{
  "caseId": "derivative",
  "assessmentType": "AI independent qualitative observations plus executable geometry/math/media checks; not human blind scoring",
  "status": "independent-audit-complete",
  "summaryZh": "89.167秒成片的核心数学通过：P/Q、正负h差商、极限、切线和x=2答案正确。仍有标签碰撞、负h段回跳、缺字与线条越出图面，不能称排版与连续性全通过。",
  "summaryEn": "Core mathematics in the 89.167-second film passes: P/Q, signed difference quotients, limit, tangent and the x=2 answer are correct. Label collisions, a negative-h reset, a missing glyph and lines crossing plot margins remain.",
  "assessmentZh": [
    "对2675个编码帧状态独立数学检查：非零h、Q=(1+h,(1+h)²)、差商2+h及切线y=2x−1一致；x=2答案为4，实际紫线y=4x−4正确。",
    "P/Q与Δx/Δy标签多时点重叠；⇒缺字，割线/切线未裁剪到绘图区而穿过图例/边距。",
    "50.215秒负h从−0.350回到−0.600再靠近0，数学仍正确，但同侧过程有未解释重启。",
    "模型附带06_tangent取帧落到提问章节；公开采用独立从最终MP4抽的67.2秒实际切线帧。结尾题目停留5秒再给正确答案。"
  ],
  "assessmentEn": [
    "Independent mathematical checks of all 2675 encoded frame states verify nonzero h, Q=(1+h,(1+h)²), quotient 2+h and tangent y=2x−1. The answer at x=2 is 4 and the actual purple line y=4x−4 is correct.",
    "P/Q labels collide with Δx/Δy at multiple times; ⇒ is a missing glyph and unclipped secant/tangent lines cross legends/margins.",
    "At 50.215s negative h resets from −0.350 to −0.600 before approaching zero again. Values remain correct but the same-side restart is unexplained.",
    "The supplied 06_tangent still belongs to the question chapter; public evidence instead uses the independent 67.2s decoded final-video tangent frame. The question holds five seconds before the correct answer."
  ],
  "checks": [
    {
      "labelZh": "核心数学",
      "labelEn": "Core mathematics",
      "status": "pass",
      "detailZh": "原生状态表达式与实际关键帧核对，无最终确认数学错误。",
      "detailEn": "Independent state expressions and targeted decoded frames show no confirmed final core math error."
    },
    {
      "labelZh": "连续性与可读性",
      "labelEn": "Continuity and legibility",
      "status": "partial",
      "detailZh": "负h回跳、标签重叠、缺字和图线布局问题仍保留。",
      "detailEn": "Negative-h reset, overlapping labels, missing glyph and plot-layout issues remain."
    }
  ],
  "independentAudit": {
    "verdict": "Core final mathematics passes; remaining confirmed issues concern visual legibility, a same-side animation reset, and ancillary frame selection.",
    "checks": [
      {
        "id": "D01",
        "status": "pass",
        "evidence": "f=x², P=(1,1), displayed Q=(1+h,(1+h)²); h stays nonzero in all 2675 encoded frame states."
      },
      {
        "id": "D02",
        "status": "pass",
        "evidence": "Displayed secant m=2+h, b=-1-h passes both P and Q; sampled video frames agree with the final source."
      },
      {
        "id": "D03",
        "status": "pass",
        "evidence": "Signed Δx/Δy and negative-window numerical values are correct; label collisions are separately V01."
      },
      {
        "id": "D04",
        "status": "pass",
        "evidence": "Positive-side approach is continuously animated within its chapter and approaches slope2 from above."
      },
      {
        "id": "D05",
        "status": "partial",
        "evidence": "Negative-side approach exists and reaches slope2 from below, but the two chapters reset h at 50.215s (V02)."
      },
      {
        "id": "D06",
        "status": "pass",
        "evidence": "Narration explicitly rejects division by zero and distinguishes a limit; no frame state uses h=0."
      },
      {
        "id": "D07",
        "status": "pass",
        "evidence": "Actual 67.2s frame shows correct y=2x-1 through P. The right panel is explicitly labelled finite-h secant quotient, close to2."
      },
      {
        "id": "D08",
        "status": "pass",
        "evidence": "Final hint uses general difference-quotient wording. Answer panel gives2a+h→2a and slope4 at a2. Actual84/89s purple line is y=4x-4 through R; the earlier wrong line is fixed, not a final error."
      },
      {
        "id": "D09",
        "status": "pass",
        "evidence": "Shared x/y transform and numbered units are consistent. The non-square screen grid is labelled by coordinate units; no screen-angle slope inference was used."
      },
      {
        "id": "D10",
        "status": "partial",
        "evidence": "Core Chinese narration captions and equations fit actual1080p frames, with no confirmed subtitle canvas clipping. Point/triangle labels overlap and ⇒ is missing (V01,V03); lines intrude into margins (V04)."
      },
      {
        "id": "D11",
        "status": "pass",
        "evidence": "MP4 reaches89.166667s, last caption ends87.939s, and89.0s decoded frame holds the answer. Question chapter has a5s pause before the answer. No truncated visual ending observed."
      },
      {
        "id": "D12",
        "status": "pass",
        "evidence": "Final hash frozen after model_finished, original media distinguished from future revoice derivatives, public tool trajectory inspected without reviewer feedback. Ancillary model frame-selection issue recorded asA01."
      }
    ],
    "confirmedFindings": [
      {
        "id": "V01",
        "type": "visual_legibility",
        "severity": "medium",
        "seconds": [
          16,
          28,
          45,
          50.1,
          50.233333
        ],
        "confirmed": true,
        "description": "P/Q point labels overlap Δx labels in actual decoded frames; at 28s Q and Δy labels also collide. Right-panel coordinates/values and the main subtitles remain readable. This is overlap, not a claim that text is outside the canvas.",
        "source": "src/render.py:58,69,74",
        "evidence": [
          "content-frame-16.000s.png",
          "content-frame-28.000s.png",
          "content-frame-45.000s.png",
          "content-frame-50.100s.png"
        ]
      },
      {
        "id": "V02",
        "type": "animation_continuity",
        "severity": "low",
        "seconds": [
          50.1,
          50.233333
        ],
        "confirmed": true,
        "description": "At the 50.215s chapter boundary, h jumps from -0.350 back to -0.600 (Q from (0.650,0.4225) back to (0.400,0.160)) and then approaches zero again. The two left-side segments each animate continuously and every value remains mathematically correct, but the same-side restart is unexplained.",
        "source": "src/render.py:30-31; output/timeline.json segment6",
        "evidence": [
          "content-frame-50.100s.png",
          "content-frame-50.233s.png"
        ]
      },
      {
        "id": "V03",
        "type": "font_glyph",
        "severity": "low",
        "seconds": [
          16,
          28,
          67.2
        ],
        "confirmed": true,
        "description": "The ⇒ in the lower-right h→0 ⇒ 斜率→2 line renders as a missing-glyph box. A mask comparison confirms the selected CJK font uses its missing-character glyph for ⇒. The ordinary arrows and the numerical formulas remain readable.",
        "source": "src/render.py:121",
        "evidence": [
          "content-frame-28.000s.png",
          "content-frame-67.200s.png",
          "mathematical-state-checks.json"
        ]
      },
      {
        "id": "V04",
        "type": "plot_layout",
        "severity": "low",
        "seconds": [
          16,
          45,
          84,
          89
        ],
        "confirmed": true,
        "description": "The infinite secant/tangent lines are not clipped to the graph panel, so they continue through the lower graph legend and into the margin; the line at 16s also continues above the graph panel. The line coordinates themselves are correct.",
        "source": "src/render.py:63,67",
        "evidence": [
          "content-frame-16.000s.png",
          "content-frame-45.000s.png",
          "content-frame-89.000s.png"
        ]
      },
      {
        "id": "A01",
        "type": "representative_frame_selection",
        "severity": "low",
        "seconds": [
          69.4
        ],
        "confirmed": true,
        "description": "The model-delivered file 06_tangent.png is sampled at 69.4s, after the tangent chapter ended at 68.86s, so it shows the question chapter. The final MP4 does contain the correct tangent from 66.8667 to 68.8333s; QA extracted 67.2s to verify it.",
        "source": "src/finalize.py shots; src/render.py state; output/timeline.json",
        "evidence": [
          "content-frame-67.200s.png",
          "mathematical-state-checks.json"
        ]
      }
    ],
    "notTested": [
      "No independent human full-length auditory pronunciation/pace acceptance.",
      "Future Kokoro public-audio derivatives and their timing/hashes are outside this original-video audit.",
      "No claim to visually inspect every one of the2675 decoded frames; all state functions were checked mathematically, and8 targeted decoded frames were visually inspected."
    ]
  },
  "localIndependentAudit": {
    "path": "qa/derivative/content-audit.json",
    "sha256": "357c5f0d78cbab7a5af5cf401465d47364459a3b698db94973ad98b5d8a2d308"
  },
  "technicalEvidence": {
    "caseId": "derivative",
    "checkedAt": "2026-10-26T18:30:03.216909+00:00",
    "sourceVideo": "cases/derivative/output/derivative_secant_to_tangent.mp4",
    "sha256": "f807b3b5f441b26670df6eeda5ff876633cd7df544f5e83bb1a844f64917e575",
    "immutableSnapshot": "qa/derivative/video-f807b3b5f441.mp4",
    "width": 1920,
    "height": 1080,
    "fps": 30.0,
    "durationSeconds": 89.166667,
    "frameCount": "2675",
    "audioStreams": [
      {
        "index": 1,
        "codec_name": "aac",
        "codec_long_name": "AAC (Advanced Audio Coding)",
        "profile": "LC",
        "codec_type": "audio",
        "codec_tag_string": "mp4a",
        "codec_tag": "0x6134706d",
        "mime_codec_string": "mp4a.40.2",
        "sample_fmt": "fltp",
        "sample_rate": "48000",
        "channels": 1,
        "channel_layout": "mono",
        "bits_per_sample": 0,
        "initial_padding": 0,
        "id": "0x2",
        "r_frame_rate": "0/0",
        "avg_frame_rate": "0/0",
        "time_base": "1/48000",
        "start_pts": 0,
        "start_time": "0.000000",
        "duration_ts": 4278672,
        "duration": "89.139000",
        "bit_rate": "186638",
        "nb_frames": "4180",
        "extradata_size": 5,
        "disposition": {
          "default": 1,
          "dub": 0,
          "original": 0,
          "comment": 0,
          "lyrics": 0,
          "karaoke": 0,
          "forced": 0,
          "hearing_impaired": 0,
          "visual_impaired": 0,
          "clean_effects": 0,
          "attached_pic": 0,
          "timed_thumbnails": 0,
          "non_diegetic": 0,
          "captions": 0,
          "descriptions": 0,
          "metadata": 0,
          "dependent": 0,
          "still_image": 0,
          "multilayer": 0
        },
        "tags": {
          "language": "und",
          "handler_name": "SoundHandler"
        }
      }
    ],
    "checks": {
      "durationWithinFrozenRange": true,
      "fullVideoAudioDecode": true,
      "dimensions": true,
      "frameRate": true,
      "motionObservedInSamples": true,
      "audioTrack": true,
      "captionsPresentAndTimed": true
    },
    "allTechnicalChecksPass": true,
    "captions": [
      {
        "path": "cases/derivative/output/subtitles.srt",
        "cueCount": 25,
        "validTimes": true,
        "lastEndSeconds": 87.939
      }
    ],
    "frames": [
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        "path": "qa/derivative/frame-00-0.100s.jpg",
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    "contactSheets": [
      "qa/derivative/contact-01.jpg",
      "qa/derivative/contact-02.jpg",
      "qa/derivative/contact-03.jpg"
    ],
    "assessmentScope": "Container,decode,timing and sampled motion only; geometry/science/visual checks are separately reported"
  },
  "requestEvidence": [
    "/evaluations/kimi-k3-1-pro-creative/derivative/attempt-01.json"
  ],
  "originalCompleteInputSha256": "f331e0e46d1a51df29d0d9610d0b87f1bd8a9365b599b3b277ed29e9b9272279",
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  "billing": {
    "basis": "subscription quota",
    "actualMonetaryCost": null
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  "officialBenchmarkScore": false,
  "reviewLimits": "No official benchmark score, blind human quality score, manufacturing/load certification or exhaustive subjective listening is claimed."
}