{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "orientation",
          "title": "Studio Goals"
        }
      },
      "source": "## META | difficulty 1 | Studio Goals\n\nThis studio compares CT traces and inspects where learners usually lose the plot: stage order, pair order, and BO output.\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "route_nav",
          "title": "Route Guardrails"
        }
      },
      "source": "## META | difficulty 1 | Route Guardrails\n\nYou are at **step 14 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 / 04 Fast Inverse GS / Lecture](../04_fast_inverse_gs/lecture.ipynb)\n- Previous notebook: [Butterfly Mechanics / 03 Fast Forward CT / Problems](problems.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](lecture.ipynb)\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** <- you are here\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": "mandatory",
          "difficulty": 3,
          "kind": "explanation",
          "title": "Same Schedule, Different Signals"
        }
      },
      "source": "## MANDATORY | difficulty 3 | Same Schedule, Different Signals\n\nThe butterfly pattern is structural.\nThe signal values change, but the pairing pattern and the zeta schedule stay tied to `n`, the modulus, and the chosen root.\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 3,
          "kind": "demo",
          "title": "Compare Two CT Traces"
        }
      },
      "outputs": [],
      "source": "# MANDATORY | difficulty 3 | Compare Two CT Traces\n\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import fast_ntt_psi_ct_trace\nfrom ntt_learning.visuals import plot_butterfly_network, plot_trace_overview\n\ntrace_a = fast_ntt_psi_ct_trace([1, 2, 3, 4], 7681, 1925)\ntrace_b = fast_ntt_psi_ct_trace([5, 6, 7, 8], 7681, 1925)\n\ndisplay(plot_trace_overview(trace_a, title=\"CT trace A\"))\ndisplay(plot_trace_overview(trace_b, title=\"CT trace B\"))\ndisplay(plot_butterfly_network(trace_a, title=\"CT network A\"))\ndisplay(plot_butterfly_network(trace_b, title=\"CT network B\"))\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "exercise",
          "title": "Debug Checklist"
        }
      },
      "source": "## MANDATORY | difficulty 2 | Debug Checklist\n\nIf a CT implementation looks wrong, inspect:\n\n1. the chosen `\u03c8`\n2. the stage pairings\n3. the zeta exponent sequence\n4. whether you remembered the final BO -> NO reorder when comparing against the direct transform\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "exercise",
          "title": "See A Wrong-Order Comparison Failure"
        }
      },
      "outputs": [],
      "source": "# MANDATORY | difficulty 2 | See A Wrong-Order Comparison Failure\n\nfrom IPython.display import display\n\nfrom ntt_learning.toy_ntt import fast_ntt_psi_ct_trace, forward_ntt_psi\nfrom ntt_learning.visuals import plot_vector_comparison\n\ntrace = fast_ntt_psi_ct_trace([1, 2, 3, 4], 7681, 1925)\ndirect = forward_ntt_psi([1, 2, 3, 4], 7681, 1925)\n\nprint(\"wrong comparison: CT BO output vs direct NO output\")\nprint(trace.raw_output, direct)\nprint(\"correct comparison: CT NO output vs direct NO output\")\nprint(trace.normal_order_output, direct)\ndisplay(\n    plot_vector_comparison(\n        trace.raw_output,\n        direct,\n        left_label=\"CT_BO\",\n        right_label=\"direct_NO\",\n        title=\"Wrong comparison: BO against NO\",\n    )\n)\ndisplay(\n    plot_vector_comparison(\n        trace.normal_order_output,\n        direct,\n        left_label=\"CT_NO\",\n        right_label=\"direct_NO\",\n        title=\"Correct comparison after reordering\",\n    )\n)\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "reflection",
          "title": "Reflection"
        }
      },
      "source": "## MANDATORY | difficulty 2 | Reflection\n\nIn one paragraph, explain why a learner can understand the direct transform and still get lost in CT if the stage order and output order are not shown visually.\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "facultative",
          "difficulty": 4,
          "kind": "exploration",
          "title": "Optional: Inspect The zeta schedule"
        }
      },
      "outputs": [],
      "source": "# FACULTATIVE | difficulty 4 | Optional: Inspect The zeta schedule\n\nfrom ntt_learning.toy_ntt import fast_ntt_psi_ct_trace\n\ntrace = fast_ntt_psi_ct_trace([1, 2, 3, 4], 7681, 1925)\nfor stage in trace.stages:\n    print(\"stage\", stage.stage_index, \"zetas:\", stage.zetas)\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "handoff",
          "title": "Next Notebook"
        }
      },
      "source": "## META | difficulty 1 | Next Notebook\n\nYou finished **Butterfly Mechanics / 03 Fast Forward CT / Studio**.\n\n**Primary next action**\n- Next notebook: [Step 15 of 27 - Butterfly Mechanics / 04 Fast Inverse GS / Lecture](../04_fast_inverse_gs/lecture.ipynb)\n\n**Recovery links if you get lost**\n- Previous notebook: [Butterfly Mechanics / 03 Fast Forward CT / Problems](problems.ipynb)\n- Restart route: [Start Here](../../START_HERE.ipynb)\n"
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    },
    "ntt_learning": {
      "title": "Studio: Fast Forward CT",
      "contract_version": "0.2",
      "sequence": [
        "notebooks/START_HERE.ipynb",
        "notebooks/COURSE_BLUEPRINT.ipynb",
        "notebooks/foundations/01_convolution_to_toy_ntt/lecture.ipynb",
        "notebooks/foundations/01_convolution_to_toy_ntt/lab.ipynb",
        "notebooks/foundations/01_convolution_to_toy_ntt/problems.ipynb",
        "notebooks/foundations/01_convolution_to_toy_ntt/studio.ipynb",
        "notebooks/foundations/02_negative_wrapped_ntt/lecture.ipynb",
        "notebooks/foundations/02_negative_wrapped_ntt/lab.ipynb",
        "notebooks/foundations/02_negative_wrapped_ntt/problems.ipynb",
        "notebooks/foundations/02_negative_wrapped_ntt/studio.ipynb",
        "notebooks/butterfly_mechanics/03_fast_forward_ct/lecture.ipynb",
        "notebooks/butterfly_mechanics/03_fast_forward_ct/lab.ipynb",
        "notebooks/butterfly_mechanics/03_fast_forward_ct/problems.ipynb",
        "notebooks/butterfly_mechanics/03_fast_forward_ct/studio.ipynb",
        "notebooks/butterfly_mechanics/04_fast_inverse_gs/lecture.ipynb",
        "notebooks/butterfly_mechanics/04_fast_inverse_gs/lab.ipynb",
        "notebooks/butterfly_mechanics/04_fast_inverse_gs/problems.ipynb",
        "notebooks/butterfly_mechanics/04_fast_inverse_gs/studio.ipynb",
        "notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/lecture.ipynb",
        "notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/lab.ipynb",
        "notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/problems.ipynb",
        "notebooks/kyber_mapping/05_kyber_ntt_and_base_multiplication/studio.ipynb",
        "notebooks/professional/06_debugging_ntt_failures/lecture.ipynb",
        "notebooks/professional/06_debugging_ntt_failures/lab.ipynb",
        "notebooks/professional/06_debugging_ntt_failures/problems.ipynb",
        "notebooks/professional/06_debugging_ntt_failures/studio.ipynb",
        "notebooks/COURSE_COMPLETE.ipynb"
      ]
    }
  },
  "nbformat": 4,
  "nbformat_minor": 5
}