fix(api): query pagination accepts non-integer limit/page → fractional OFFSET/LIMIT

apps/api/src/schemas/query-schemas.ts と apps/api/src/routes/query.ts の DynamicQueryRequestSchema と validatePaginationFields から始め、次に packages/ai/src/query/index.ts の QuerySchema と limit/offset のビルダーを調べます。issue に記載されている小数値の入力を再現し、リグレッションテストを追加します。limit/page の値が有限でない、または整数でない場合に期待される 400 のバリデーションレスポンスを受け取り、有効なページネーションでは引き続き整数互換の句が構築されれば完了です。

Describe the bug
POST /v1/query DynamicQueryRequest accepts non-integer limit/page without validation and produces fractional LIMIT/OFFSET that fail ClickHouse Int32 binding.

Affected code:

• apps/api/src/schemas/query-schemas.ts:49-50 DynamicQueryRequestSchema: t.Optional(t.Number()) — no minimum/integer constraint.
• apps/api/src/routes/query.ts:294-308 validatePaginationFields only checks <1 and >10000/<1 for page, not Number.isInteger/isFinite.
• apps/api/src/routes/query.ts:1040-1041 limit: request.limit || 100, offset: request.page ? (request.page-1)*(request.limit||100) :0 → with limit=1.5, page=1.5 yields offset=0.75 (fractional).
• packages/ai/src/query/simple-builder.ts:1148-1154 buildLimitClause/buildOffsetClause emit LIMIT 1.5 OFFSET 0.75 vs. builders LIMIT {limit:Int32} OFFSET {offset:Int32} (packages/ai/src/query/builders/pages.ts:182, sessions.ts:318, etc.).
• Internal packages/ai/src/query/index.ts:61-62 QuerySchema: z.number().min(1).max(1000) also allows floats (missing .int()).

To Reproduce

1. Authenticated request:

POST /v1/query?website_id=<id>&timezone=UTC
Content-Type: application/json
{
  "parameters": ["top_pages"],
  "startDate": "2026-01-01",
  "endDate": "2026-01-02",
  "limit": 1.5,
  "page": 1.5
}

2. Also try {"limit": 0.5}, {"page": 1.5}, {"limit": 1.5, "page": 2.3}.

Expected behavior
400 VALIDATION_ERROR with details like:

{ "field":"limit", "message":"Limit must be an integer" }
{ "field":"page", "message":"Page must be an integer" }

limit/page should require finite integer, limit 1..10000, page 1...

Actual behavior
No validation error; request reaches ClickHouse with fractional values. Reproduced locally with copy of validatePaginationFields (D:\tmp\repro_pagination.js):

float limit {limit:1.5} => errors=[] limit=1.5 offset=0  BUG non-integer passed
float page {page:1.5} => errors=[] limit=100 offset=50  BUG
both float => offset 0.75 BUG not integer
Infinity/NaN similarly slip through (JSON NaN not encodable but Elysia coercion from query string can produce floats).

buildLimitClause(NaN) → '' (unbounded), buildLimitClause(0) → ''.

Screenshots
N/A

Environment

• OS: Windows, Bun 1.4.2 (package.json:30 [email protected] pinned)
• Commit: 92c15273d (origin/staging)

Additional context

• limit default fallback || 100 masks 0/NaN in apps/api/src/routes/query.ts:1040, simple-builder.ts:1149 fallback similarly.
• limit max mismatch: API allows 10000 (validatePaginationFields:301), internal QuerySchema allows 1000 — not part of this bug but worth aligning.
• No existing open issue covers this (checked gh issue list).
• Minimal fix proposal: tighten DynamicQueryRequestSchema (TypeBox minimum), add Number.isInteger/isFinite in validatePaginationFields, add .int() to QuerySchema (packages/ai/src/query/index.ts:61-62), add regression test.

AI disclosure
Issue drafted with assistance from Muse Spark (opencode/muse-spark-1.2-contributor-free) and human-verified via local reproduction (node D:\tmp\repro_pagination.js).