| # Complete 3-D Cross-n FOURIN Spectral Coupling |
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| You are given a reduced source snapshot from a TERPSICHORE-style ideal MHD |
| stability workflow. |
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| The current implementation handles simpler spectral settings, but the included |
| 3-D plasma-only reproduction exposes an incomplete capability: cross-n spectral |
| coupling is not consistently preserved through the coefficient and downstream |
| matrix/energy path. |
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| Inspect the source and run: |
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| ```bash |
| python reproduce.py |
| ``` |
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| The reproduction writes the candidate workflow's raw observations under |
| `outputs/`. The command returns nonzero if those observations are empty, |
| incomplete, or non-finite; it does not apply verifier-only capability |
| thresholds. |
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| Your task is to complete the implementation so that a genuinely |
| three-dimensional mode set with multiple toroidal `n` groups is handled |
| consistently. |
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| The intended capability chain is: |
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| ```text |
| mode table -> trigonometric lookup -> branch metadata reduction -> FOURIN coefficients -> matrix assembly -> energy accounting |
| ``` |
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| Do not hard-code: |
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| - the included case; |
| - a fixed list of expected numbers; |
| - a fixed mode table; |
| - a single coefficient or matrix block. |
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| Do not bypass the coefficient path by writing directly into matrix outputs. The |
| implementation should support the general 3-D spectral-coupling workflow |
| represented by the supplied task. |
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| Internet access is not available during evaluation. |
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