[{"type":"thinking","thinking":"Clean: 13 pages, 0 overfull, 0 undefined. Report the three changes. Note the new theorem clause + label. Also mention the app:numerics label addition (minor, for symmetry). Keep concise.","signature":""},{"type":"text","text":"All three items done; compile clean — 13 pages, zero overfull boxes, zero undefined refs.\n\n**1. Trust-boundary sentence + Theorem 2** (paperA.tex:174-186):\n- Theorem 2 now closes with: *\"The formal reduction of this statement is subject to exactly seven explicit perimeter inputs, itemized with provenance in Appendix B.\"* — phrased as a property of the formal reduction, so it doesn't reopen the \"not additional conjectural assumptions\" framing in the next paragraph.\n- The following paragraph now opens: *\"The two assumptions displayed are the two principal computational inputs appearing in the headline statement.\"*\n- Added `\\label{app:formal}` to Appendix B so the theorem's pointer is a real cross-reference (renders as \"Appendix B\"). Also added `\\label{app:numerics}` to Appendix A for symmetry — unused, harmless; delete if you'd rather keep labels minimal.\n\n**2. Introduction** (paperA.tex:91): now *\"every project-generated numerical input is produced by a deterministic, archived script.\"*\n\n**3. Appendix A heading** (paperA.tex:431): now `Li-coefficient machinery (E-011/E-015/E-021/E-023/E-023b)` — E-023 kept alongside E-023b since E-023's margin-assembly outputs are still used; E-023b's certificate content itself is described in Appendix B's MZeroProp paragraph.\n\nReady for your read of the refreshed PDF whenever you are."}]