"source": "## META\n\n<div class=\"ntt-cell-head ntt-role-meta\">\n <span class=\"ntt-difficulty-pill\">Level 1</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">META</span>\n <span class=\"ntt-kind-pill\">route nav</span>\n </div>\n <div class=\"ntt-cell-title\">Route Guardrails</div>\n</div>\n\nYou are at **step 11 of 27** in the only supported route.\n\nNever choose the next notebook manually from the file tree. Use only the links in this cell and the final handoff cell.\n\n**Immediate navigation**\n- Next notebook: [Butterfly Mechanics / 03 Fast Forward CT / Lab](lab.ipynb)\n- Previous notebook: [Foundations / 02 Negative Wrapped NTT / Studio](../../foundations/02_negative_wrapped_ntt/studio.ipynb)\n- Restart route: [Start Here](../../START_HERE.ipynb)\n\n**Official route chain**\n1. [Start Here](../../START_HERE.ipynb)\n2. [Course Blueprint](../../COURSE_BLUEPRINT.ipynb)\n3. [Foundations / 01 Convolution To Toy NTT / Lecture](../../foundations/01_convolution_to_toy_ntt/lecture.ipynb)\n4. [Foundations / 01 Convolution To Toy NTT / Lab](../../foundations/01_convolution_to_toy_ntt/lab.ipynb)\n5. [Foundations / 01 Convolution To Toy NTT / Problems](../../foundations/01_convolution_to_toy_ntt/problems.ipynb)\n6. [Foundations / 01 Convolution To Toy NTT / Studio](../../foundations/01_convolution_to_toy_ntt/studio.ipynb)\n7. [Foundations / 02 Negative Wrapped NTT / Lecture](../../foundations/02_negative_wrapped_ntt/lecture.ipynb)\n8. [Foundations / 02 Negative Wrapped NTT / Lab](../../foundations/02_negative_wrapped_ntt/lab.ipynb)\n9. [Foundations / 02 Negative Wrapped NTT / Problems](../../foundations/02_negative_wrapped_ntt/problems.ipynb)\n10. [Foundations / 02 Negative Wrapped NTT / Studio](../../foundations/02_negative_wrapped_ntt/studio.ipynb)\n11. **Butterfly Mechanics / 03 Fast Forward CT / Lecture** <- you are here\n12. [Butterfly Mechanics / 03 Fast Forward CT / Lab](lab.ipynb)\n13. [Butterfly Mechanics / 03 Fast Forward CT / Problems](problems.ipynb)\n14. [Butterfly Mechanics / 03 Fast Forward CT / Studio](studio.ipynb)\n15. [Butterfly Mechanics / 04 Fast Inverse GS / Lecture](../04_fast_inverse_gs/lecture.ipynb)\n16. [Butterfly Mechanics / 04 Fast Inverse GS / Lab](../04_fast_inverse_gs/lab.ipynb)\n17. [Butterfly Mechanics / 04 Fast Inverse GS / Problems](../04_fast_inverse_gs/problems.ipynb)\n18. [Butterfly Mechanics / 04 Fast Inverse GS / Studio](../04_fast_inverse_gs/studio.ipynb)\n19. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Lecture](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb)\n20. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Lab](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/lab.ipynb)\n21. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Problems](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/problems.ipynb)\n22. [Kyber Mapping / 05 Kyber NTT And Base Multiplication / Studio](../../kyber_mapping/05_kyber_ntt_and_base_multiplication/studio.ipynb)\n23. [Professional / 06 Debugging NTT Failures / Lecture](../../professional/06_debugging_ntt_failures/lecture.ipynb)\n24. [Professional / 06 Debugging NTT Failures / Lab](../../professional/06_debugging_ntt_failures/lab.ipynb)\n25. [Professional / 06 Debugging NTT Failures / Problems](../../professional/06_debugging_ntt_failures/problems.ipynb)\n26. [Professional / 06 Debugging NTT Failures / Studio](../../professional/06_debugging_ntt_failures/studio.ipynb)\n27. [Course Complete](../../COURSE_COMPLETE.ipynb)\n"
},
{
"cell_type": "markdown",
"metadata": {
"pedagogy": {
"role": "meta",
"difficulty": 1,
"kind": "orientation",
"title": "Objectives"
}
},
"source": "## META\n\n<div class=\"ntt-cell-head ntt-role-meta\">\n <span class=\"ntt-difficulty-pill\">Level 1</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">META</span>\n <span class=\"ntt-kind-pill\">orientation</span>\n </div>\n <div class=\"ntt-cell-title\">Objectives</div>\n</div>\n\nThis bundle is where the transform stops being a full matrix multiplication and becomes a staged butterfly network.\n\nFocus:\n\n- CT as the fast forward NTT strategy\n- visible stage arrays\n- explicit zeta values per pair\n- BO output vs NO output\n"
"source": "## MANDATORY\n\n<div class=\"ntt-cell-head ntt-role-mandatory\">\n <span class=\"ntt-difficulty-pill\">Level 3</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">MANDATORY</span>\n <span class=\"ntt-kind-pill\">explanation</span>\n </div>\n <div class=\"ntt-cell-title\">CT Is A Schedule For Reusing Work</div>\n</div>\n\nThe point of the CT butterfly is not to invent a new transform.\nThe point is to compute the same transform by reusing shared bracket terms instead of recomputing everything from scratch.\n"
"source": "## MANDATORY\n\n<div class=\"ntt-cell-head ntt-role-mandatory\">\n <span class=\"ntt-difficulty-pill\">Level 3</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">MANDATORY</span>\n <span class=\"ntt-kind-pill\">explanation</span>\n </div>\n <div class=\"ntt-cell-title\">What You Should Notice In The Stage Viewer</div>\n</div>\n\nDo not just read the final answer.\nNotice:\n\n- which pairs talk to each other in each stage\n- which `zeta` each pair uses\n- how the array order changes before the final bit-reversal correction\n"
"source": "## MANDATORY\n\n<div class=\"ntt-cell-head ntt-role-mandatory\">\n <span class=\"ntt-difficulty-pill\">Level 2</span>\n <div class=\"ntt-cell-row\">\n <span class=\"ntt-role-pill\">MANDATORY</span>\n <span class=\"ntt-kind-pill\">quiz</span>\n </div>\n <div class=\"ntt-cell-title\">Retrieval Check</div>\n</div>\n\n1. What does CT change: the transform definition or the computation schedule?\n2. Why is the output naturally in BO rather than NO?\n3. In a stage diagram, what are the first three things you should inspect before any formula?\n"
