The Interior File Takes Its Two Same-Week Results: Splitting Is Forbidden in Arithmetic, and Incompleteness Survives the Regular Black Holes

Join packet pricing two same-week results into the black-hole interior file at their exact scopes. (i) The fragmentation constraint map (Cacciapaglia et al., PRD 114, 084072 / arXiv:2606.24642): its Schwarzschild row verified in arithmetic — with A proportional to M^2, a split into fM and (1-f)M has total area ratio f^2 + (1-f)^2 = 1 - 2f(1-f) < 1 for every genuine split (tabulated 0.5000 to 0.9050), so the area law forbids every Schwarzschild fragmentation; the Kerr row (kinematic prevention except possibly near-extremal) carried as the authors' analysis and labelled as carried. Applied to the house line: the Mass-Inflation Clock Grid's corrected spin cap a_max = 0.16102674 at l = 0.5 (packet #300) stands far outside the map's only open, near-extremal window. (ii) Di Filippo's singularity theorem for quasi-topological gravities (arXiv:2611.02190): joined at scope — it quantifies over QTG classes and moves no GR house number, contradicts none, and fences the future move of leaning on a non-singular core in a modified theory, since incompleteness survives non-singular solutions there. EXTENSION. Quantum gravity NOT SOLVED; vacuum catastrophe NOT SOLVED.