← NS-INRS / DCRP91/X72R74 · Filamentation Terminal Elimination and the Directional-Diffusion Compiler
Continuing from DCRP90's closure of the material-support escape, leaving only the material filamentation escape R_fil, and drawing on the curvature/direction compiler from DCRP50, the time-sliced Morrey law from DCRP71, the filamentation-is-noncompactness result from DCRP79–80, the scale-gap debt from DCRP85, and the finite ancestry depth from DCRP88–90. It proves that R_fil is not an independent terminal coordinate: the exact tube-volume formula |T_r(C)|=πr²L(C) shows that bounded support plus a positive reach radius gives a uniform upper bound on loop length, so length blow-up must force the reach radius to collapse, which in turn splits into either tube self-approach/multiplicity (state noncompactness) or curvature-scale collapse. On the carrier-locked rank-two branch, the D50 curvature compiler converts curvature folding into rank transition, filtered-vorticity-magnitude-direction activity, or second-order tube geometry (collectively R_FV), while filamentation witnesses that tend toward shrinking relative scale are exactly D85's scale-gap debt. This round explicitly does not identify the material line tangent with the vorticity direction, nor does it claim that R_fil implies X72. Conclusion: R_fil is fully absorbed as R_fil⟹R_state∨R_FV∨D_gap∨R_crit; there is no longer any generic 'tail' or 'filamentation' placeholder — the entire shared-ancestry material-regeneration branch now terminates only in already-declared finite-scale/state/reservoir coordinates, and the remaining problem is a recursion/budget question about these already-visible defects rather than further escape classification — left for DCRP92 to seek a single joint recursive budget.
Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.
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