9 November 2026. Two questions: (1) does a neutrino bound in two of our three directions plus one direction from each pair avoid charge; (2) do charge, color and alignment line up with the level indices n. Scripts: placements.py (this directory), ../index-alignment-20261109/index_tests.py. Not mailed to the principal.
1. Depth-five placements under Q_ang
Charge integral divided by w (lower-component norm fraction), quadrature with the operator in its defining form. Seed A = (Gamma_4 +1, normal degree 0), seed B = (Gamma_4 -1, normal degree 3); both have table charge 0 and beta = +1. M = (A + B)/sqrt(2).
| Bound directions | A | B | M |
|---|---|---|---|
| first five (case document) | +1/15 | -1/15 | 0 |
| our three + one pair | -1/5 | +1/5 | 0 |
| our three + one from each of two pairs | -1/15 | +1/15 | 0 |
| two of ours + fourth + one pair | -1/5 | +1/5 | 0 |
| two of ours + one pair + one from another | -1/5 | +1/5 | 0 |
| two of ours + one from each pair (alternative placement) | -1/15 | +1/15 | 0 |
| one of ours + two pairs | -1/5 | +1/5 | 0 |
| one of ours + fourth + one pair + one more | -1/5 | +1/5 | 0 |
| fourth + two pairs | -1/5 | +1/5 | 0 |
| two pairs + one more, no base | +1/15 | -1/15 | 0 |
- No placement is exactly neutral with seed A or seed B alone. The smallest size is w/15; the stated placement is one of the four that reach it.
- The two neutral seeds have equal and opposite errors in every placement. Their equal mix is exactly neutral in all ten (largest value 2e-18). The cross terms vanish because the two seeds differ in all three normal pairs.
- So exact neutrality at depth five is available for any placement, with the mixed value. The depth-three (down quark) error of addendum 1 is not affected: there is no second value with table charge -1/3.
2. Index test (fifteen indices; bottom taken as 16, and as 17)
- Sums a + b = c among the indices: 12 (11 with bottom 17). Random index sets of the same sizes give 7.3 to 8.4 on average and reach the observed number in 6 to 21 percent of trials. Index arithmetic in general is at chance level.
- One structured relation: charged lepton = up-type + neutrino in generations 1 and 2 (13 = 3 + 10, 35 = 20 + 15). Some rule of this kind (any family as the sum of two others) holding in two or more generations occurs in 0.5 percent of random sets, and in 2.8 percent when the actual numbers are kept and generations are shuffled within families. Found after looking, so these percentages overstate the surprise.
- Geometric reading: the electron's six bound directions are the union of the up-type quark's four and the neutrino's five, for the placements "our three + one pair" and "two of ours + fourth + one pair". It does not hold for the stated placement (the union has seven directions) or for the case document's first five in a useful way (the up set is contained in it).
- Generation 3 fails: the rule gives n = 94 at depth six, 30.8 GeV. No such particle; the tau is at depth ten with n = 23.