61 / C6-L: Singular Carrier Profiles, Spectator Decoupling, and Secondary-Scale Defect Rebinding

The hardest gap C6-K left behind is: are the recurrence cores tracked by $TS$, $GP$, and $HF$ actually genuine carriers of the singular critical mass? C6-L is the first round to put singular critical mass and defect labels into the same measure-theoretic object. It defines the critical-mass probability measure $d\mu_n=|U_n|^3/\|U_n\|_3^3\,dx$, together with each defect label's own normalized carrier probability measure $\eta_n$ (constructed separately: TS from C6-F's shared-source density, GP from Q-weighted geometry, HF from the high component/sign set), and defines the visibility $\Omega_{D3,n}=1-d_{TV}(\mu_n,\eta_n)\in[0,1]$. C6-L.1 Singular-Carrier Extraction Theorem proves that if $\Omega_{D3,n}\ge\omega_0>0$, one can build a joint measure $\xi_n=(\mu_n\wedge\eta_n)/\Omega_{D3,n}$ such that any $\xi_n(B)\ge\vartheta$ simultaneously and exactly implies $\mu_n(B),\eta_n(B)\ge\omega_0\vartheta$ — the first time "defect-visible" and "genuinely-singular-mass-visible" are genuinely tied together through the same set. Conversely, C6-L.2 Spectator Separation Theorem sharpens the vague description left by C6-K into a stricter conclusion: if $\Omega_{D3,n}\to0$, one can precisely extract a separating set $A_n$ such that $\mu_n(A_n)\to1$ while $\eta_n(A_n)\to0$ — Defect–Fiber Decoupling is not "low overlap," but genuine asymptotic measure separation. Applying this toolkit to the full finite alphabet $\{TS,GP,HF\}$ (C6-L.3 Finite Defect-Label Carrier Lemma): either at least one label has quantitative visibility, or the entire current alphabet is simultaneously a spectator — formally defining a "Carrier-Complete Defect Alphabet" as the new goal, and explicitly stating that C6 has not yet proved it. The round's real methodological correction is a re-examination of C6-K's sub-scale restart: C6-K only rescales a single time slice, which is not a genuine dynamical symmetry. C6-L.7 Exact Physical Inner Rescaling switches instead to a genuine physical $(x,t)$-domain N–S rescaling (inner scale $\ell_n=\sqrt{T^\ast-t_n}\,\rho_n$), leading to the round's most unexpected discovery — C6-L.8 Secondary-Scale Horizon Theorem: the inner future horizon $H_n^+=\rho_n^{-2}\to\infty$ — that is, the deeper the sub-scale core goes, the further away — infinitely far, in fact — the original terminal time $T^\ast$ recedes in its own parabolic clock. The sub-scale restart is therefore not the same backward blow-up cycle replayed at a smaller scale, but a new dynamical problem with a horizon of an entirely different type (from finite $O(1)$ to infinite) — under sufficient compactness hypotheses it could even produce a genuine eternal N–S solution (C6-L.9, conditional). It then systematically classifies which C6 metadata automatically carries over under this rescaling (C6-L.10 Defect Rebinding Covariance Principle: the middle gap, the strain/Q direction, the sign fraction, the pressure signature, Duhamel coherence, and shared-source overlap are all dimensionless and covariant), and which must be re-verified in the inner layer (source identity, causal ancestry, the shared far-field pressure relation, cross-generation heredity, theorem-window membership, and even the horizon type itself) — "geometric covariance does not imply theorem-admission covariance." The round's one genuinely constructive visibility theorem is C6-L.12 (First-Derivative Sign-Thickness → Local Critical $L^3$ Visibility): for a genuine $k=1$ (first-derivative) sign-thick bad core, via a chord-integral plus neighborhood estimate, it proves directly a scale-independent positive lower bound on the critical $L^3$ mass, $\int_B|u|^3dx\ge c_{\rm vis}(\lambda,\delta,\widetilde{\mathcal C}_1)>0$ — "a genuine first-derivative sign-thick harmonic-gate failure can never be a carrier of zero critical mass." But the document immediately, honestly, draws a boundary (Section 56): this is only an absolute lower bound, not a relative one — because $\|u(t)\|_3^3\to\infty$, this absolute mass, once divided by the diverging global mass, can still tend to zero — "absolute critical visibility is not the same as relative singular-mass visibility," and spectator escape has not been fully closed off even for this most concrete theorem. It also adds a crucial warning (pressure nonlocality): an $L^3$ spectator does not mean a pressure spectator — a profile that vanishes in local $L^3$ mass can still influence the tracked GP core through far-field pressure, so a complete carrier theory cannot rely on the $L^3$ channel alone. C6-L.13 Spectator-Cycle Incompleteness Theorem gathers all of this into a formal conclusion: if the combined visibility of the whole $\{TS,GP,HF\}$ set tends to zero, the recurrent defect cycle is not a complete model of the hypothetical singular point — explicitly flagged as "proved at the level of carrier measures," with the pressure-nonlocality caveat attached. C6-L.14 Secondary Rebinding Horizon No-Go is a strict semantic rule for cycles: any cycle proof that directly identifies the outer level with inner-layer defect dynamics without updating the horizon metadata is illegitimate. It refines C6-K's three-way classification (CORE/INNER/SPECTATOR) into CORE-L (a labeled same-scale singular carrier), INNER-L (a labeled sub-scale genuine physical rebinding), and SPECTATOR-U (an unlabeled/spectator singular carrier). Formally hands off to C6-M — Carrier Completeness, Spectral/Pressure Visibility, and Nested-Rebinding Rigidity, with ten constituent obligations (M1, spectral visibility, through M10, recomputing the candidate graph after removing spectator cycles), directly attacking "carrier completeness" — the newest and most fundamental open problem.