prompts: the fact-check bar, the thinking fields, adaptation, LaTeX everywhere

Accuracy (shared, one law across every agent): the target shifts from
surface facts to understanding itself — 'the deeper risk isn't a wrong
name or date, it's a wrong understanding: an interpretation of an idea
that seems solid and isn't.' The bar is the doubt itself: checks are
cheap, and weighing whether a doubt is worth checking is how errors slip
through. Thinking stays the agent's own.

Research (teacher 40-jobs): floor framing — verify your understanding
before it becomes his; dispatch before the fact crosses your lips, teach
around the gap until the brief lands. Planning (10-planning): planning is
the natural moment for verification; the map is a hypothesis and the
probe only its first sketch — rewriting is a normal, common event (the
session adapts to what teaching reveals); and plan_init IS the
presentation — never draw the plan again in prose (the double-plan bug).

New shared segment 16-mental-model.md: the thinking fields are the
session's primary data — read them in full, measure what they reveal,
adapt everything on the model they build. Composes into teacher, prober,
and practice (shared-fragments list updated).

Practice: the rarely-needed framing is dead — fact checks get their own
law (a wrong model solution grades the learner against a lie; pose once
the brief lands), files and map readers become plain side tools.

LaTeX: the question-tools craft list gains the point-of-use bullet
('LaTeX everywhere — plain-text math in a question is a craft failure'),
the formatting law names EVERY field, and the practice problem statement
line carries it too.

Prompt pins updated: felt-doubt bar + mental-model doctrine in both
teacher and practice compositions, no-double-plan rule, rewrite-is-
normal law, rarely-needed framing asserted gone.

src/agent/prompt-segments.ts

@@ -34,14 +34,13 @@ import { FRAGMENT_RE, isValidSegmentPath, type PromptAgent, type PromptSegmentIn
 
 const PROMPTS_DIR = path.join(PATHS.root, "src", "agent", "prompts");
 
-/** Shared fragments the PRACTICE agent composes: the VOICE and ACCURACY
- *  chunks joined the formatting guide (owner round 13, 2026-10-05) —
- *  personality and the truth contract are ONE law across every agent;
- *  practice once carried stale near-copies ("You have no research tool
- *  here" was false the moment round 10 gave it research). The
- *  question/confidence/file mechanics stay out (practice has no such
- *  tools). */
-const PRACTICE_SHARED_FRAGMENTS = ["10-voice.md", "15-accuracy.md", "40-formatting.md"];
+/** Shared fragments the PRACTICE agent composes: the VOICE, ACCURACY,
+ *  and MENTAL-MODEL chunks joined the formatting guide (owner rounds 13
+ *  and the prompt-refinement round of 2026-10-07) — personality, the
+ *  truth contract, and the thinking-fields doctrine are ONE law across
+ *  every agent. The question/confidence/file mechanics stay out
+ *  (practice has no such tools). */
+const PRACTICE_SHARED_FRAGMENTS = ["10-voice.md", "15-accuracy.md", "16-mental-model.md", "40-formatting.md"];
 
 /** Absolute path for an override file (unchecked — validate first). */
 function overrideFileFor(segmentPath: string): string {