Repair Week 1 Day 2 RoPE learner contract

[skyzh]

Summary

• Rewrite Week 1 Day 2 around the intentionally empty RoPE starter and the exact frequency-table construction learners own.
• Turn the two pair layouts into capability-led checkpoints with honest first-run feedback, dtype preservation, and the Day 3 query/key handoff.
• Add public dtype preservation and contrasting N=2, D=8, base=10 witnesses across both layouts while retaining independent mx.fast.rope value oracles.

Verification

• pdm run test --week 1 --day 2 -- -k task_1 -q — expected red on the empty starter.
• pdm run test --week 1 --day 2 -- -q --tb=no — expected red on the empty starter.
• pdm run test-refsol --week 1 --day 2 -- -k task_1 -q — 16 passed, 16 deselected.
• pdm run test-refsol --week 1 --day 2 -- -q — 32 passed.
• mdbook build book — passed.
• ruff format --check tests_refsol/test_week_1_day_2.py — passed.
• Exact two-path, link/command/equation, test-byte, complement-record, and symlink preservation checks — passed.

Scope

Only book/src/week1-02-positional-encodings.md and tests_refsol/test_week_1_day_2.py change. Starter/reference implementation, tooling, navigation, adjacent and later lessons, Week 4, and publication surfaces remain unchanged.

AI-Assisted: GPT-5.6 Sol + Sentinel