← NS-INRS / DCRP89/X72R72 · Ancestry-Exit Pricing and the Supplier-Speed Normal Form

NS-INRS · DCRP89/X72R72 Quantification 2026-08

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.

This round's status: Quantification — Taken from the file's own Executive result / STOP node, meaning preserved, not a full verbatim translation. The original paper itself was authored directly in English; only this page's own commentary (title, status, and summary) is translated here.

Connections

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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