practice live-test fixes — scroll containers, session math delimiters, header guidance, sweep heartbeat (owner live test 2026-09-29)

src/agent/subagents/practice.ts

@@ -188,7 +188,7 @@ INPUTS (in the user message):
   THE CUE DISTANCE: 0 Lesson context · 1 Adjacent context · 2 Far context — how far the situation sits from the cues the learner has already met: the lesson's own examples AND every previous problem's situation. Far context is the edge of the recognizable band — the proposition must still genuinely apply, and the learner must be able to find it by looking.
   THE PRESENTATION: Theory (the subject's own terms — symbols, formal objects, native vocabulary) or Application (a concrete worldly affair in which the proposition's structure appears in the wild). It dresses the situation; it never changes the rung or the cue distance.
   Apply Part II step 2: degrade honestly if the target cannot support them — the degradation shows in the problem's own shape, never in meta-commentary.
-- FORMATTING: your statement, solution, and rubric are rendered as full Markdown — use everything it offers. Mathematics is always LaTeX: inline as $…$, display as $$…$$ on its own lines. Code, pseudocode, and formal systems live in fenced code blocks with a language tag; identifiers and symbols inline as \`code\`. Use tables for parallel structure and comparisons, lists for enumerations. Prose-only renderings of mathematical or structured content are a defect: if a sentence carries an equation, a derivation, or a piece of code, format it as what it is.
+- FORMATTING: your statement, solution, and rubric are rendered as full Markdown — use everything it offers. Mathematics is always LaTeX: inline as \\(…\\), display as \\[…\\] on its own lines — a bare $ is literal currency and never starts math. Inside math, use LaTeX commands for symbols, not unicode stand-ins (they fail to render). Code, pseudocode, and formal systems live in fenced code blocks with a language tag; identifiers and symbols inline as \`code\`. Use tables for parallel structure and comparisons, lists for enumerations. Skip headers — at this size they are pointless decoration; structure with paragraphs, bold labels, and lists (a genuinely long derivation may earn one). Prose-only renderings of mathematical or structured content are a defect: if a sentence carries an equation, a derivation, or a piece of code, format it as what it is.
 - PREVIOUS PROBLEMS: problems the learner has already answered, with the chains they exercised. Do not rebuild one; keep your situation distant from theirs — cue distance counts previous problems' situations (Part I, "Cue distance").
 
 OUTPUT — your entire deliverable is ONE submit_problem call:
@@ -228,7 +228,7 @@ THE VERDICT (exactly one):
 - "partial": some of the target came to mind; the answer is materially incomplete or partly wrong.
 - "missed": the targeted proposition(s) did not come to mind — the answer is empty or on the wrong track.
 
-Feedback renders as full Markdown. Mathematics is always LaTeX — inline as $…$, display as $$…$$ on its own lines. Code in fenced blocks with a language tag, identifiers inline as \`code\`. Lists and tables wherever they carry structure. Name the failed recall and teach the boundary in properly formatted prose, not plain text.
+Feedback renders as full Markdown. Mathematics is always LaTeX — inline as \\(…\\), display as \\[…\\] on its own lines (a bare $ is literal currency). Inside math, LaTeX commands for symbols, not unicode stand-ins. Code in fenced blocks with a language tag, identifiers inline as \`code\`. Lists and tables wherever they carry structure; no headers — feedback is short-form, structure it with paragraphs and bold labels. Name the failed recall and teach the boundary in properly formatted prose, not plain text.
 
 OUTPUT — your entire deliverable is ONE submit_grade call: "verdict" and "feedback" (non-empty; the boundary-teaching text above).`;