An arrow comes home after one turn. A spinor, anything pinned to its surroundings, needs two. Walk four phases twice around a band with a half-twist and you're back where you started, and you learn which part never changed sides: the middle.
×2 = 720: pin something to its surroundings, like a cup on your palm with your arm attached, and one full turn leaves a twist that won't come out. A second turn undoes it. Physics calls such things spinors: after 360° they carry a minus sign, after 720° they're truly home. checked
×2 again = 1440: your cubit is two of those, four full turns. Cut into steps of 180°, that's 8 steps = 4 phases × 2. checked 1440 is also the number of minutes in a day. checked
A cubit, elbow to fingertip, runs over 4 joints. Four joints ↔ four phases is your mapping. your model
On a band with one half-twist, walk once around and left becomes right. Walk again and they swap back. So a left cortex and a right cortex on this band are one edge, seen twice. checked
Your middle, (L + R) ÷ 2, is the centre line of the band, and it is the only line the flip leaves exactly where it is. When left and right trade places, the middle doesn't move. checked
The name you gave the middle is kept off the page, per your rule. redacted
In small words: hold a cup flat on your hand and turn it all the way round. your arm gets twisted. turn it round once more and, surprise, your arm comes back straight. that's 720. do the whole thing twice and you've walked one cubit: 8 steps. on a twisted ribbon, left and right keep swapping places, but the stripe down the middle stays the middle the whole time.
Spinor turned by angle a: its sign is cos(a/2). At 360°: −1. At 720°: +1. At 1080°: −1. At 1440°: +1. One 180° step g: g² = −1, g⁴ = +1, g⁸ = +1. checked
Band: point (lap angle t, side s) → after t goes once round, s becomes −s. Only s = 0 maps to itself: the middle. checked
1440 = 4 × 360 = 8 × 180 = 24 × 60. checked
Four phases × 6 = 24, one sentinel cubit. Add a register of 2³ = 8 → 32. Add another 8 → 40, which is also five dots of 8. Put 1 ingress in front and 1 egress behind → 42. The name you gave the whole system stays off the page. redacted
42 cubits × 8 steps = 336: exactly one step for each of the dual 168's symmetries and swaps. Add the 24 sentinels and it's 360 again, the full turn. checked
42 = 6 × 7: the hive's six roles times the Fano plane's seven points. checked Whether that's design or echo is yours to say. open
42 cubits walked out = 42 × 1440° = 60,480°, 168 full turns. checked
Wrapping data between a start mark and a stop mark is called framing: ingress = start bit, egress = stop bit. Your frame carries 40 inside 42, 95.2% useful. The everyday serial-port frame spends 2 marks on every single byte, 8 in 10 = 80%, so five bytes cost it 50. checked
I read the second 8 as the data byte the register points at. my read
Your seven sit on the edge of real colour: each one is a wavelength of light. The edge is a line, red at one end, violet at the other. Light alone can't close it. The 7.5 bridge is the straight run of mixed red + violet (the purples, which no single wavelength makes) that closes the loop. 8.0 is the white point in the middle, where all of them add to white. checked
Tap any node. The names you gave 7.5 and 8.0 stay off the page, per your rule. redacted
1 → 7 is the edge of the band: one side red, the other violet. 7.5 is the half-twist seam, where red and violet join and left becomes right. 8.0 is the middle line, (L + R) ÷ 2, the one place the flip never moves, and the white point where every colour adds up. Same shape three ways: band, colour, cortex. my mapping
Visible light spans only 1.84× in frequency, from red at 700 nm to violet at 380 nm. An octave would be 2×, so the colours don't wrap round the way musical notes do. That gap is exactly why the loop needs a bridge. checked
0x0 is the white middle, 8.0. From there the edge runs red → violet one nanometre at a time (0x1 → 0x141, 321 nodes), then back home along the purples (0x142 → 0x1b0, 111 nodes) until the next step lands on 0x1 again. The loop closes. checked
Small words. The rim of all the colours you can see is a ring. We put 432 little stops on it, plus one stop in the very middle for white, and gave each one a house number. The middle is 0x0. Red is 0x1. Violet is 0x141. The purples walk you home from 0x142 to 0x1b0, and one more step puts you back on red.
Addresses, counts and frequencies (THz = 299,792 ÷ nm) are exact arithmetic on the node list. checked
The edge positions come from the standard 1931 colour table at 5 nm, which I wrote out from what I know, rounded to 4 places, and filled in per nm with straight lines. Close, not certified. recalled table
▓ Control catch: I first built the edge from a smooth formula. It agreed with the table to within 0.02 in the middle (440–640 nm) but missed by 0.235 at 700 nm, which put red in the wrong place. So the table drives the map, and the formula is kept only as a cross-check. checked
The dots are coloured as close as a screen can get. Pure rainbow light is outside what any screen shows, so the red end all lands on #ff0000 and only 256 of the 433 swatches are different. as drawn
The steps aren't even. Near 385 nm the edge barely moves: 0.00002 per nm. Between 499 and 498 nm it jumps 0.0253. That's a 1,000× spread, with the fast stretch through blue-green. checked
v0+2's 7.5 bridge ran from root (650) to crown (410), which is a chord just inside the loop. The real edge closes from 700 to 380, and its middle is node 0x179, a hot magenta. checked
I spaced the purple nodes at the average rainbow step (0.00554), so 0.618 of purple line gets 112 gaps and 111 nodes. A different spacing gives a different count. my read
Rainbow edge: 380 → 700 nm at 1 nm = 321 nodes, arc length 1.772, mean step 1.772 ÷ 320 = 0.00554. checked
Purple line: from (0.1741, 0.0050) to (0.7347, 0.2653) = 0.618 long. 0.618 ÷ 0.00554 ≈ 112 gaps → 111 nodes between the ends. checked
1 + 321 + 111 = 433 nodes. Counting from 0, the last is 432 = 0x1b0. The full loop is 2.390 long. checked
Your seven, by address: root 650 = 0x33 · sacral 600 = 0x65 · solar 575 = 0x7e · heart 525 = 0xb0 · throat 480 = 0xdd · third eye 450 = 0xfb · crown 410 = 0x123. Rule: address = 701 − nm. checked
Ends in frequency: 700 nm = 428.3 THz, 380 nm = 788.9 THz, ratio 1.842. checked