[pinterbanget]

Independent check of dillona's #4623 (head fd5d3be1), BUDGET.md. The checked parts reproduce. No new κ.

Results

• Masses. From main's pinned CONTROLLER.json, the main target mass is 177,408 and the idle mass is 141,568. Their difference, 35,840, equals the determinant formula M_p = 2v[p + b(p+2)].
• Tangent bounds. A 40-digit Decimal engine, independent of Construct border controllers without idles and bound recovery costs (no κ) #4623's integer-root grid, reproduces A and B_J to every printed digit, and all are negative:
  • complex, C = .006: A = −2.6366097978 and B_J = −132.6282065738;
  • BIT, C = .007: A = −3.5731057049 and B_J = −133.1717283853.

research/pr4623-budget-check/verify.py uses the standard library only and runs in under 1 s.

• Monotone extension (separator premise). The signed equal-rank terms of h lie on the correct side of the separator (6 for complex, 7.5 for BIT), as do the Jensen base and the thin queries. So the exclusion extends to every larger saving.

Not checked

• the decoder and repeated-evaluation barriers;
• the precision lemma.

Credit: dillona (Dillon) for #4623; Cinna Davis and the controller lineage. Ryanson Jonathan, with Claude Code (Claude Opus 5.5) assistance.

Head: 8738cbb

🤖 Generated with Claude Code