64 / C6-O: Peak-Scale Defect Inheritance, Type-II Ancient Carriers, and Mass–Peak Two-Scale Closure

C6-N proved that a relative-dominant Type-II carrier must split into two layers, with the mass scale $\ell_n$ far larger than the peak-amplitude scale $a_n$. C6-O formally asks: if the entire global critical mass runs off to spatial infinity in the ancient peak frame, can the TS/GP/HF defect labels still remain in the bounded peak core? In other words, critical mass inheritance ≠ defect inheritance. C6-O.1 Peak Relative-Mass Escape Theorem uses a simple volume estimate under record normalization to prove directly that $\mu_{3,n}^{peak}(B_R)\to0$ holds for every fixed $R$ — the peak-tightness coefficient $\Theta_3^{peak}=0$: the global relative $L^3$ carrier is completely non-compact in the ancient peak frame. C6-O.2 Peak-Tight Defect / Relative-Mass Decoupling further proves: if the defect carrier genuinely remains compact in the peak frame ($\Theta_D^{peak}=1$), it must be a global relative $L^3$ spectator — so "relative singular-mass overlap" simply cannot serve as the inheritance criterion for an ancient-peak defect, formally tightening C6-N's absolute/relative distinction into: ancient inheritance can only use a local absolute defect load, never a global relative fraction. C6-O.3 Local Absolute Defect Inheritance Lemma proves that a nonzero local absolute defect load genuinely does carry over to the ancient limit, under sufficiently strong local convergence. It then axiomatizes the peak derivative scale: $\widehat A_{k,n}^{peak}=A_{k,n}/A_{0,n}^{k+1}$; the Derivative-to-Peak Trichotomy (C6-O.4) splits into three branches — flattening (→0), peak-scale derivative (→finite), and subpeak derivative escape (→∞) — and if the derivative amplitude genuinely escapes, the Derivative-Tower Restart Theorem (C6-O.5) proves that a smaller scale $b_{k,n}\ll a_n$ must exist, at which the higher-order HF defect must be rebound below the peak scale — hence the HF Peak-Inheritance Gate (C6-O.6) explicitly lists the four conditions needed for the global HF label to be legitimately inherited; TS additionally requires a Peak Time-Window Gate, while GP's local geometry can be inherited under $C^2_{\rm loc}$ convergence plus a nondegenerate $Q$ mass. The round's genuine technical highlight is on the pressure side: the Mass-Tail / Peak-Pressure Decoupling Theorem (C6-O.8) performs a direct far-field estimate on the Calderón–Zygmund pressure-Hessian kernel, proving that, under bounded record normalization, the spatial tail carrying almost all of the global relative mass has only an $O(R^{-2})$ Hessian influence on any fixed peak core — that is, "global critical-mass dominance" does not imply "local GP pressure dominance," fully closing off the loophole C6-L/M kept worrying about, namely that "a huge spectator mass might secretly drive the peak through far-field pressure." C6-O.9 Conditional Ancient GP Inheritance Theorem proves that, under four conditions — strong local convergence, a nonzero local $Q$ load, a nondegenerate boundary remainder, and the pressure source re-partitioning at the peak — the local GP metadata genuinely can be carried over to the ancient limit. The round gathers all of this into the Mass–Peak Two-Scale Closure Theorem (C6-O.10), a three-way split: O-A Peak-Inherited Ancient Defect (the bounded peak region genuinely carries a nonzero local absolute defect load, allowing conditional extraction of $D^{anc}$), O-B Mass-Scale Defect / Peak Escape (the defect is not compact, or the local load vanishes; for this label the ancient peak is an unlabeled/partially labeled object, and the defect still lives at scale $\ell_n$ or larger), and O-C Subpeak Derivative Restart (some necessary derivative order escapes, and the defect must be rebound below the amplitude scale) — explicitly warning that "ancient inheritance ≠ ancient recurrence": peak inheritance alone does not prove recurrence. It also cites Seregin's most recent 2026 Type-II analysis (arXiv:2606.29468), formally logging the Euler scaling limit in certain Type-II scenarios as an independent conditional external interface, EULER_TYPEII, kept separate from the N–S ancient state. Formally hands off to C6-P — Ancient Defect-State Classification, Derivative-Tower Rigidity, and Peak-Local Pressure Closure, with ten constituent obligations directly attacking: the stability conditions for ancient TS/GP/HF, whether the derivative tower can repeat indefinitely, and whether the ancient pressure source can become a genuinely inheritable structure as $\tau\to-\infty$.