestre 254.4 (1433); L'Argentiere-la-Bessee 271.7 (1530); Briancon 286.0 (1610); Col de Montgenevre 293.7 (1654); Susa 331.0 (1864); Turin 383.4 (2159)
- **R4c**: Loriol 74.4 (419); Crest 91.1 (513); Die 127.4 (717); Luc-en-Diois 144.5 (814); Col de Cabre 161.1 (907); Gap 203.0 (1143); Tallard 214.8 (1209); Guillestre 274.1 (1543); Briancon 305.6 (1721); Col de Montgenevre 313.4 (1764); Turin 403.0 (2269)
- **R5**: Sisteron 161.2 (908); Tallard 195.1 (1099); Guillestre 254.4 (1433); Abries 283.0 (1593); Refuge du Viso 298.3 (1679); Col de la Traversette 300.0 (1689); Pian del Re 302.7 (1704); Paesana 317.3 (1787); Saluzzo 338.1 (1904); Turin 392.1 (2208)
- **R5g**: Loriol 74.4 (419); Crest 91.1 (513); Die 127.4 (717); Col de Grimone 156.8 (883); Gap 211.7 (1192); Guillestre 282.7 (1592); Col de la Traversette 328.3 (1849); Saluzzo 366.4 (2063); Turin 420.4 (2367)
- **R6**: Sisteron 161.2 (908); Tallard 195.1 (1099); Le Lauzet-Ubaye 228.2 (1285); Barcelonnette 247.4 (1393); Jausiers 255.4 (1438); Col de Larche 275.0 (1548); Vinadio 302.7 (1704); Cuneo 337.9 (1903); Savigliano 367.6 (2070); Turin 416.0 (2342)
- **R7**: Lyon 91.7 (516); Les Echelles 176.7 (995); Geneva 275.7 (1552); Martigny 379.2 (2135); Col du Grand-Saint-Bernard 416.2 (2344); Aosta 438.4 (2468); Ivrea 504.6 (2841); Turin 555.1 (3126)

### Table F. Viewshed of the Po plain (viewshed.py; plain = DEM < 400 m, east of 7.3E, north of 44.4N; 0.25 deg rays to 120 km; k = 0.13; observer 2 m)

| col | DEM height (m) | from the col: plain visible, % of azimuths, nearest plain km | first point on the descent with plain visible (km from col; % az) | +100 m knoll | +300 m knoll | vantage scan: cells <=1.5 km & <=300 m above seeing plain / scanned; best % az (height, distance) |
|---|---|---|---|---|---|---|
| Col du Mont-Cenis | 2088 | no, 0.0%, - | none within 10 km | no 0.0% (2197 m, 370 m away) | yes 0.2% (2394 m, 767 m away) | 3 / 61; best 0.5% (2383 m, 1053 m away) |
| Col Clapier | 2479 | yes, 0.6%, 80 km | 1.00 km; 4.9% | no 0.0% (2580 m, 290 m away) | no 0.0% (2795 m, 661 m away) | 29 / 56; best 8.1% (2712 m, 1400 m away) |
| Col du Petit Mont-Cenis | 2181 | no, 0.0%, - | none within 10 km | no 0.0% (2296 m, 458 m away) | no 0.0% (2567 m, 770 m away) | 0 / 57; best 0.0% (2456 m, 1496 m away) |
| Col du Petit-Saint-Bernard | 2189 | no, 0.0%, - | none within 10 km | no 0.0% (2303 m, 404 m away) | no 0.0% (2512 m, 1009 m away) | 0 / 89; best 0.0% (2288 m, 1489 m away) |
| Col de Montgenevre | 1853 | no, 0.0%, - | none within 10 km | no 0.0% (1956 m, 387 m away) | no 0.0% (2156 m, 1090 m away) | 0 / 91; best 0.0% (2142 m, 1253 m away) |
| Col de la Traversette | 2912 | yes, 17.3%, 26 km | 0.25 km; 11.5% | yes 21.7% (3048 m, 220 m away) | none within 2.5 km | 14 / 18; best 25.6% (3001 m, 960 m away) |
| Col de Larche | 1996 | no, 0.0%, - | none within 10 km | no 0.0% (2098 m, 420 m away) | no 0.0% (2298 m, 847 m away) | 0 / 68; best 0.0% (2132 m, 1475 m away) |
| Col du Grand-Saint-Bernard | 2472 | no, 0.0%, - | none within 10 km | no 0.0% (2576 m, 201 m away) | no 0.0% (2780 m, 643 m away) | 0 / 57; best 0.0% (2753 m, 1419 m away) |
| Col Agnel | 2731 | no, 0.0%, - | n/a (not on a modelled route) | no 0.0% (2833 m, 564 m away) | no 0.0% (3056 m, 1283 m away) | 0 / 47; best 0.0% (2736 m, 1246 m away) |

### Table H. Rhone crossing -> Po plain in total, against Polybius 3.39.9-10 (1400 + 1200 = 2600 stades = 462 km at 177.6 m, 481 km at 185 m)

| route | Island | crossing option | crossing->Island km | Island->plain km | total km | total stades (177.6 / 185) | % of 2600 st (177.6) |
|---|---|---|---|---|---|---|---|
| R1 | Isere | Fourques/Arles | 159 | 277 | 436 | 2453 / 2354 | 94% |
| R1 | Isere | Beaucaire-Tarascon | 144 | 277 | 421 | 2370 / 2275 | 91% |
| R1 | Isere | Roquemaure | 111 | 277 | 387 | 2181 / 2094 | 84% |
| R2 | Isere | Fourques/Arles | 159 | 268 | 427 | 2405 / 2308 | 92% |
| R2 | Isere | Beaucaire-Tarascon | 144 | 268 | 412 | 2322 / 2230 | 89% |
| R2 | Isere | Roquemaure | 111 | 268 | 379 | 2133 / 2048 | 82% |
| R2b | Isere | Fourques/Arles | 159 | 272 | 431 | 2424 / 2327 | 93% |
| R2b | Isere | Beaucaire-Tarascon | 144 | 272 | 416 | 2342 / 2248 | 90% |
| R2b | Isere | Roquemaure | 111 | 272 | 382 | 2153 / 2067 | 83% |
| R3 | Isere | Fourques/Arles | 159 | 304 | 463 | 2606 / 2502 | 100% |
| R3 | Isere | Beaucaire-Tarascon | 144 | 304 | 448 | 2524 / 2423 | 97% |
| R3 | Isere | Roquemaure | 111 | 304 | 415 | 2334 / 2241 | 90% |
| R4 | Aygues | Fourques/Arles | 57 | 345 | 402 | 2262 / 2172 | 87% |
| R4 | Aygues | Beaucaire-Tarascon | 42 | 345 | 387 | 2180 / 2093 | 84% |
| R4 | Aygues | Roquemaure | 9 | 345 | 354 | 1990 / 1911 | 77% |
| R4c | Aygues | Fourques/Arles | 57 | 364 | 421 | 2373 / 2278 | 91% |
| R4c | Aygues | Beaucaire-Tarascon | 42 | 364 | 407 | 2291 / 2199 | 88% |
| R4c | Aygues | Roquemaure | 9 | 364 | 373 | 2102 / 2018 | 81% |
| R5 | Aygues | Fourques/Arles | 57 | 328 | 385 | 2168 / 2081 | 83% |
| R5 | Aygues | Beaucaire-Tarascon | 42 | 328 | 370 | 2085 / 2002 | 80% |
| R5 | Aygues | Roquemaure | 9 | 328 | 337 | 1896 / 1820 | 73% |
| R5g | Aygues | Fourques/Arles | 57 | 356 | 413 | 2328 / 2235 | 90% |
| R5g | Aygues | Beaucaire-Tarascon | 42 | 356 | 399 | 2246 / 2156 | 86% |
| R5g | Aygues | Roquemaure | 9 | 356 | 365 | 2057 / 1974 | 79% |
| R5c | Aygues | Fourques/Arles | 57 | 348 | 405 | 2279 / 2188 | 88% |
| R5c | Aygues | Beaucaire-Tarascon | 42 | 348 | 390 | 2197 / 2109 | 84% |
| R5c | Aygues | Roquemaure | 9 | 348 | 357 | 2007 / 1927 | 77% |
| R6 | Aygues | Fourques/Arles | 57 | 354 | 411 | 2313 / 2220 | 89% |
| R6 | Aygues | Beaucaire-Tarascon | 42 | 354 | 396 | 2230 / 2141 | 86% |
| R6 | Aygues | Roquemaure | 9 | 354 | 363 | 2041 / 1959 | 79% |
| R6v | Aygues | Fourques/Arles | 57 | 384 | 440 | 2480 / 2381 | 95% |
| R6v | Aygues | Beaucaire-Tarascon | 42 | 384 | 426 | 2398 / 2302 | 92% |
| R6v | Aygues | Roquemaure | 9 | 384 | 392 | 2209 / 2120 | 85% |
| R7 | Isere | Fourques/Arles | 159 | 468 | 627 | 3528 / 3387 | 136% |
| R7 | Isere | Beaucaire-Tarascon | 144 | 468 | 612 | 3446 / 3308 | 133% |
| R7 | Isere | Roquemaure | 111 | 468 | 578 | 3256 / 3126 | 125% |

### Table G. Pleiades (Alcyone) phases in 218 BC at 45 N, proleptic Julian calendar (pleiades.py)

| event | sun -0.833 (true) | h = 6 | h = 7.5 | h = 9 | h = 11 (Schoch) | pyephem cross-check agrees |
|---|---|---|---|---|---|---|
| morning setting | 29 Oct 218 BC | 4 Nov 218 BC | 6 Nov 218 BC | 7 Nov 218 BC | 9 Nov 218 BC | yes |
| evening setting | 24 Apr 218 BC | 18 Apr 218 BC | 16 Apr 218 BC | 15 Apr 218 BC | 12 Apr 218 BC | yes |
| acronychal rising | 14 Oct 218 BC | 30 Sep 218 BC | 25 Sep 218 BC | 21 Sep 218 BC | 15 Sep 218 BC | yes |
| heliacal rising | 17 Apr 218 BC | 2 May 218 BC | 6 May 218 BC | 11 May 218 BC | 17 May 218 BC | yes |