Triple Products See the Phase — and Lose the Third Cell: The Eighth Factored Class

Works register item D-361-409-45 (house packet #408's expiry condition, grade C) at its Wave 22 shape -- seven factored classes closed, the survivor carrying phase arrangement and magnitude jointly through no factored class -- via route (b), a genuinely non-lag-1 joint constraint language; reports an eighth factored class closed at INCREMENTAL grade; the item is not retired. The candidate, ordered triple-profile recovery (equality, at every refinement, of T_j = f_j * fⱼ₊₁ * conj(fⱼ₊₂), each entry a degree-3 monomial over a consecutive triple with each cell used exactly once and total phase coefficient +1), is stated in full, gated in chain order on all predecessor exhibits digit-for-digit -- the coherence packet's exhibits first among them (lag-1 profile not identical where the rectangle doubles, 0.066393 to 0.132786; alternating carrier identical at exactly 0.000000, rectangle 0.082991, endpoint 0.552475; anchored reconstruction 3.612e-15) -- and attacked against all standing counter-carriers on the chain's priced grid (6,000 cells, 5,998 entries): it separates the point carrier (5,998 of 5,998), the phase-scrambled carrier (2,999), the rearrangement carrier (204), the doubled-density carrier (all 5,998 -- doubled-density test passed; scale fixed), the translation carrier (all 5,998; additive level seen), the pointwise carrier (all 5,998), the alternating carrier (all 5,998), the global-phase rotation (all 5,998, maximum 0.043790) and the constant-potential carrier (all 5,998, maximum 0.038603 -- absolute phase fixed); and it is NOT completable by a single absolute datum (constructive counter-density: identical profile at 1.4e-17, 5,987 cells differing, rectangle 0.007897 against 0.066393; two data determine it algebraically through an ill-conditioned recurrence (floating-point drift 0.6639), printed as its price). It fails on this crew's period-3 carrier ((2, 2, 1/4) repeating: profile identical at exactly 0.000000 while the rectangle moves 0.066393 to 0.093863 and the endpoint integral 0.441980 to 0.626139; the (1/2, 1/2, 4) pattern identical again, rectangle 0.111042), and the failure is class-wide: all eight degree-3 monomial profiles over a consecutive triple are invariant at exactly 0.000000. The packet argues class-distinctness honestly (the triple language evades the printed lag-1 falsifier itself -- it separates that class's three killers -- and dies one period up, by the same mechanism in a longer window) and prices the survivor tighter by a proved pattern: a unit-exponent monomial window of any length L is blind to period-L rescalings whose factors multiply to 1 over the window. No fifth hypothesis is proposed; route (i) stands discharged; #167's Door two untouched. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.