Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/schemas/generate-request.schema.ts, line 43:

<comment>The new topic requirement treats empty strings as valid, so invalid requests can pass schema validation and fail later in retrieval.</comment>

<file context>
@@ -25,14 +25,32 @@ export const GenerateRequestSchema = z.object({
 
   source_problem_text: z.string().optional(),
+}).superRefine((request, ctx) => {
+  if (request.topic === undefined && request.topic_code === undefined) {
+    ctx.addIssue({
+      code: z.ZodIssueCode.custom,
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/steps/sympy-verification.ts, line 59:

<comment>Hard-failing when `question_text` lacks `=` makes all non-equation candidates automatically rejected by policy.</comment>

<file context>
@@ -16,8 +16,88 @@ export interface SympyVerificationOutput {
+  mathEngine: MathEngineClient,
+  candidate: GeneratedProblem,
+): Promise<boolean> {
+  if (!candidate.question_text.includes("=")) {
+    throw new Error("SymPy verification supports equation candidates only");
+  }
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/tools/schema-loader.ts, line 46:

<comment>`load(code)` does not verify that the YAML's `strategy.code` matches the requested code, which can return/cache the wrong strategy for that lookup.</comment>

<file context>
@@ -22,7 +31,64 @@ export interface FsStrategyLoaderOptions {
+    }
+    const strategy = await readStrategyFile(join(opts.strategiesDir, `${code}.yaml`));
+    if (strategy === null) return null;
+    cache.set(strategy.code, strategy);
+    return strategy;
+  }
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/schemas/generate-request.schema.ts, line 55:

<comment>`getGenerateRequestTopicCode` can return an empty `topic_code` and ignore a valid `topic`, which breaks fallback semantics.</comment>

<file context>
@@ -25,14 +25,32 @@ export const GenerateRequestSchema = z.object({
 export type GenerateRequest = z.infer<typeof GenerateRequestSchema>;
+
+export function getGenerateRequestTopicCode(request: GenerateRequest): string {
+  return request.topic_code ?? request.topic ?? "";
+}
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/index.ts, line 45:

<comment>Hard-coded `allowedHosts` blocks all non-local LLM base URLs, breaking valid `openai-compatible` / `anthropic-via-compatible` configurations.</comment>

<file context>
@@ -1,14 +1,70 @@
+          modelId: llmModel,
+          baseUrl: llmBaseUrl,
+          apiKey: llmApiKey ?? "openmath-local",
+          allowedHosts: ["localhost", "127.0.0.1"],
+        }),
+        modelId: llmModel,
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/steps/sympy-verification.ts, line 80:

<comment>Use a word-bounded, case-insensitive `or` delimiter to avoid malformed answer tokenization.</comment>

<file context>
@@ -16,8 +16,88 @@ export interface SympyVerificationOutput {
+
+function parseExpectedSolutions(answer: string): string[] {
+  return answer
+    .split(/[,;]|또는|or/)
+    .map((part) => part.trim())
+    .map((part) => part.replace(/^[a-zA-Z]\s*=\s*/, ""))
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/web/app/app/new/verify/page.tsx, line 20:

<comment>This page duplicates query parsing logic (`parseMode`/`parseDims`) that already exists in nearby pages; extract and reuse a shared parser to prevent divergence.</comment>

<file context>
@@ -0,0 +1,49 @@
+  };
+};
+
+function parseMode(raw: string | null): "structural" | "conceptual" | null {
+  if (raw === "structural" || raw === "conceptual") return raw;
+  return null;
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/prompts/problem-generator.md, line 60:

<comment>Prompt instructs LLM to output `question_text` and `expected_answer` in KaTeX LaTeX format, but the downstream SymPy verification pipeline expects standard SymPy expressions. The math engine (`packages/math-engine/src/routers/math.py`) uses `sympy.parsing.sympy_parser.parse_expr` with `standard_transformations + implicit_multiplication_application + convert_xor` — this can parse `x**2`, `sqrt(7)`, `2*x + 3` but CANNOT parse LaTeX syntax like `x^{2}`, `\sqrt{7}`, `5x`. No LaTeX-to-SymPy conversion exists in the pipeline. The `formatLatex` function (`packages/agent/src/tools/latex-formatter.ts`) converts from SymPy → KaTeX, not the reverse. Result: when the LLM follows the prompt and outputs LaTeX, both the generation step's `normalizeExpectedAnswer` (in `problem-generation.ts:137`) and the verification step's `verifyWithSympy` (in `sympy-verification.ts:68,73`) will send unparseable expressions to the math engine, causing HTTP 400 parse errors and cascading step failures.</comment>

<file context>
@@ -57,8 +57,10 @@ updated: 2026-05-18
 JSON으로만 응답.
-- `question_text`는 SymPy가 풀 수 있는 `x` 방정식 문자열이어야 한다. 예: `x**2 - 7 = 0`, `2*x + 3 = 11`.
-- `expected_answer`는 `sqrt(7), -sqrt(7)`처럼 쉼표로 구분한다. 서버가 SymPy로 다시 계산해 최종 정답을 검증한다.
+- `question_text`는 KaTeX가 바로 렌더링할 수 있는 LaTeX `x` 방정식 문자열이어야 한다. `**`, `*`를 쓰지 말고 지수는 `x^{2}`, 곱셈은 `5x`, 제곱근은 `\\sqrt{7}`처럼 쓴다.
+- `expected_answer`도 LaTeX로 쓴다. 예: `2, 5`, `\\sqrt{7}, -\\sqrt{7}`.
+- 예시 출력: `{ "question_text": "x^{2} - 7x + 10 = 0", "expected_answer": "2, 5", "proposed_solution_trace": "인수분해하면 (x - 2)(x - 5) = 0이므로 x = 2 또는 x = 5이다." }`
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/tools/latex-formatter.ts, line 29:

<comment>Global `*` replacement corrupts unresolved power operators (`**`) into whitespace, producing mathematically incorrect LaTeX output.</comment>

<file context>
@@ -0,0 +1,87 @@
+}
+
+function formatMultiplication(value: string): string {
+  return value.replace(/\s*\*\s*/g, " ");
+}
+
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/steps/problem-generation.ts, line 109:

<comment>The failure path never returns `gate: failed` because `await Promise.reject(err)` throws during object construction.</comment>

<file context>
@@ -27,16 +33,111 @@ export interface ProblemGenerationInput {
+    };
+  } catch (err) {
+    return {
+      data: await Promise.reject(err),
+      gate: {
+        step: "generate",
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/web/app/globals.css, line 2213:

<comment>Keyboard-focus branch is unreachable because `.book-cover` elements are not focusable, so `:focus-visible` never applies.</comment>

<file context>
@@ -2059,722 +2059,426 @@
-    display: flex;
-    gap: 8px;
+  .book-cover:hover .book-cover-front,
+  .book-cover:focus-visible .book-cover-front {
+    transform: rotateY(-168deg);
   }
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/agents/refiner-agent.ts, line 39:

<comment>RefinerAgent ignores its configured refiner prompt/model and always reuses GeneratorAgent, making refiner-specific wiring dead and potentially bypassing intended refinement behavior.</comment>

<file context>
@@ -16,9 +21,29 @@ export interface RefinerAgent {
+        ...input.hints.map((hint) => `- ${hint}`),
+      ].join("\n");
+
+      return deps.generator.generate({
+        request: input.request,
+        intent: input.intent,
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/web/components/landing/book-stage.tsx, line 134:

<comment>Parallax mouse tracking is bound to `window`, so off-stage mouse movement keeps driving stage transforms and breaks the intended stage-local behavior.</comment>

<file context>
@@ -69,287 +112,98 @@ export function BookStage() {
+      node.style.setProperty("--mouse-x", "0");
+      node.style.setProperty("--mouse-y", "0");
+    };
+    window.addEventListener("mousemove", handleMove, { passive: true });
+    node.addEventListener("mouseleave", handleLeave);
+    return () => {
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/steps/independent-resolve.ts, line 92:

<comment>`parseAnswers` splits on `or` as a plain substring, which can corrupt valid expressions (e.g. `floor(x)`) and create false re-solve mismatches.</comment>

<file context>
@@ -16,12 +18,89 @@ export interface IndependentResolveInput {
+
+function parseAnswers(answer: string): string[] {
+  return answer
+    .split(/[,;]|또는|or/)
+    .map((part) => part.trim())
+    .map((part) => part.replace(/^[a-zA-Z]\s*=\s*/, ""))
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/workflows/verification-workflow.ts, line 66:

<comment>Top-level dependency assertion can throw before first yield, causing `/api/generate` SSE to terminate without a structured error event.</comment>

<file context>
@@ -63,15 +61,20 @@ export type WorkflowReturn = {
-  _options?: RunOptions,
+  options?: RunOptions,
 ): AsyncGenerator<WorkflowYield, WorkflowReturn, void> {
+  assertRequiredDeps(deps);
+
   const timestamp = () => new Date().toISOString();
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/src/steps/objective-mapping.ts, line 161:

<comment>Duplicate `normalizeMathText` logic was added instead of reusing a shared utility, creating a drift-prone normalization path.</comment>

<file context>
@@ -2,31 +2,165 @@
+  return normalizeMathText(left) === normalizeMathText(right);
+}
+
+function normalizeMathText(value: string): string {
+  return value
+    .replace(/²/g, "**2")
</file context>

Check if this issue is valid — if so, understand the root cause and fix it. At packages/agent/.env.example, line 28:

<comment>Canonical alias priority is described backwards. The comment says to use `LLM_BASE_URL`/`LLM_API_KEY`/`LLM_MODEL` "when none of the above 3 options map" (fallback), but in `src/index.ts` they are the **highest-priority** values checked first via `??`. If a user follows 옵션 2 (OpenAI direct) by uncommenting `OPENAI_API_KEY`/`OPENAI_MODEL` and switching `LLM_PROVIDER=openai` without also disabling the canonical aliases, `LLM_BASE_URL=http://localhost:8317/v1` and `LLM_API_KEY=dummy-key` would silently override the OpenAI settings — routing to CLIProxy with dummy key instead of OpenAI.</comment>

<file context>
@@ -1,20 +1,31 @@
+# OPENAI_API_KEY=sk-...
+# OPENAI_MODEL=gpt-4o
+
+# Canonical aliases — 위 3가지 옵션 중 어느 것도 매핑되지 않으면 이 3개로 직접 지정 가능
 LLM_BASE_URL=http://localhost:8317/v1
 LLM_API_KEY=dummy-key
</file context>