The European Union's Ecodesign for Sustainable Products Regulation (ESPR, EU 2024/1781) and the Green Claims Directive (ECGT, EU 825/2024) establish binding requirements for verified, traceable sustainability claims at product level. This paper describes algorithmic material exhaustion control — a verification mechanism that cross-checks certified material volumes declared in Transaction Certificates against actual garment production at gram-per-unit granularity, automatically blocking label issuance when certified material is mathematically exhausted. An industry audit covering 656,309 yards of production identified 44.21% non-compliant material in a real brand deployment. The paper defines the architectural requirements for compliant DPP verification and situates the approach within the regulatory obligations of ESPR, ECGT, CSRD, and CSDDD.