← NS-INRS / DCRP89/X72R72 · Ancestry-Exit Pricing and the Supplier-Speed Normal Form
Continuing from DCRP88's proof that every circulation atom must exit any compact loop-state class within a finite backward depth N*, this round prices that first exit, drawing on the native Morrey law from DCRP31 and the Bedrossian–Germain–Harrop-Griffiths warning about vortex-filament solutions (that circulation alone does not guarantee a volumetric energy lower bound). It proves: for a first exit whose support carries circulation ≥c_Γ and is geometrically tame, after filtering at a fixed tube scale ℓ*, if the filtering error carries at least half the circulation then it reverts to the existing increment/scale compiler; otherwise the filtered circulation remains ≥c_Γ/2, which via Young's inequality forces a fixed positive local tail-energy atom E_tube≥c_E>0. For J tame suppliers with overlap multiplicity M_J and maximum radius R_J, the native Morrey law gives the exact packing trade-off R_JM_J≳J (Theorem D89.7, the 'tail-packing NO-GO', explicitly flagged as 'an important correction to prevent overclaiming', since the Morrey law alone does not rule out an infinite sequence of tame suppliers). Conclusion: repeated regeneration cannot draw on a stationary, zero-cost tail source; this yields two new quantified normal forms — bounded overlap forces suppliers into at least linear-speed escape (the linear-speed supplier conveyor S_tail^lin), or bounded radius forces divergent supplier multiplicity (S_mult) — left for DCRP90 to test whether the linear-speed supplier can coexist with the existing far-field/PFET/interaction costs.
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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