Presented here is latest arithmetical (and geometrical) analysis centred on the sectorial template, migratory patterns and signifiers of the Migrator Model -based on Garry Sacco's 1574.4-day orbit periodicity and my proposition the inner middle-ring asteroid belt around Tabby's Star (KIC 8462852) is being mined in a systematic sectorial operation. The 'Beginner's Guide' is the place to start. A deeper exposition can be found in my Kindle book: 'The Mystery of Tabby's Star: The Migrator Model.'
The Migrator Model started with the template, a simplistic division of Sacco's orbit - I was looking for evidence of a sector-by-sector asteroid harvesting operation and at the time was unfamiliar with the Where's the Flux paper by Boyajian et. al. - which may have been a blessing in disguise as I would have tried to fit the 48.4, or as 24.2, day spacing into Sacco's orbit. Ironically now that is one of the accomplishments of the model (re: the quadratic correlation†). Though obviously aware of Sacco's paper - it is his orbit proposition on which my work rests, I did not get round to reading it for a little while after proposing the template. Indeed, such was my naivety and inexperience in the field, in looking for a sector structure I was using the Wikipedia dates on the star - unaware that the dates I was looking at were for where the dips began - whereas most of the dates used by the astrophysics community were actually for where the dips peaked at maximum depth. This meant when I came to the data, I was not handicapped by the conventions of the science - I noted a consistency for a 29-day rhythm between a number of key dips - but of course the nearest complete multiple 29 in Sacco's 1574.4-day orbit is 1566 days, leaving an 8-day shortfall. The positions of Skara-Brae and Angkor in 2017, with respect to D800 ways back in 2011, pointed to an axis line bisecting the orbit (the fulcrum) and I split the 8 days either side to create two extended 33-day sectors. At this point, I had no idea of how to accommodate the 0.4 fraction missing from the template's 1574 days =
52 * 29 = 1508
2 * 33 = 66
The proposition of the fulcrum cycle was an attempt to address the 0,4 shortfall and also to interpret Bruce Gary's 2019 October-November-December data. Every 2.5 orbits (2.5 * 1574.4 = 3936), the fulcrum advances one calendar day, allowing the 1574 template to keep apace with Sacco's full 1574.4 orbit (consistent with a signalling premise). Then a while back, looking at Bourne's 776 days and Solorzano's base 10 non-spurious, I found this intriguing route:
776 + 77.6 = 853.6
853.6 - 787.2 (half orbit) = 66.4
Tantalising not just because (as shown) the route can be expressed algebraically, but because the structural relations here pointed to the template's two extended 33-day sectors along with the 0.4 fraction missing from the template. But I still at this time did hit upon the fulcrum cross method. Now the 928 days proposed by Kiefer et al. was one the earliest pointers to the consistency of the template, it comprises 32 * 29-day regular sectors and (so far) they are the only two dips that fall on the sector boundary datelines exactly (sectors #8 and #40 respectively). Following the findings of the separation of the fraction (re: opposite migratory momentums), this route emerged...
1508 (= the template's 52 regular sectors) / 0.625 = 2412.8
928 (Kiefer) / 0.625 = 1484.8
2412.8 + 3897.6
3897.6 - 2323.2 (= 48 * 48.4; re: separation of the fraction) = 1574.4 (Sacco's orbit)
But I still overlooked the path to the fulcrum cross, preoccupied with the π findings (re: the 3014.4 signal), and the finding that all the completed dip signifiers become a multiple of 48.4 by simply adding 1/10th of the signifier to itself. The route can be reversed and by dividing key multiples of 48.4 by 1.1, the completed dip signifiers manifest. So now we can start running through these fascinating new findings...
310 (days between Elsie and Evangeline) - 66.4 = 243.6
= 92.8 + 150.8
Thus:
243.6 / 0.625 = 389.76
The difference between 52 * 29 and 52 * 24.2 = 249.6 (re: the academic download reprise)/ Simply by adding 1/10th of 748.8 (= 3 * 249.6)...
389.76 + 74.88 = 464.64 (= 9.6 * 48.4)
The sidereal pointer:
464.64 - 98.4 (= 1/16th 1574.4) = 366.24 (terrestrial sidereal year).
XXX
But getting back on track, the fulcrum cross method multiples the result (yielded by subtracting the two extended 33-day sectors with the 0.4 restored to the fulcrum separating the two sectors) by 4...
310 - 66.4 = 243.6
4 * 243.6 = 974.4
974.4 - 393.6 (= quarter orbit or as 1/10th fulcrum cycle) = 580.8
580.8 = 12 * 48.4
580.8 / 1.1 = 528
The completed dip signifier for D1520 (the mother of all dips at 21%). Taking the pointer, the distance between D1520 and Evangeline = 1851 days, and crosses the fulcrum twice over the time period (2 * 66.4 = 132.8)...
1851 - 132.8 = 1718.2
= 71 * 24.2 (or 35.5 * 48.4)
XXX
An important finding as one of the propositions of the model is that the generative dynamic for the 48.4-day migration is launched from within the two extended sectors. And we haven't even began to scratch the surface. 837 (days between Elsie and TESS)...
837 - 66.4 = 770.6
4 * 770.6 = 3082.4
3082.4 = 1574.4 + 1508
3082.4 + 66.4 = 3148.8 (= 2 * 1574.4)
3082.4 - 66.4 = 3016 (= the Skara-Angkor '54-platform and 2 * 1508 ††)
The completed dip signifier for the TESS dip is 2904:
4 * 837 = 3348
3348 - 444 (the π lockdown number) = 2904
XXX
And it goes on:
928 (Kiefer) - 66.4 = 861.6
4 * 861.6 = 3446.4
3446.4 - 1704 (= Kiefer 928 + Bourne 776) = 1742.4
= 36 * 48.4
1742.4 / 1.1 = 1584 (= completed dip signifier for Elsie)
XXX
Bourne's periodicity...
776 - 66.4 = 709.6
4 * 709.6 = 2838.4
2838.4 - 393.6 = 2444.8
Part of the 1440 π route (where n = non-integers):
31415 (10,000 * π - n) / 0.312.5 = 100528
100528 / 0.625 = 160844.8
160844.8 - 144000 = 16844.8
16844.8 - 14400 = 2444.8
2444.8 - 1440 = 1004.8
0.3125 * 1004.8 = 314 (= 100 * π - n)
XXX
1536 from the opposite migratory momentums and separation of the fraction proposition...
1536 - 66.4 = 1469.6
4 * 1469.6 = 5878.4
5878.4 - 3936 = 1942.4
1942.4 - 393.6 = 1548.8
= 32 * 48.4
A pointer to the hexadecimal findings as 1574.4 - 1548.8 = 25.6. The difference between the two parts of the quadratic correlation. There's even more, but that I will present in the next academic download. But here is the fulcrum cross applied to the first part of the quadratic correlation....
XXX
† Tom Johnson, Masters Theoretical Physics and Advanced Mathematics (thesis on black holes and vacuums), turned my 492 signal into the crisp quadratic equation:
S = 1574.4
B = 48.4
T = 52
XXX
492 - 66.4 = 425.6
4 * 425.6 = 1702.4
1702.4 - 928 (Kiefer) = 774.4
XXX
774.4 - 66.4 = 708
The completed dip signifier for D800, marking the half orbit line, is 792:
708 + 79.2 = 787.2 (half orbit)
XXX
928 - 774.4 = 153.6
= 1/10th of the 1536 days of the separation of the fraction.
XXX
†† 3132, the '52-platform' of the Skara-Angkor signifier shows a route through π to 24 * 48.4 (1161.6), applying the fulcrum cross:
3132 - 66.4 = 3065.6
4 * 3065.6 = 12262.4
12262.4 - 11616 = 646.4
= difference between 928 and 1574.4
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So next step will be to look at distances between other key dips and see what the fulcrum cross method has to say - sure I have only just caught the tip of the iceberg here.
Recently covered, but a nice route (where 'n' = non-integers):
1,000, 000 * π - n = 3141592
It's a concise number, as is ten multiples of the fulcrum cross:
3141592 - 664 = 3140928
3140928 = 1995 * 1574.4
More on 1995 bellow, but also divisible by the 'abstract ellipse' of the 3014.4 signal:
3140928 = 23370 * 134.4
XXX
4 * 1995 = 444 + (24 * 314)
XXX
8 * 23370 = 190160
= 444 + (594 * 314)
Crossover of the fulcrum cross and Sacco's '65' multiplier (65 * 24.2 = 1573)
1573 - 66.4 = 1506.6
3016 (= 2 * 1508 or the Skara-Angkor '54-platform) = 1509.4
1574.4 - 1509.4 = 65
Remember too:
1508 + 65 = 1573 (= 65 * 24.2)
This particular route probably won't make into the next academic download due to it coming close to the pitfall of circular logic (ultimately all pure math follows circular logic) - which is why gradually rendering key findings in algebraic form to afford transparency to the logic. Though I learnt much during my brief collaboration with Tom Johnson (Masters Theoretical Physics and Advanced Mathematics), I'm bound to make a few mistakes along the way (the route above may still hold something). Indeed, as I move towards completing the Migrator Model, getting more scientific help will be the priority.
The route might be stronger than I thought, because although '65' is a factor of 1573 (in relation to 24.2), it is not a factor in 1574.4. Also it takes two multiples of 1508 to extract the path to 65.
The route to 32 * 48.4 through 1536 manifests in the key three multiples of 249.6 (= 748.8) used in the completed dip signifier for Skara/Angkor route†:
748.8 - 66.4 = 682.4
4 * 682.4 = 2729.6
2729.6 - 1180.8 (= 3 * 393.6) = 1548.8
XXX
1536 - 66.4 = 1469.6
4 * 1469.6 = 5878.4
5878.4 - (11 * 393.6 = 4329.6) = 1548.8
XXX
†
1.1 * 4224 (completed dip signifier for Skara Brae and Angkor) = 4646.4
= 96 * 48.4
4646.4 - 748.8 = 3897.6
= (1508 + 928) / 0.625
3897.6 - 748.8 = 3148.8
= 2 * 1574.4
The '249.6' structure block derived from:
52 * 29 (length in days of one of the 52 regular sectors in the template) = 1508
52 * 24.2 = 1258.4
1508 - 1258.4 = 249.6
So something I missed (or I may have stumbled across earlier but significance overlooked)...
1536 (the migration sans the 96 * 0.4 migratory landing spokes) - 748.8 = 787.2
half orbit.
2 * 1536 = 3072
3072 - 748.8 = 2323.2 (= 48 * 48.4)
here '48' = half the '96' migratory spokes, the migrations meeting first at the half orbit line:
2323.2 - 1536 = 787.2
Like pieces of a jigsaw, for 3072 manifests in the application of the Elsie method to the quadratic correlation.
Though not (directly) connected with the fulcrum cross method, a new minor route through π using the 748.8 'structure block' (where 'n' = non-integers):
1704 (Bourbe 776 + Kiefer 928) + (38 * 748.8)
= 0.96(10,000 * π -n)