Enforce half-split layout for cos/sin in RoPE challenge test data

[baqizhaobenshan]

Summary

Fixes the RoPE challenge test data so cos and sin follow the half-split layout described by the problem.
For RoPE with rotate_half, paired dimensions j and j + D/2 should use the same cosine and sine values. Previously, several generated test cases used fully independent random values for all D dimensions, so cos[:, j] != cos[:, j + D/2] and sin[:, j] != sin[:, j + D/2] in general.
This PR keeps the existing random data generation style unchanged and only enforces:

value[:, D // 2 :] = value[:, : D // 2]

Changes

• Added a small helper to enforce half-split layout for generated cos and sin tables.
• Updated generated RoPE test inputs so paired dimensions share the same cos / sin values.
• Updated the fixed mixed_values test case to satisfy the same layout.
• Documented the half-split cos / sin requirement in the challenge description.

Motivation

The current random cos / sin test data prevents implementations from using the standard half-split RoPE assumption that paired dimensions share the same rotation values. This makes the test data inconsistent with the expected RoPE layout and forces extra cos / sin loads that should not be necessary for this formulation.

Testing

• python3 -m py_compile challenges/medium/61_rope_embedding/challenge.py
• git diff --check -- challenges/medium/61_rope_embedding/challenge.py challenges/medium/61_rope_embedding/challenge.html

[baqizhaobenshan]

Hi maintainers, gentle ping on this PR.

I verified the change locally with:

• black --check challenges/medium/61_rope_embedding/challenge.py
• isort --check-only challenges/medium/61_rope_embedding/challenge.py
• flake8 challenges/medium/61_rope_embedding/challenge.py
• python3 -m py_compile challenges/medium/61_rope_embedding/challenge.py
• git diff --check -- challenges/medium/61_rope_embedding/challenge.py challenges/medium/61_rope_embedding/challenge.html

All checks passed locally. The Checks tab currently shows “completed with no jobs”, so I am not sure whether CI was skipped because of path filters or fork permissions.

The intended invariant here is that RoPE uses rotate_half / half-split layout, so dimensions j and j + D/2 form a pair and should share the same cos/sin values. The current random test generation samples all D dimensions independently, which breaks this invariant. This PR only fixes the test data generation and documents the invariant; it does not change the solve signature or the expected output formula.

@kunal-mansukhani Sorry for the ping — when you have time, could you take a look at whether this matches the intended RoPE layout for this challenge?