04 / C3-B: Bihelical Critical-Energy Equalization, Heterochiral Triad Decomposition, and Unique-Sign UV Escape

Opens with an epistemic correction: for the $\mathcal E_+-\mathcal E_-=c_0$-type identity obtained in the previous round, C3-A, a literature check found that Lei–Lin–Zhou had already established the equivalent critical-helicity energy identity — it is not a new theorem of this paper. What this paper adds is connecting it to blow-up escape, Waleffe helical-triad algebra, the unique-chirality sign mode as the true source, and the multiscale legality chain of the X-Integration. Core result: from that external identity together with divergence of the critical size under blow-up, it derives that the two chirality sectors' accumulated critical energies $\mathcal E_\pm(t_n)$ must simultaneously tend to infinity along some sequence (Theorem 5.1), with ratio $\mathcal E_+/\mathcal E_-\to1$ (Corollary 6.1) — no matter how large the initial helicity bias $c_0$ is, as long as the critical energy genuinely escapes to infinity, the fixed initial difference eventually becomes negligible. Using Waleffe helical-triad algebra, it formally splits the heterochiral triads into Class II $(+--)$, III $(+-+)$, and IV $(++-)$, and proves that homochiral triads (Class I) make exactly zero contribution to positive critical absolute helicity (homochiral triads do not produce positive critical absolute helicity). Every heterochiral triad has a unique chirality-sign mode, and pair production can be rewritten entirely as "the wavenumber-weighted energy transfer of that unique sign mode," $\mathcal R_\tau=r_\tau\dot e_{\rm uniq}$. Theorem 21.1 (one of the paper's hardest estimates): using the Bernstein inequality together with the Leray energy inequality, it proves that the contribution of the unique sign mode below a fixed cutoff $K$ has finite time integral — so a fixed low-frequency opposite-chirality catalyst cannot repeatedly drive unbounded critical production. Combined with the known divergence of the overall production rate, this yields the Unique-Sign UV Escape Theorem (Theorem 23.1): the unique sign mode genuinely responsible for pair production must itself escape every fixed frequency — finer than C1a's statement that "the velocity field's high-frequency tail must escape," since it pins down the specific mode causing the production. The triangle inequality further proves (Corollary 25.1) that a unique sign mode escaping to high frequency requires at least one comparable-wavenumber high-frequency partner to exist simultaneously (High–High necessity), ruling out a "high frequency ← low + low frequency" generation pattern. The document also formally downgrades the candidate minority-$\dot H^{1/2}$ estimate proposed in C3-A to OPEN (an exact triad audit shows that each monomial containing a minority sign is not enough to place a global minority factor in $\dot H^{1/2}$), replacing it with a weaker but usable minority-dissipation-factor estimate, which is itself still not enough to close off global regularity.