THE IRISH ANNALS AGAINST THE 521-YEAR CYCLE (Armagh). Offsets tested: [-1042, -532, -521, 0, 521, 532, 1042]. 521 Julian years = 190,295 d = 6443.996 synodic = 6992.998 draconic = 6906.12 anomalistic months = 27185 weeks. A. DAY-TEETH: for each offset, the nearest eclipse of that body to the stated day (Δ days), visible at Armagh, magnitude at Armagh, and the stated hour / weekday / lunar age against the sky. id offset Δd vis mag hour(stated→sky) feria(stated→sky) luna(stated→sky) says U664.1 -1042 1 . 0.0 9→2.1✗ darkness ✗ U664.1 -532 31 . 9→ darkness U664.1 -521 1 v 0.89 9→8.5✓ darkness ✗ U664.1 +0 0 v 1.0 9→9.7✓ darkness ✓ U664.1 +521 0 v 0.95 9→7.3✓ darkness ✓ U664.1 +532 -31 . 9→ darkness U664.1 +1042 0 v 0.68 9→3.7✗ darkness ✗ U692.5 -1042 137 . colour of blood U692.5 -532 -158 . colour of blood U692.5 -521 137 . colour of blood U692.5 +0 136 . colour of blood U692.5 +521 136 . colour of blood U692.5 +532 105 . colour of blood U692.5 +1042 136 . colour of blood U734.2 -1042 3 . U734.2 -532 33 . U734.2 -521 2 . U734.2 +0 2 . U734.2 +521 2 . U734.2 +532 -29 . U734.2 +1042 2 . T734.2 -1042 1 v 1.0 T734.2 -532 31 . T734.2 -521 0 v 1.0 T734.2 +0 0 v 1.0 T734.2 +521 0 v 1.0 T734.2 +532 -31 . T734.2 +1042 0 . 1.0 U865.1 -1042 1 . 0.0 moon same month ✗ U865.1 -532 31 . U865.1 -521 1 v 0.81 moon same month ✗ U865.1 +0 0 v 1.0 moon same month ✓ U865.1 +521 0 v 0.93 moon same month ✓ U865.1 +532 -31 . U865.1 +1042 0 . 0.0 moon same month ✗ U878.8 -1042 -1 v 0.68 4→3✗ 14→14.1✓ about the third watch U878.8 -532 31 . 4→ 14→ about the third watch U878.8 -521 -1 v 0.87 4→3✗ 14→14.5✓ about the third watch U878.8 +0 0 v 1.0 4→4✓ 14→15.1✓ about the third watch U878.8 +521 0 . 1.0 4→4✓ 14→15.5✓ about the third watch U878.8 +532 -32 . 4→ 14→ about the third watch U878.8 +1042 -1 . 1.0 4→4✓ 14→15.6✗ about the third watch U921.9 -1042 0 . 0.91 1→7.3✗ 3→2✗ U921.9 -532 30 . 1→ 3→ U921.9 -521 -1 v 1.0 1→1.7✓ 3→2✗ U921.9 +0 -1 v 1.0 1→1.9✓ 3→2✗ U921.9 +521 -1 v 1.0 1→10.6✗ 3→2✗ U921.9 +532 -32 . 1→ 3→ U921.9 +1042 -1 . 1.0 1→3.8✗ 3→2✗ U1023.1 -1042 -1 v 0.56 5→4✗ 14→14.0✓ solar a fortnight after ✗ U1023.1 -532 31 . 5→ 14→ U1023.1 -521 -1 v 0.69 5→4✗ 14→14.2✓ solar a fortnight after ✓ U1023.1 +0 -1 v 0.91 5→4✗ 14→14.8✓ solar a fortnight after ✓ U1023.1 +521 0 v 1.0 5→5✓ 14→15.4✓ solar a fortnight after ✓ U1023.1 +532 -32 . 5→ 14→ U1023.1 +1042 -1 v 1.0 5→5✓ 14→15.6✗ solar a fortnight after ✓ M664.4 -1042 -1 . 0.0 M664.4 -532 29 . M664.4 -521 -1 v 0.89 M664.4 +0 -2 . M664.4 +521 -2 . M664.4 +532 -33 . M664.4 +1042 -2 . M1030.8 -1042 0 . 0.0 M1030.8 -532 31 . M1030.8 -521 0 v 0.36 M1030.8 +0 0 v 0.72 M1030.8 +521 0 v 0.56 M1030.8 +532 -31 . M1030.8 +1042 -1 v 0.19 B. YEAR-LEVEL AND DESCRIPTIVE ENTRIES: at each offset, is there an eclipse of that body visible at Armagh in the stated year, and does the description fit (max magnitude at Armagh that year; 'stars seen'/'darkness' need ≥0.95, 'colour of blood' needs a total lunar eclipse, 'morning'/'midday'/'ninth hour' need the hour). year body says -1042 -532 -521 +0 +521 +532 +1042 496 sun visible ✓0.26 ✓0.70 . . ✓0.47 . . 512 sun ✓0.17 . ✓0.16 ✓0.18 ✓0.68 ✓0.79 ✓0.28 591 sun dark morning . v0.24 . ✓0.14 v0.08 . v0.24 689 sun part of the sun . . . . . . . 718 moon at its full . ✓0.22 . ✓0.14 ✓0.34 ✓0.26 ✓0.50 807 moon colour of blood ✓1.00 ✓1.00 ✓1.00 ✓1.00 v0.94 v0.88 v0.77 885 sun stars seen v0.93 . v0.89 ✓0.98 v0.84 . ✓0.97 674 sun T: heavenly arc, fourth . ✓0.27 ✓0.29 . . . . 692 moon T: bloody colour, St Mar . . . . . . . 734 moon T: 9 Kal Feb ✓1.00 ✓1.00 ✓1.00 ✓1.00 ✓1.00 ✓1.00 ✓1.00 1023 sun T: at midday + lunar sam . . v0.60 ✓0.98 v0.92 . v0.83 444 sun AI: ninth hour . . v0.66 . . ✓0.28 . 594 sun AI: morning ✓0.53 . ✓0.58 ✓1.00 . . . 626 sun AI . ✓0.28 ✓0.83 . ✓0.81 . ✓0.54 865 sun AI: on the Kalend . . ✓0.81 ✓1.00 ✓0.93 . . 1023 sun AI: black cloud . . ✓0.60 ✓0.98 ✓0.92 . ✓0.83 1039 sun AI ✓0.54 ✓0.85 . ✓0.89 ✓0.63 ✓0.41 ✓0.83 fits by offset: {-1042: 6, -532: 7, -521: 8, 0: 11, 521: 8, 532: 5, 1042: 7} (visible only: {-1042: 7, -532: 8, -521: 11, 0: 11, 521: 12, 532: 6, 1042: 10}) of 17 C. THE KALENDS COMB: 295 year-lines with a weekday and a moon's age for 1 January. At each offset: weekday matches (exact), moon's age matches (±1 day, true sky), both. 532 is the computus' own cycle; 521 is the sky's. offset -1042: weekday 140/295 moon age 164/295 both 84/295 offset -532: weekday 5/295 moon age 149/295 both 1/295 offset -521: weekday 73/295 moon age 158/295 both 42/295 offset +0: weekday 5/295 moon age 149/295 both 2/295 offset +521: weekday 3/295 moon age 134/295 both 1/295 offset +532: weekday 5/295 moon age 10/295 both 1/295 offset +1042: weekday 2/295 moon age 124/295 both 1/295 (lines per annal: {'Annals of Ulster': 295}) D. THE KALENDS COMB SCANNED FINELY around 0, ±521, ±532, ±1042: weekday matches / moon-age matches / both, of 295 -1046: weekday 0 age 0 both 0 -1045: weekday 3 age 20 both 0 -1044: weekday 1 age 0 both 0 -1043: weekday 76 age 0 both 0 -1042: weekday 140 age 164 both 84 ← best both -1041: weekday 0 age 2 both 0 -1040: weekday 0 age 1 both 0 -1039: weekday 2 age 2 both 0 -1038: weekday 1 age 0 both 0 -536: weekday 0 age 0 both 0 -535: weekday 2 age 4 both 0 -534: weekday 1 age 0 both 0 -533: weekday 217 age 0 both 0 -532: weekday 5 age 149 both 1 -531: weekday 0 age 0 both 0 -530: weekday 3 age 0 both 0 -529: weekday 1 age 24 both 0 -528: weekday 3 age 0 both 0 -525: weekday 0 age 0 both 0 -524: weekday 3 age 27 both 0 -523: weekday 2 age 0 both 0 -522: weekday 148 age 0 both 0 -521: weekday 73 age 158 both 42 -520: weekday 0 age 2 both 0 -519: weekday 1 age 1 both 0 -518: weekday 1 age 3 both 1 -517: weekday 1 age 0 both 0 -8: weekday 1 age 20 both 0 -7: weekday 76 age 0 both 0 -6: weekday 140 age 1 both 0 -5: weekday 0 age 2 both 0 -4: weekday 0 age 0 both 0 -3: weekday 2 age 41 both 0 -2: weekday 1 age 0 both 0 -1: weekday 217 age 0 both 0 +0: weekday 5 age 149 both 2 +1: weekday 0 age 2 both 0 +2: weekday 3 age 2 both 0 +3: weekday 1 age 3 both 1 +4: weekday 3 age 0 both 0 +5: weekday 211 age 4 both 4 +6: weekday 2 age 0 both 0 +7: weekday 0 age 0 both 0 +8: weekday 3 age 160 both 2 +517: weekday 1 age 0 both 0 +518: weekday 1 age 47 both 0 +519: weekday 1 age 0 both 0 +520: weekday 283 age 0 both 0 ← best weekday +521: weekday 3 age 134 both 1 +522: weekday 0 age 2 both 0 +523: weekday 3 age 2 both 0 +524: weekday 1 age 3 both 1 +525: weekday 76 age 0 both 0 +528: weekday 0 age 0 both 0 +529: weekday 2 age 169 both 1 +530: weekday 1 age 1 both 0 +531: weekday 217 age 0 both 0 +532: weekday 5 age 10 both 1 +533: weekday 0 age 0 both 0 +534: weekday 3 age 2 both 0 +535: weekday 1 age 2 both 1 +536: weekday 3 age 0 both 0 +1038: weekday 3 age 0 both 0 +1039: weekday 1 age 60 both 0 +1040: weekday 3 age 0 both 0 +1041: weekday 211 age 0 both 0 +1042: weekday 2 age 124 both 1 +1043: weekday 0 age 2 both 0 +1044: weekday 3 age 1 both 0 +1045: weekday 2 age 3 both 1 +1046: weekday 148 age 0 both 0 weekday matches by century of entry, at offset 0 and at +520: 400s: n= 40 at 0: 3 at +520: 36 at +1: 0 at -1: 28 500s: n= 63 at 0: 0 at +520: 60 at +1: 0 at -1: 47 600s: n= 58 at 0: 1 at +520: 56 at +1: 0 at -1: 44 700s: n= 1 at 0: 0 at +520: 1 at +1: 0 at -1: 1 900s: n= 6 at 0: 0 at +520: 4 at +1: 0 at -1: 2 1000s: n= 97 at 0: 1 at +520: 96 at +1: 0 at -1: 72