{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "orientation",
          "title": "Problem Set Goals"
        }
      },
      "source": "## META | difficulty 1 | Problem Set Goals\n\nThis notebook checks whether the main NTT bug classes are now distinct in memory.\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "quiz",
          "title": "Multiple-Choice Retrieval"
        }
      },
      "source": "## MANDATORY | difficulty 2 | Multiple-Choice Retrieval\n\nChoose one answer for each:\n\n1. A shuffled but otherwise familiar forward result most strongly suggests:\n   A. missing final scaling\n   B. wrong BO / NO comparison\n   C. wrong modulus\n\n2. An inverse output that looks like a clean multiple of the target most strongly suggests:\n   A. missing `n^-1`\n   B. wrong wraparound sign\n   C. wrong bit-reversal map\n\n3. A local pair that already looks broken in stage 1 most strongly suggests:\n   A. wrong zeta\n   B. correct CT output\n   C. harmless ordering noise\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "quiz",
          "title": "Answer Key"
        }
      },
      "outputs": [],
      "source": "# MANDATORY | difficulty 2 | Answer Key\n\nanswers = {1: \"B\", 2: \"A\", 3: \"A\"}\nprint(answers)\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "exercise",
          "title": "Debug Priority Check"
        }
      },
      "source": "## MANDATORY | difficulty 2 | Debug Priority Check\n\nList the first four checks you would run on a suspicious iNTT output.\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "exercise",
          "title": "One Good Ordering"
        }
      },
      "outputs": [],
      "source": "# MANDATORY | difficulty 2 | One Good Ordering\n\ndebug_order = [\n    \"check BO / NO assumption\",\n    \"check root / zeta schedule\",\n    \"check final n^-1 scaling\",\n    \"check sign / wraparound conventions\",\n]\nprint(debug_order)\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "mandatory",
          "difficulty": 2,
          "kind": "reflection",
          "title": "Written Reflection"
        }
      },
      "source": "## MANDATORY | difficulty 2 | Written Reflection\n\nIn one paragraph, explain why visible traces are much better debugging tools than only comparing final vectors.\n"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "pedagogy": {
          "role": "facultative",
          "difficulty": 4,
          "kind": "exploration",
          "title": "Optional Challenge"
        }
      },
      "outputs": [],
      "source": "# FACULTATIVE | difficulty 4 | Optional Challenge\n\nmistakes = {\n    \"wrong_order\": \"fix the permutation first\",\n    \"missing_scale\": \"multiply by n^-1\",\n    \"wrong_zeta\": \"rebuild the twiddle schedule\",\n    \"wrong_sign\": \"inspect the quotient ring\",\n}\nfor key, value in mistakes.items():\n    print(key, \"->\", value)\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "pedagogy": {
          "role": "meta",
          "difficulty": 1,
          "kind": "handoff",
          "title": "Next Notebook"
        }
      },
      "source": "## META | difficulty 1 | Next Notebook\n\nNext notebook: `studio.ipynb`\n"
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    },
    "ntt_learning": {
      "title": "Problems: Debugging NTT Failures",
      "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
}