[Brendan-Lim]

Quack already diagnoses missing inner factors and verifies corrections, but chain-rule mistakes could not lead to targeted practice. Add bounded sine, cosine and exponential composition questions to the existing verified-key practice flow, My Mistakes and recap recommendations. Frontend and backend topic types are extended together; routing, inference budgets, PostgreSQL accounting, authentication, verification rules and database schema are unchanged.

Add ten offline API tutoring/failure episodes using existing HTTP doubles and the real isolated verifier, independent symbolic key checks, and a browser journey from a mistake to completed practice. Repair the existing adaptive evaluation report to select Algebra by ID rather than catalog position. These checks measure deterministic software contracts, not handwriting accuracy, learning gains or a student's mental cause.

Validation before merge:

• Full release workflow with PostgreSQL 18 and locked Modal/tooling dependencies, zero required skips and no paid model calls.
• Baseline/feature comparison using identical offline evaluator and fixture hashes; all ten episodes already run as backend tests in CI.
• Exact PR scope, publication policy, secrets, dependency audits and hosted CI results.

Production rollout is excluded. No Vercel or Modal deployment is authorized by this PR; later rollout must be backend first.

Release verification found and fixed a synthetic browser-fixture omission: generated exponential answers need e and p, which were absent from the stroke alphabet. Add those glyphs without changing existing glyph data, plus a regression rendering all 27 distinct generated questions and answers. No application behavior or test assertion is weakened. The repaired browser journey passes three local repetitions; 69 focused backend checks pass.

Hosted evidence:

• Initial run https://github.com/Brendan-Lim/Quack/actions/runs/43014011587: 3,521 backend tests passed (all 20 PostgreSQL accounting cases and eight Modal checks included), 361 frontend tests passed, nine compiled browser checks passed, and 248/249 development journeys passed. Zero required skips. The sole failure was the missing exponential glyph; retained logs/traces explain the repair.
• Full verification of repair head 01c3546 PASSED: https://github.com/Brendan-Lim/Quack/actions/runs/43022128304. All 3,522 backend tests, 361 frontend tests, 249 development browser journeys and nine compiled browser checks passed. Zero required skips or flaky browser cases; dependency audits, publication guard, secret scans, lint, types and build passed.
• Identical offline evaluator/fixture hashes reproduce 6/10 baseline to 10/10 complete episodes, zero regressions. Synthetic contract coverage does not measure handwriting accuracy or learning gains.

Merged normally as ec266b50eccfe1dcc6538621161e9cccbe9bf3d2; its source tree exactly matches tested repair head 01c3546. Automatic main CI PASSED: https://github.com/Brendan-Lim/Quack/actions/runs/43029006117. It independently reports the same 3,522 backend, 361 frontend, 249 browser journey and nine compiled-browser passes, zero required skips/flaky cases, and all 16 release checks passed.

Post-merge read-only provider verification confirms both existing production deployments remain at 6784a07; all 72 Modal runtime files match that baseline, and Vercel's alias/deployment is unchanged. Production deployment remains pending separate authorization. No paid model calls were made.