[{"type":"thinking","thinking":"All checks pass:\n- 38 display equation paragraphs (oMathPara) — matches the 38 $$ blocks\n- 74 oMath total (38 display + 36 inline math segments)\n- 4 borderBox — exactly the 4 \\boxed equations (e/2 > 1, H_low identity, q_high, n ≤ (T₀−1)²)\n- No raw LaTeX left in text runs\n\nDone. Report to user concisely. The docx is at research/paper/note_on_the_right-horizontal.docx. Note: uncommitted (and it's outside the frozen paperA — this is the correspondence note, a separate artifact; I won't commit it without being asked).","signature":""},{"type":"text","text":"Done. **`research/paper/note_on_the_right-horizontal.docx`** — the note with its exact text, and all math as native Word equations (double-click any equation to edit it in Word's equation editor).\n\nVerification:\n- 38 display equations — all converted, zero fallbacks, no raw LaTeX residue\n- 36 inline math segments converted\n- All 4 `\\boxed{}` results (the \\(e/2>1\\) display, the dog-leg identity, \\(q_{\\rm high}\\), and \\(n\\le(T_0-1)^2\\)) render with real boxes\n- Title, headings, bold/italic, code spans, and the numbered question list preserved\n\nThe converter script is saved at `research/paper/build_note_docx.py` — re-run it any time the `.txt` changes and it regenerates the `.docx` in place. Neither file is committed; say the word if you want them in git (the note looks like part of your correspondence package, so I left that call to you)."}]