محاضرة رياضيات لأستاذ كلب خاضع للرقابة

{
  "type": "surreal photorealistic classroom scene with detailed chalkboard math lesson",
  "style": "high-resolution realistic photo, slightly absurd internet meme tone, natural indoor classroom lighting, sharp chalk writing, 4:3 composition",
  "main_subject": {
    "description": "a humanoid [Shiba Inu dog] teacher standing at the front of a classroom, wearing [a white dress shirt, dark gray slacks, and a black belt], one hand in pocket, holding a thin metal pointer in the other hand and pointing toward equations on the chalkboard",
    "head": "orange-and-white Shiba Inu head with upright ears; the central face area is covered by a flat opaque square censor block in tan beige, creating a comically overdone moderation effect",
    "pose": "confident lecturer pose, facing the students while pointing to the board"
  },
  "setting": {
    "location": "Japanese classroom lecture room",
    "foreground": "backs of 5 seated students visible at the bottom edge, mostly dark hair, one student in a gray hoodie on the right, all looking toward the teacher",
    "furniture": "small wooden teacher podium centered near the bottom with an open gray laptop on top",
    "background": "large dark green chalkboard spanning the wall, metal chalk tray along the bottom, chalk eraser on the far right"
  },
  "chalkboard": {
    "overall_text_style": "white chalk handwriting in Japanese with mathematical notation, clean but hand-drawn, dense lecture notes",
    "main_title": {
      "position": "upper left",
      "text": "[定数係数の常微分方程式]"
    },
    "topic_intro": {
      "position": "upper left below title",
      "text": "次のような常微分方程式を考える。"
    },
    "central_equation": {
      "position": "upper left to center",
      "text": "a_n y^(n) + a_{n-1} y^(n-1) + … + a_1 y' + a_0 y = 0"
    },
    "note": {
      "position": "below central equation",
      "text": "ここで、a_n, a_{n-1}, …, a_0 は定数、a_n ≠ 0 とする。"
    },
    "sections_count": 4,
    "sections": [
      {
        "label": "(1) 特性方程式",
        "position": "left middle",
        "content": "a_n r^n + a_{n-1} r^{n-1} + … + a_1 r + a_0 = 0"
      },
      {
        "label": "(2) 解の形",
        "position": "left lower",
        "content": "three bullet cases: distinct real roots r1, r2, …, rn; repeated root r of multiplicity m; complex conjugate roots α ± βi"
      },
      {
        "label": "example panel",
        "position": "right side separated by a vertical chalk line",
        "title": "【例】",
        "content": "y'' − 3y' + 2y = 0; characteristic equation r^2 − 3r + 2 = 0; (r − 1)(r − 2) = 0; r = 1, 2; therefore y = C1 e^x + C2 e^{2x}"
      },
      {
        "label": "solution formulas",
        "position": "left lower continuation",
        "content": "y = C1 e^{r1 x} + C2 e^{r2 x} + … + Cn e^{rn x}; y = (C1 + C2 x + … + Cm x^{m−1}) e^{rx}; y = e^{αx}(C1 cos βx + C2 sin βx)"
      }
    ]
  },
  "composition": {
    "camera": "student-eye-level view from the back of the classroom, medium-wide shot",
    "framing": "teacher slightly right of center, pointer angled diagonally left toward the characteristic equation, chalkboard fills most of the image",
    "mood": "serious academic lecture made absurd by the dog-headed teacher and censor square",
    "quality": "photorealistic, coherent perspective, realistic fabric, fur, chalk dust texture, classroom depth of field"
  },
  "lesson_topic": "[constant-coefficient ordinary differential equations]"
}