05 / C3-C: The Class-II Nonlocality Quadratic Tax, Radial-Drift Congestion, and the Class III/IV Forward-Surviving Family

C3-B compressed the hypothetical singular production core down to the High–High Heterochiral UV Pair-Production Chain. This round first tackles Class II $(+--)$, asking: if $k\ll p\sim q$, can Class II really serve as a high-efficiency UV generation mechanism? The answer is "it can exist, but strongly nonlocal instances must simultaneously pay a quadratic critical-production tax plus radial-drift congestion." Triangle geometry directly gives $|\mathcal R_{\rm II}|\le k^2|\Theta_\tau|$, and comparing this against the hidden high-frequency exchange scale $X_{\rm hi}\ge p^2|\Theta_\tau|$ yields Theorem 5.1: $|\mathcal R_{\rm II}|\le(k/p)^2X_{\rm hi}$ — every additional dyadic scale separation cuts the production efficiency by a further factor of 4. The document explicitly calls this a "congestion certificate," not a finite-budget theorem: the nonlocality tax only says "the more nonlocal the production, the larger the hidden high-frequency exchange cycle behind it must be" — there is no proven global bound on absolute exchange variation to rule it out. Theorem 13.1 (Radial-Drift Congestion Lemma): if the Class-II high-end genealogy's wavenumbers diverge, then the sum of the nonlocality ratios $\chi_n=k_n/p_n$ must diverge — still not a contradiction, but it establishes a Quadratic-Tax-plus-Linear-Congestion situation: the more nonlocal, the lower the per-step efficiency and the more steps needed to cross one scale. On the other hand, for Class III $(+-+)$ and Class IV $(++-)$ the lowest-wavenumber mode is always the donor, so the direction is directly forward-compatible; under strong nonlocality there is no $(k/p)^2$ suppression at all ($|\mathcal R_{\rm III}|\sim p^2|\Theta_\tau|$), making these genuine nonlocal survivors. The document further notes that Class IV is the only class that places the unique chirality sign on the triad's largest wavenumber — making it directly frontier-capable as a generation class, flagged as the PRIMARY FRONTIER SURVIVOR. The document closes with an important no-go (§24): a contradiction cannot currently be derived directly from the nonlocality tax, because there is no proven global bound $\int\sum_\tau X_{\rm hi,\tau}\,dt<\infty$ — nonlocality tax ≠ finite-budget proof, and this distinction must be explicitly preserved. The research frontier formally converges on C3-D: Forward Heterochiral Frontier Rigidity, with the surviving core being Class III/IV together with the non-negligible local part of Class II.