63 / C6-N: Near-Lossless Carrier Concentration, Ancient-Profile Extraction, and Defect-Complete Rigidity

C6-M left "near-lossless carrier retention + scale→0 + horizon→∞" for C6-N to pursue: can such a nested structure be fed directly into an ancient/eternal profile and then connected to Liouville rigidity? C6-N gives an answer more refined than expected, and makes a permanent correction to the visibility semantics of C6-L/M. It first formally splits visibility into two: absolute critical carrier $m_{3,n}^{abs}=\int_{C_n}|u|^3dx$ (liminf>0 means Absolutely $L^3$-Visible) versus relative critical carrier $\chi_{3,n}^{rel}=\mu_{3,n}(C_n)$. C6-N.1 Carrier Visibility Hierarchy proves Relative Dominant ⟹ Absolute Divergent ⟹ Absolute Visible, but not the reverse — so $\chi_{3,n}^{rel}\to0$ does not imply "this core is not a genuine singular carrier." Citing Albritton–Barker's local $L^3$ concentration theorem and Barker–Prange's Type-I parabolic-scale concentration lower bound, both of which are absolute lower bounds rather than global fractions — C6-N.5 Type-I Carrier Classification thereby proves that "relative spectator status is compatible with being the actual singular point," formally overturning C6-L/M's reading of vanishing relative visibility as spectator status. It then proves that a genuinely relative-dominant carrier must in fact be Type-II: C6-N.2 Relative Carrier Amplitude Theorem gives $\ell_nA_n^C\ge c_3^{-1/3}\beta_\ast^{1/3}\|u(t_n)\|_3\to\infty$ (Carrier-Scale Type-II Escalation), C6-N.3 further proves that a relative-dominant carrier at the parabolic scale must be a Type-II amplitude branch with $\sqrt{T^\ast-t_n}\|u(t_n)\|_\infty\to\infty$, while C6-N.4 Type-I Relative-Visibility No-Go conversely proves that a Type-I bounded parabolic core cannot be relative-dominant — though it can still carry a fixed absolute critical load. C6-N.6 Amplitude-Scale Separation Theorem reveals that a relative-dominant mass carrier necessarily hides, inside itself, a far smaller peak-amplitude scale $a_n^C\ll\ell_n$; performing a record-time N–S rescaling at the peak scale, C6-N.8 Bounded Ancient Peak Extraction Principle genuinely extracts a nontrivial bounded ancient solution (with external support from Albritton–Barker's singular-point zoom-in theorem), but C6-N.9 Conditional Ancient $L^3$ Kill Gate honestly states that the general 3D bounded ancient Liouville problem of Koch–Nadirashvili–Seregin–Šverák remains open, so the kill condition does not hold automatically. Whether the defect label follows along is a new gap of its own: "ancient peak extraction ⇏ defect-labeled ancient extraction" — the Peak-Scale Defect Visibility Gate (C6-N.10/11) splits it into the N-PVIS/N-PESC dichotomy. Another main line of the round corrects C6-M's nested-product formalism itself: C6-N.12 Fixed-Slice Infinite-Nesting No-Go uses measure continuity to prove that a fixed smooth slice cannot contain a genuinely infinitely deep nested chain that maintains a fixed positive fraction all the way down to zero diameter (a normalized $L^3$ density has no atoms); a genuinely infinite nesting can only be asymptotic atomization across generations (C6-N.13 Atomic Limit Theorem, C6-N.14 Multi-Channel Co-Atomicity — the mass, spectral, and defect measures can converge to the same atomic point in the weak limit). The round's genuine central insight lies in a two-scale obstruction: C6-N.15/16 prove that bounded amplitude and relative carrier completeness are mutually exclusive (relative dominance is, at bottom, a Type-II/non-compact-amplitude phenomenon), while C6-N.17 Ancient-Peak Critical-Tail Escape proves the converse — the bounded ancient profile extracted at the peak scale must be a relative $L^3$ spectator with respect to the original global critical mass; C6-N.18 Mass-vs-Peak Rescaling Dichotomy formally proves that no single rescaling can simultaneously keep a fixed fraction of the relative carrier bounded and normalize the peak amplitude to $O(1)$ — the mass-compactification scale and the ancient-profile compactification scale are two structurally different scales. This forces a methodological pivot (Section 66): demoting "a fixed global fraction" (Strong Global Carrier Completeness) to a Type-II-specific branch, and instead adopting "at least one label per singular generation carries a nonzero absolute critical load" (Local Singular-Carrier Completeness) as the minimum standard a general regularity program should actually use — consistent with the already-known Type-I concentration theory. C6-N.19 Defect-Complete Rigidity Reduction gathers this into a three-way split: N-A Type-I Absolute Carrier, N-B Type-II Relative-Dominant Carrier, N-C Carrier/Peak Label Escape. Formally hands off to C6-O — Peak-Scale Defect Inheritance, Type-II Ancient Carriers, and Mass–Peak Two-Scale Closure, with ten constituent obligations directly attacking: rebuilding TS/GP/HF at the peak scale, whether the defect label can survive under ancient compactness, exactly where the relative mass ends up as $|z|\sim\ell_n/a_n\to\infty$, and whether there is any way to genuinely trigger an ancient Liouville killer.