Every Cheap Core Passes: Six Saturation Principles Tried Inside the Frame, a No-Go for the Stated Class, and the Tube Clauses Close Final

Attempts, inside the frame, the saturation principle paper #440 named as the only exit from its equivalence: inside the phase-slip dress, a micro-tear bound below the 168,921-event walk scale is exactly g(1) > 4.579e-34, while paper #325's admissible completions drive g(1) to zero (threshold crossed at n* = 2.184e33). Gated digit-for-digit on #440's exhibits (attempt budget 396.608 nats, action requirement 384.571 nats, canonical-class conditional bound log10 expected events -1.8236e35 at its labeled model strength, destruction at n = 1e34 with ln expected events +312.6) and on #325's (S_unit = 8.397867e35 nats, canonical g(1) = 0.828427 / 0.693147 / 0.500000, the family g_n(y) = tanh(ny^2)/n with values 0.761594 / 0.1 / 0.01 / 1e-6). Six principles are attempted and fail in six computed shapes: uniform analyticity (each member's radius in y^2 is pi/(2n), shrinking without floor; no uniform radius is owned), a steepness cap (the family obeys g' <= 2y everywhere while its maximum slope falls as 1.1131/sqrt(n); the cheapness is a plateau of height 1/n no slope condition can see), a one-nat minimum action (granted in full it floors g(1) at 1.191e-36, short of the threshold by the exact factor 384.571), an exterior-energy floor (the slip is a saddle through the core and the dress has one formula, S_grain = g(1) S_unit, into which no exterior quantity enters), a core-tension floor (no owned inequality floors the core tension; the canonical class spreads it by 3.7 and the tension's outer scale is absent from the record), and closedness of the admissible class (the family converges pointwise to the identically zero function, not a completion; the exact quadratic corner survives per member only on width sqrt(1.915/n)). A seventh candidate, the bare assertion that the core cannot be arbitrarily cheap, is refused in print as the conclusion restated and the declined declaration in disguise. Behind the attempts stands a no-go: every condition in the stated class C1-C8 (quadratic corner with coefficient exactly 1, monotonicity, saturation, positivity, slope no steeper than the exterior, g <= y^2, real-analyticity, no scale but the frame's own, integer index allowed) is obeyed by every member of the family, whose g(1) has infimum zero, so no consequence of that class implies any positive lower bound on g(1); any closing principle must import a uniform or quantitative datum the frame's owned mechanics does not supply. No derivation lands: clauses C2 and C3 of paper #99 (items D-081-120-51 and D-081-120-52) stand final at strengthened-obstruction form, with the reopening condition printed. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.