import marimo

__generated_with = "0.23.16"
app = marimo.App(width="medium", app_title="進階 RAG：父子檢索、混合搜尋與 Rerank（實驗場）")


@app.cell(hide_code=True)
def _(mo):
    mo.md(
        r"""
    # 🧪 進階 RAG：父子檢索、混合搜尋與 Rerank（實驗場）

    這是本課的**實驗場**。每一節都有拉桿和開關——拉完，下面的分數立刻用
    **41 題有標準答案的考卷**重新打一次，所有數字都是你的瀏覽器當場算的。

    素材都是真的：一份虛構咖啡機「拿鐵大師 LM-500／500S／700」的手冊（20 節、90 句）；
    句子與問題的**真向量**由 jina-embed（jinaai/jina-embeddings-v5-text-small-retrieval，1024 維）
    實測算好打包在這裡；**BM25、融合、所有指標都在這裡現場算**；
    rerank 分數是事先用 cross-encoder `BAAI/bge-reranker-v2-m3` 在 CPU 上算好的實測值
    （cross-encoder 是個 5 億多參數的模型，瀏覽器裡跑不動）。實測日期 2026-09。
    """
    )
    return


@app.cell
def _():
    import marimo as mo
    return (mo,)


@app.cell
def _():
    # 科學套件集中在這格 import，回傳給全 notebook 用
    import base64
    import html as html_mod
    import re

    import matplotlib.pyplot as plt
    import numpy as np
    return base64, html_mod, np, plt, re


@app.cell
def _():
    # ── DATA BEGIN（由 _spikes/spike_genai_rag_advanced.py --part emit 產生；勿手改，重產方式見 NOTES.md）──
    # 手冊：20 節（父塊）× 每節幾句（子塊）。虛構教材，模型不可能背過。
    SECTIONS = [
        ('開箱與首次使用', [
            '包裝內含主機、水箱、雙份濾杯把手、蒸氣鋼杯，以及一包 DC-300 除垢劑。',
            '首次使用前，先把濾水芯浸泡在冷水中 5 分鐘，再裝進水箱底部的卡槽。',
            '水箱裝滿冷水、不放咖啡粉，按沖煮鍵讓水流完；這樣的空水循環要連做兩次。',
            '接著打開蒸氣旋鈕空噴 10 秒，把蒸氣管裡的製造殘留排乾淨。',
            '最後在設定選單把水質硬度設成你家的等級（1 到 4 級，出廠值為 3 級）。',
        ]),
        ('機型差異', [
            'LM-500 是單鍋爐機型，同一時間只能沖煮或打奶泡其中一件事。',
            'LM-500S 加裝蒸氣預熱，從沖煮切換到打奶泡只要約 5 秒。',
            'LM-700 是雙鍋爐機型，可以一邊萃取一邊打奶泡。',
            'LM-700 的水箱為 1.8 公升，LM-500 與 LM-500S 為 1.2 公升。',
            'LM-500 與 LM-500S 使用 54 mm 把手，LM-700 使用 58 mm 把手。',
        ]),
        ('沖煮義式濃縮', [
            '單份濃縮用 18 公克咖啡粉，雙份濾杯用 20 公克。',
            '填粉後以約 15 公斤的力道垂直壓粉，粉面要壓平。',
            '把手鎖緊後按單杯鍵，理想萃取時間是 25 到 30 秒，萃取量約 36 毫升。',
            '不到 20 秒就流完，代表研磨太粗或粉量不足。',
            '超過 35 秒還在滴，代表研磨太細或壓粉太用力。',
        ]),
        ('研磨設定', [
            '內建錐刀磨豆機共有 15 段刻度，1 最細、15 最粗。',
            '義式濃縮建議從第 5 段開始，每次只調一格。',
            '調整刻度必須在磨豆機運轉時進行，停機時硬轉會卡住刀盤。',
            '研磨過細會導致過度萃取、流速變慢，嚴重時觸發防堵塞保護而自動停機。',
        ]),
        ('沖煮溫度', [
            '預設沖煮溫度為 92°C，可以 1°C 為單位調整，範圍 88 到 96°C。',
            '淺焙豆適合 93 到 95°C；深焙豆建議 88 到 90°C，可以減少苦味。',
            '溫度越高萃取越強，苦味也越明顯。',
        ]),
        ('奶泡與蒸氣', [
            '請使用冷藏約 4°C 的鮮奶，奶量不超過鋼杯的一半。',
            '蒸氣管先空噴 2 秒排掉冷凝水，再把噴頭埋入奶面下約 1 公分。',
            '聽到嘶嘶的進氣聲約 3 秒後，把噴頭壓深，讓牛奶旋轉加熱到 60 到 65°C。',
            '用完立刻以濕布擦拭蒸氣管並空噴 1 秒，避免奶垢堵住噴孔。',
        ]),
        ('熱水功能', [
            '轉開熱水旋鈕即可出熱水，出水溫度約 85°C。',
            '熱水與蒸氣共用同一支管路，出熱水前請先空噴 2 秒。',
            '泡茶時建議先出 50 毫升熱水溫杯，再倒掉。',
        ]),
        ('除垢', [
            '有裝濾水芯時，除垢週期可以從 3 個月延長到 6 個月。',
            '除垢燈亮起代表累積用水量已達設定值，請在一週內完成除垢。',
            '先取下濾水芯，再把一包 DC-300 除垢劑與 1 公升清水混合倒入水箱。',
            '長按沖煮鍵 5 秒進入除垢模式，機器會分段流出除垢液，全程約 20 分鐘。',
            '除垢液流完後，沖洗水箱並裝滿清水，再按一次沖煮鍵跑完清水循環。',
            '最後裝回濾水芯，除垢燈熄滅即完成；除垢途中請勿關機。',
        ]),
        ('日常清潔', [
            '滴水盤與粉渣盒每天清空，滴水盤的浮標升起時要立刻倒掉。',
            '沖煮頭每週以溫水沖洗一次，並用附贈的刷子刷掉殘粉。',
            '每月逆洗沖煮頭一次：把盲碗裝進把手、放入一錠清潔錠，長按單杯鍵 10 秒。',
            '機身以擰乾的濕布擦拭，切勿整機沖水或放進洗碗機。',
        ]),
        ('零件與耗材型號', [
            'WF-12：濾水芯，LM-500 與 LM-500S 用，每 2 個月或 50 公升更換一次。',
            'WF-21：濾水芯，LM-700 專用，每 3 個月或 80 公升更換一次；與 WF-12 外觀相似，不可混用。',
            'DC-300：除垢劑，一盒 3 包，一包兌 1 公升清水。',
            'CL-10：沖煮頭清潔錠，一盒 8 錠，每月逆洗用一錠。',
            'GS-54：矽膠墊圈，54 mm 把手用，建議每年更換。',
            'GS-58：矽膠墊圈，58 mm 把手用，建議每年更換。',
            'SN-4：四孔蒸氣噴頭，可替換原廠的單孔噴頭 SN-1，奶泡更快更細。',
            'BK-20：20 公克雙份濾杯，另售的 BK-14 為 14 公克單份濾杯。',
        ]),
        ('省電與待機', [
            '機器閒置 30 分鐘後自動進入省電待機，按任意鍵即可喚醒。',
            '喚醒後約 40 秒完成預熱，指示燈由閃爍轉為恆亮。',
            '自動待機時間可在設定選單改成 15、30 或 60 分鐘。',
        ]),
        ('設定選單', [
            '同時長按單杯鍵與雙杯鍵 3 秒進入設定選單。',
            '用單杯鍵往下、雙杯鍵往上切換項目，按沖煮鍵確認。',
            '可設定的項目有沖煮溫度、自動待機時間、水質硬度與單杯萃取量。',
            '長按沖煮鍵 10 秒可恢復出廠設定。',
        ]),
        ('App 連線', [
            'LM-500S 與 LM-700 可用「拿鐵大師」App 連線，LM-500 不支援。',
            '首次配對時長按雙杯鍵 5 秒，指示燈快閃即進入配對模式。',
            'App 可以遠端預熱、記錄每杯萃取時間，並在需要除垢時推播提醒。',
        ]),
        ('安全注意事項', [
            '運轉中的沖煮頭與蒸氣管溫度很高，請勿直接觸碰。',
            '請使用 110V 單獨插座，不要與電暖器共用延長線。',
            '兒童須在大人陪同下使用。',
            '長時間不使用時，請倒空水箱與滴水盤並拔掉插頭。',
        ]),
        ('故障碼 E01–E05：水路', [
            'E01：水箱缺水或沒有放好，請加水並確認水箱卡到底。',
            'E02：水泵抽不到水，多半是水路進了空氣，請跑兩次清水循環排氣。',
            'E03：流量計沒有訊號，請取下濾水芯後重開機；仍出現請送修。',
            'E04：水路壓力過高，通常是沖煮頭堵塞，請做一次逆洗。',
            'E05：除垢程序被中斷，請重新長按沖煮鍵 5 秒完成除垢。',
        ]),
        ('故障碼 E06–E10：研磨與沖煮', [
            'E06：豆槽沒有咖啡豆，請補充咖啡豆。',
            'E07：研磨室堵塞，請關機拔插頭，取下豆槽後用附贈的刷子清出卡住的粉塊。',
            'E08：粉渣盒已滿或沒有裝好，請清空後重新裝回。',
            'E09：把手沒有鎖到定位，請重新鎖緊把手。',
            'E10：萃取流速過慢，請把研磨調粗一格後再試。',
        ]),
        ('故障碼 E11–E15：溫度與蒸氣', [
            'E11：溫度感測器異常，請關機 10 分鐘後重開，持續出現請送修。',
            'E12：加熱器過熱保護啟動，請關機冷卻 30 分鐘。',
            'E13：蒸氣壓力過高，請先關閉蒸氣旋鈕，等待 3 分鐘洩壓。',
            'E14：蒸氣管堵塞，請用通針疏通噴孔後空噴 5 秒。',
            'E15：預熱逾時，請確認室溫高於 5°C，並檢查電壓是否為 110V。',
        ]),
        ('故障碼 E16–E20：電子與連線', [
            'E16：主機板通訊錯誤，請拔插頭 1 分鐘後重開，仍出現請送修。',
            'E17：觸控面板沒有回應，請用乾布擦乾面板後重開機。',
            'E18：App 連線失敗，請確認手機與機器連在同一個 2.4GHz Wi-Fi。',
            'E19：韌體更新失敗，請保持連線並重新執行更新，更新中勿拔插頭。',
            'E20：滴水盤沒有裝好，請推到底直到聽見喀一聲。',
        ]),
        ('常見問題', [
            '咖啡變苦：多半是過度萃取，把研磨調粗一格，或把沖煮溫度調低 2°C。',
            '咖啡偏酸、喝起來水水的：多半是萃取不足，把研磨調細一格，或多加 1 公克粉。',
            '奶泡太粗、泡泡很大：噴頭埋得太淺，或鮮奶不夠冰。',
            '沖煮頭周圍漏水：通常是矽膠墊圈老化，或把手沒有鎖緊。',
            '機器完全沒反應：確認電源線兩端插緊、插座有電，再按下機身背面的過熱保護復位鈕。',
        ]),
        ('保固與送修', [
            '本產品自購買日起提供 2 年保固，送修時需出示發票或電子保卡。',
            '人為損壞、摔落，以及未定期除垢造成的水垢堵塞，不在保固範圍內。',
            '送修前請倒空水箱與滴水盤，並用原廠紙箱或同等級的緩衝材包裝。',
            '保固期外的維修收取檢測費 500 元，維修報價經你同意後才會施工。',
        ]),
    ]
    # 考卷：(問題, 題型, 標準答案＝第幾個子塊)；proc＝步驟題 pin＝單點題 kw＝型號／故障碼 para＝換句話說
    QUESTIONS = [
        ('除垢的完整步驟是什麼？', 'proc', [31, 32, 33, 34]),
        ('新機第一次使用前要做哪些準備？', 'proc', [1, 2, 3, 4]),
        ('怎麼打出綿密的奶泡？', 'proc', [22, 23, 24]),
        ('怎麼沖一杯標準的義式濃縮？', 'proc', [10, 11, 12]),
        ('萃取時間不對，要怎麼判斷問題出在哪？', 'proc', [13, 14]),
        ('日常清潔要做哪些事？', 'proc', [35, 36, 37, 38]),
        ('送修要準備什麼？', 'proc', [86, 88]),
        ('手機 App 要怎麼配對？', 'proc', [54, 55]),
        ('奶泡的牛奶要加熱到幾度？', 'pin', [24]),
        ('單份濃縮要放幾公克咖啡粉？', 'pin', [10]),
        ('機器閒置多久會自動待機？', 'pin', [47]),
        ('水質硬度出廠設定是幾級？', 'pin', [4]),
        ('保固期外維修要付多少檢測費？', 'pin', [89]),
        ('研磨刻度可以在停機時調整嗎？', 'pin', [17]),
        ('深焙豆適合用幾度沖煮？', 'pin', [20]),
        ('熱水出水溫度大約幾度？', 'pin', [26]),
        ('螢幕顯示 E07 怎麼辦？', 'kw', [67]),
        ('E05 是什麼意思？', 'kw', [65]),
        ('出現 E13 要怎麼處理？', 'kw', [73]),
        ('E16 錯誤碼代表什麼？', 'kw', [76]),
        ('E11 一直出現怎麼辦？', 'kw', [71]),
        ('E18 怎麼排除？', 'kw', [78]),
        ('E03 需要送修嗎？', 'kw', [63]),
        ('E09 怎麼辦？', 'kw', [69]),
        ('WF-12 多久要換一次？', 'kw', [39]),
        ('WF-21 可以裝在 LM-500 上嗎？', 'kw', [40]),
        ('CL-10 要怎麼用？', 'kw', [42, 37]),
        ('GS-58 適用哪一台？', 'kw', [44, 9]),
        ('DC-300 一包要配多少水？', 'kw', [41, 31]),
        ('LM-700 的水箱多大？', 'kw', [8]),
        ('SN-4 是什麼？', 'kw', [45]),
        ('咖啡喝起來很苦，該怎麼調？', 'para', [81]),
        ('打出來的牛奶都是大泡泡，哪裡做錯了？', 'para', [83]),
        ('插了電卻完全不會動，怎麼辦？', 'para', [85]),
        ('把手旁邊一直滴水是什麼問題？', 'para', [84]),
        ('味道很淡又帶酸，是什麼原因？', 'para', [82]),
        ('早上按下去要等多久才能用？', 'para', [48]),
        ('摔到地上壞掉可以免費修嗎？', 'para', [87]),
        ('除垢做到一半停電了會怎樣？', 'para', [65, 34]),
        ('出國兩個月不在家，機器要怎麼處理？', 'para', [60]),
        ('可以一邊萃取一邊打奶泡嗎？', 'para', [5, 7]),
    ]
    # 真向量：jina-embed (jinaai/jina-embeddings-v5-text-small-retrieval)，1024 維，int8 對稱量化（每向量一個 scale）
    Q_B64 = (
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    )
    Q_SCALES = [0.00086328, 0.000846987, 0.000979713, 0.000873947, 0.00101265, 0.000862807, 0.000977533, 0.00103923, 0.000909901, 0.00087732, 0.000870308, 0.00113795, 0.00124622, 0.000942253, 0.00100843, 0.00106013, 0.00121509, 0.0011294, 0.000904188, 0.00110584, 0.000972158, 0.00110733, 0.00103876, 0.00110035, 0.000966678, 0.000878684, 0.00098774, 0.000832259, 0.0010385, 0.000938085, 0.000959409, 0.000934178, 0.00113092, 0.000985519, 0.00109702, 0.00140182, 0.00110718, 0.00108778, 0.00129006, 0.000869695, 0.000806455]
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        "C90e6+D19fsSBAoI7Bv9HwwLJPAWDjTf7jv3+APbExL1GjMHABzlAwbm9zAK+czr+Rb0J+8W4hcPHgAi6drEB/Dz6PD+++fW"
        "8h/T/N8XCgQDGC4K/QAG+/gb3SLiLBzg7BjJ+gr14+386BP06P4KJxDsDPn/EvZACAvo/RYUCPffGAHj4Pv5Hy/y+SEc/gL6"
        "6RwUDvQLCCL5LPAg1/D29hII+vEQ6vQdGAnW+QT5FQcACBQB+83YBg0E0vnqBicgN+8T2Rb55QkCBR36+R0qEw3nART1/OT9"
        "+wH7/Qf1/ffmBf0I+w3hA/EPDgoP4fb3EQcE/M8kKSfnGv8X/vX/8gveCOzjuOIUNCPwDgYPAR7A5fz4/v/+HxD+8wf9/RgI"
        "CPfbQALo78oT/O3T99v96Q/tB/r3AxYg5v8V9gEF7QslBEPwGR8H+wjx7u76ExLrHQXiAgYOEPYF/uP59eolCA/kAw/15CXi"
    )
    C_SCALES = [0.00109466, 0.000864467, 0.000923477, 0.00136707, 0.00100419, 0.00106592, 0.00100476, 0.000848935, 0.000928687, 0.000932456, 0.000855341, 0.00172954, 0.00106816, 0.0013869, 0.00124128, 0.00112955, 0.00119738, 0.00104737, 0.000960886, 0.00119709, 0.00103849, 0.00109269, 0.00099696, 0.00129837, 0.00103706, 0.00132364, 0.000982643, 0.00111492, 0.000924257, 0.000811916, 0.00114605, 0.00104634, 0.00107372, 0.00117515, 0.0013583, 0.00106941, 0.00129486, 0.00116316, 0.00102857, 0.00086004, 0.000934975, 0.00101153, 0.00132545, 0.00104272, 0.00109493, 0.0009702, 0.000964792, 0.00107311, 0.00117587, 0.000998218, 0.00104274, 0.00116604, 0.000979923, 0.00134781, 0.000910829, 0.00104758, 0.00106048, 0.00113391, 0.00110161, 0.00149883, 0.000975586, 0.00121653, 0.00106594, 0.00128147, 0.00115967, 0.00139934, 0.00117531, 0.000984227, 0.00112544, 0.00127517, 0.00104557, 0.00132123, 0.00117018, 0.00132121, 0.00150295, 0.00112086, 0.00127951, 0.00126854, 0.00126803, 0.00127703, 0.00135943, 0.000882622, 0.00101694, 0.00100551, 0.00105304, 0.001134, 0.00122589, 0.00134344, 0.00122964, 0.00124437]
    # 預先算好的相似度矩陣（int16，÷10000）：子塊前面加上章節標題再算向量的版本、固定大小切塊的版本
    HDR_B64 = (
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        "2xP8E8gSnAtOCzoUhhBBCjYKmgeHCuwFAwj2A6sKlAyICugMegRfB08O7ApFB3sHCw7PCZoKrwrWDagSjwoADssN2gxdDXEH"
        "igjtCRAKGQilBt8IaAXEB/oJZQnuB10Hegw2CmoI0BETDi8KBBITFSERcxLiD1MHIgwTCOYIygdgBYgHFgheB5kHkAiJC40M"
        "ggmbBrcDbgMKCh0NKQkjDhsGgQ0PC/gJWgtbDrIM/Q27Do0Kggy6C3ASxArjCq8L/wl5Cm8KJwkJCEIL6wzeCKUKMwvrCGAM"
        "YgfeDJYKfgoNC+0KRBCUC+wJjQpZC64Kcgh9CpILuAosCjEIqgiECcwJ9QpqCb4KWAnJCaQKpQTPBK4HDghaDoAKhAoJE20J"
        "vwuQC6YSRA/jCxAPhhKmEOIGNwUXDqEOTREoDjkP2gd9DogKaQz2CAAKdQpPGJ0YTxfPFcMJOwv7DzMH9QUjC30MQQt7C+4I"
        "CQriDQILwwedBwEIjglAB54G4Q+DCl4IlwiVBlwQ/RJeDisLmgzzCTcMvAs+CFkG0AnmB+0I7QeCCyYKxgyeDdgLMAu0DbsG"
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        "uQ0DDgsOmA/YEhsR2RAEDlcKngqUE7sJZgkPDXcOXw0/DBELkg5AEXELZAl4CdYJlQwqBtcFPAtBDZoISQoKB1wPSRWbElQL"
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        "8wo0CEILmgkiCZkLyAncCxsLbwjuBi0HGwnpBloHYAcQB3sKHAWfB+AIqge/CBcHUgtHDN0KtwytC7MLkgqFC2wMzQsnC/IK"
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        "twXNBP4D1wP6BCYGGgalBiYFvQa/BAAEtARdBdcHvgbZB9gDQQWVBzEJigP+A3EE1QRpBmQGygRAA0gJHgfQCFYPWAutBrcN"
        "zQ9MGeURKgWtBUkHpwSMBSoFYQZcBSgGpwR9BdMFjwlsBnIGpgUHBmgGsQXwBvQIpxArCvQHIANPA84CWQXPB7MFYQTYBVQE"
        "DQpVCt4OtAuXC+IPyhPYDwAIcwTyC1EMqQ9iDUsOSwdPDJYI6QdVFfIUxBCYHmUYYR9dFNUSEQ6QFDcHAgctCA0M4Qf2CJgG"
        "lAmXC+cHBwYsBmcG/wbnBH4E1Qy3CM8HFA18B5wLtQ8oELkJDAtDCe8LqRImDVsHXQk1B68G7AaRCoAKpgo3C6UKZQlpC0IN"
        "6Q+NDr8NoQ8UBhEH5waoBvcG9g4KC5sUNwnVCTwFRQaeBiEGTAzPCTwUXQhxC48NfQx4DG0IkwWWINgW+hfzE3ITNg3oFU4M"
        "7At0DL0O0wrmD80L6gzmCAMIoQdDEasIigchDGkLhgiLCIwIgQk8DcwFYgkdCV8MuQvIBiYHrgl5EFoH6wgXB/YMAxEID5gH"
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        "nQm7CiMKqAtkCHUIGw29CIIIkwb/ArwEcAtXB2AK2wqNB40Nkg0DCFQF9AJNBzcKignqCTsIjAiTBekLGgzlBtIQywjmC+YI"
        "zAd0CfYOpAmuCQUIcQexCAUIzQVMBeAc6BPhGqwMsQgUDZsP9gY5DMwLYAiOCWYG4xGWCuEJSAo1CjoLGQnsC1cLewtfCsEM"
        "MA6kDPkKvAw0C/8LDApmCuIKZgQvAw0FmAdMEl0L1Am+CMUI4AuHDRYNvQhmIcYFsAcWBewKsAX7Bk8J9wogC9sLaw17EHsN"
        "FAwmDuAKxAv5CN8IGgkhCF0QhArlDHQNSQ86DiQMrgy/DY4JHwrfCT8Kjw0/DUsMfgsLCqQJtAiaCSsFogezB9oJ2goZE1cN"
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        "5wgAGB0UIRMLEJcOfhP2C20gIBbUF0EMAg7DDOYNDgzVDKMJ9wtVCYQKDwxdDEYKPgjTBdMFOQluCOsGbQtXB44IhQwHElAK"
        "yQbeBi0N9hPYDYcFgw2LDZQO4w2MEHwP5Af1CRAKgQlWC3kQPhJZEVYRABLCBqAH/Qe0B3EL6AzwC8wJuAyqCu0GZQw5CRQJ"
        "ZQjIB24IwQlRCucHLAqICz8KgQm1AvQFsQXkB/MIUAUECIIJOAvHB5wFJAZ/B9sJuwcQC3cIFAjtBTcHOg1oCMoLUAmhDXsI"
        "8AfbB04MjAcfCRwI6QfHCFcIDQkQBkkN4A3jCtANXA2gCYMRJwv1CRIL4AmAC/AF4QjCEl4QJBIcEusSjhD7EgcToRK1EbcS"
        "EhEMEdIRwBG6ERUW+xAYElkRhgfKBtoIiQpJEo8KXArrCHgJxgYrBisGfQRFCPALJwvZBVcKuwwUAxIFXwUeBrgHiQVZChIE"
        "3QUpBNEDCgSMA6kDFQP6A3IFBgQOBloEpgW5BBQHRwSwBYwDrAR0BNsFtQlKBbYG5AZXCi8KSgXMBVMHzAdVB5gGhwYqBmMH"
        "dQoJCKkFUwS8B/MEugR7FbAS1xIBE0YUyw2uDRMPZg+RDvEPAQ9IDgoPphDsDaAOJw66DgkO4gPkA+0CyATwB3gGtwVfBlIJ"
        "rQpGCTAJNwuGCpUDYQVBBIIEaARqBMEGaQc3BoUI1wUlB8QHPQkEBSYEIwRsBWcI3wWOCvIGlgccBT4I4AoXDLYK+grkCykJ"
        "SwmnCSkKSQgnCCQLWApnCGQI8AZ/BhELTAkcCLcK8AkqB9gMqARjBxIJEQn9CfQImQpQDxANbQ5OD3YP4gv3DWQOPg/fDd0Q"
        "FBHNEx0R1A/HDaEQtA1JD38O/QSCBD8G4gm5C60IrwkVClsHvAU7BI0FBgZwBzsG3wawBBYGGAVrBTQFRga7CHAJJAbLBmQG"
        "0gnRBpwEvARlBkYFIwdRBtkFtwWHA/4E7ge1BJUH/APbBesDlwN3BDUFCQbsBZQG6wgBB2MGuAhgBp8HxwgzCGgHVAjMBYUJ"
        "NwWYCLEF8QbGCY0FQwZOFtkS2ROBFREVMhRDFCQWZRauFYUW/BWrFikXChfqGrkZHBpFGlYYRAaYBVEHbQnhCj8JAgp/B5EI"
        "SQfPBh8JTQldCTAG0QclBl4FUwWYBH0GGQdnCBQKDwaqCI8ItAtrBw4F6wRXB3oIGQfkCe8HzwamBfMGyQvyBqEJUgi1CoAI"
        "MQj7CNsJlgi+COAGmAqiCE4IxwdRBYIMuAx+C7ILmAviCLkOUAcsCn4Kbgm7D7kG/AmAFIYSPBMyFKYTIRE/EoETRRPgEgEb"
        "qxg7GBoY3hgdFI0VVxRbFWATKggjCPwJVAz2EL0J6Qg/COAHAgkBCJgJ9Ap5CTUFTAbEBQEH7QWaCIUH4QcNCBIJiQR4CIAG"
        "BQo5BoYGWQelBzIJfgY2DNgHHwjvBx0I5gpMC8sKNAtMDNwIAwhzCGcKPQefB0kJAQkICEkMuAaYB+4HSgi2BmMI0AnQBykJ"
        "2gV4Bq4JSAl5CuAIzwvlD1gPBQ5eEP4PIwwKDnoOfg0jDvsPMRAMEYoReRBkDlcQphEeEMEPqwjPCOwHEgpKCgUGvwgjCQwH"
        "XQuyCIMIKAhACQEH/wc7Bi4IQgdWAf0CgQR0Bu4H3QXlBqMILAmqAyMEKwO4A+wEdQQ8B+gEDQeVA2ILzQrNChMJYwkbC3AH"
        "UAivBScKQgvqCkEOFQn3CioKcAgmBZ0JUwj6BtkFVwVYBVoJVAYxBYQGPgbnCIcGFAqrE7AQ9hMQEuERGhCIEIIRaBEIELIP"
        "Dg6wDvANIg4VEawP1QykD+wPWQUaBYwEuwlZCzUSoBFoEtsRpQasBhcJ5gdbCasF+AZfBiAF7gVTBGgGoga/Bk4HBgRvCCIH"
        "iQebCHsG0QSnBcoG+AQxCWoGqQWoBYQG5AeBCFwJXQgQCh0HUAfyBysIOgYhBi4IkAfbB9UHcAbbBW8KMQntCO8JDAq9B8YM"
        "fwcYB2YI9gaMCE8FggdNEZIPxg+kEIIRXw/ED7IQmRNrEGgOhg2/DRgOXA2dDSsQEQ7hEKMOXAYdBuYF1weHCi8HOwjOB70H"
        "2QkODcsKkwr7CkAF4QerBDMIpwWhA3cDpwc9BksHzAdCCZ8HQAd3BoMCTQJPBroIdAUzCgkGzwkeB3wRwQyPCn4K+AljC3UK"
        "gwsUC0IM7BjAGG8L4gsYDJ0LMAtuCtoIzQiqCjIIFQiJBgIK4AIlCdsGrQb1CNQGWA1jCnIKiguzCqgJjQZHB9sIxggMCGIK"
        "Bgv8CU4KpwkCB8YIKwhSCYMJJwQCBMgFnAfhBg8PDwwEDFYKkwncB+4GiQV0BisSpxCsDZwRyRIKBKEEuwSdBZgEewdqBn4F"
        "uAUrBE0CAwIRBYsGOAQIB7EEQQVZBi8E8wPNBsIHRQZpBtgEoQXHBW4KcRNLE0AICAjgBysHmAe0BwwHKAV4BnsF7AavBmwH"
        "MBE+BiMFYAWwCEkFjQYHC48KrAqYCcEJpwVfBiwHYwdhBpEKYgm0CDsKXgr9B/8ISAnQCGAJ2AHsAtsDXgSyB1sGOwWEB5MG"
        "jgm5CqAK1wvXCnAIaQlLCJsIGQl2Bj0IAQnZB8YI0wfvCdMGbweoBYQE3gSDCKEIPAZTCdEFPAccB4YGGgmNCrkJfgm9CToH"
        "8gmyCzkLKwnVCHMKgBZAB3oGewdLB2YJpQgSCBULawvHB1sMiAnbCbkIWwcqC40JnQl2CDIHVwjVCPAI8wiiCTcKKQvGC7UK"
        "EgpGCm4KFQqxB9IJIQidCHYI4QTEBAEGiQfeCHwG7wXEB7QFaAbXAzoDHQTGBv0IDwmABSsKCw1sBQAElQPaA24EzQRoCEIE"
        "kgQTBDcFVwL+A+wDOgSEBIkGTgVJBlICeQPqA2wFSAOfA1gAvgK7AnUGkgaeBPgFVATDDqEV2gaiBn8EfASdBFkFvgWBBPwE"
        "YQp5BeYDvAPsBTQF5wORB3YGTQb3BqUHTAQRBVcGXgVLBRwGtQWVBX0GWQcKBTUGkAiIBnMEfgLDAjQDPAP+Bp0E6wNaA0kE"
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        "VQa4B7AGUQZmBJUEwgRCBK8FYxCVD9UREQcYBsUDZgSDBVUD"
    )
    WIN_SIZES = [60, 150, 300, 600]
    WINDOWS = {
        60: [[0, 1], [2], [3], [4], [5, 6], [7], [8, 9], [10], [11, 12], [13, 14], [15], [16, 17, 18], [19, 20], [21, 22], [23, 24], [25, 26], [27, 28], [29], [30], [31, 32, 33], [34, 35, 36], [37, 38], [39], [40], [41, 42], [43, 44, 45], [46], [47, 48], [49], [50], [51, 52], [53, 54], [55], [56, 57], [58, 59], [60, 61, 62], [63, 64], [65, 66], [67], [68, 69], [70, 71, 72], [73, 74, 75], [76, 77], [78, 79], [80, 81], [82, 83], [84, 85], [86, 87], [88, 89], [90, 91], [92, 93], [94, 95], [96], [97, 98], [99, 100], [101], [102, 103], [104, 105], [106], [107], [108], [109]],
        150: [[0, 1, 2, 3, 4], [5, 6, 7, 8, 9], [10, 11, 12, 13], [14, 15, 16, 17, 18, 19], [20, 21, 22, 23, 24], [25, 26, 27, 28, 29], [30, 31, 32, 33, 34, 35, 36], [37, 38, 39, 40], [41, 42, 43, 44, 45], [46, 47, 48, 49], [50, 51, 52, 53], [54, 55, 56, 57, 58], [59, 60, 61, 62, 63, 64], [65, 66, 67, 68, 69, 70], [71, 72, 73, 74, 75, 76], [77, 78, 79, 80, 81], [82, 83, 84, 85, 86, 87], [88, 89, 90, 91, 92], [93, 94, 95, 96, 97], [98, 99, 100, 101, 102], [103, 104, 105, 106, 107], [108, 109]],
        300: [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32], [33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [45, 46, 47, 48, 49, 50, 51, 52, 53], [54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66], [67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78], [79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89], [90, 91, 92, 93, 94, 95, 96, 97, 98, 99], [100, 101, 102, 103, 104, 105, 106, 107, 108, 109]],
        600: [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], [45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66], [67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89], [90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109]],
    }
    WIN_B64 = {
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            "2RGPEXkS2BNWGQwJPwyhCCkI3gjsBe0HUwoHB5QIKQmMCGUJ7QmfC7sK2guuE2MQZBL/F/8UvgsfDwgJ4wkpCDUIugfSCYEI"
            "wgojCvoJ1AhjCZAMpAhzCW8Ozg1jDukQzA+OC7kKJwl2Ct0IuQWxBeAH1gQpB1QMVgqICpcMGQp2Bk0JvQ8tEQcP7A+zEIwI"
            "CQ9zE3EIqQjHBT0GRwmTBr0HjwhSCDkHdAe4CeEIrwrGDpsOzw9cDlcPuAlcCpkIBwtRCJ0GtwgeCLUEUgmTEEQN8xWUGC0P"
            "zgkxCKEKLAu2BkkNwAkhB0sLzA2dCPwPqw+MBrgG0gNNBxIH0wZqEC0Rago5BgwPGApsCAgHagk3CXMFzAdaCE4LaQqqCQUJ"
            "8AhuBiQJXArfCd8KZQ0RCpYJIAyOCvoHLggEDPcIngZdCc8HDQUFCTEJ8QQqBlIFGQYYBJwCqQVEB7cPLwQ+B8YGtAQ6BUcG"
            "MAcZAy4GCwOLFV0N7hBJDOkLpQoKDOoQ/AvOCowQrQuTCyYK8QvNC18KlwhbAxoLvgl2DPENkRS6HEUJUwlVB7MKPQ7LDBwP"
            "4BFiCoAJFhAtDDMMOgm6CKIESwndCy4PdgLwBKICHwOJBJ0ESwTFAgoDuAMHBHUNWwT4BNcEIgWDA/oF3wYUAhgG1gNvEesR"
            "RxGMEX8VshVnD8wMEAxJDLoL2Q19EgUS8gk7DgQUIgvdB1AfzgwgCEkN2BHJC+0Lag6qESEUagqGC7YKDQpED20LvAxgD58Q"
            "rQ/4DkMK5ROQD6QI1AsLCfcFcQkYCuwFMAthDHQMwwpFCpcNhQplC+QTmxHtD0YSRRJcC9EUCQwPDH8LcwthCtULEwdtDDAO"
            "sA5nDkoPBg6vCsILbhBcE8oOIA8VDBQRjBQ+DzgG5AcNBgYGMQhZCpwGIgjOBaEH4gc5ByoHkwcKCXsKygm1CZYJ3xMDC94G"
            "Aw2jCfUHCQ9ZCncIBwtfDn8KTgsYC0kOXxLoDZoJhAiOB7UKfAfNBRkJKwi0BSQGHwR3BW0GswPiBZgI9Ai9CAIKXwmnBBEI"
            "vwnCC3kJHwq2DGwIVw+nFCAQagzYCBQNrA+OCrgQ9BX7FGIQhw8pEM8NGA4cEgkTJw/bEmUOrwwtFEEOzA5oCy0I1gtSDL4H"
            "Mw0CEP8OdQ/kDTQPjQzLDssOEA3BC4APgg4ZCE8QSg+6ETEUVw6ZFGwS2RSRE7UL+wsMDMcJcBBaE1cSoQpLDCgRkQl/BWMS"
            "WQmdBQ=="
        ),
        300: (
            "og9ICjsMkRaHEqwLmQoPD/kM3AxXERwKeAsCDoMNwQ18DF0K0A3LCpEUyxCsFr4PDAzCFLgQBBHxDAEUWBXHGeAVthFlDyYU"
            "9RG8E2ALHBVtDfEPPRB6D2kLUw5aEKkSkxJ2EuYKJAbJBsQPTRIlCA0HgAlsCbwGNQn3Bg0IFQrZCo8JqwoOC18OsQxvBw4G"
            "fAYhBjMFxwygDTAG7w09BZUSQQ4bG3IRmAr6EdMQFRAmDVISxBLFGdkS3w1pDIoRxA6wEfYHZhO0Cx8LOgz1DBULLRF3DHoL"
            "xQ45CwwQCQ0TDsoPBQ1+DWUK9wthC2AMIgjcB6MIKw2mC7QJfAs7DEoP7A46DDMPMxQhC30L3w+jDFkPDw3NDOQSjhPZGQoR"
            "/g0VEWEPfROYCswSSw/nDLUU/hfYDIsNKA8QEPAO+w0UCzIJowrQCoMIsgxMEJAQ7hQ6DOwJ5gg1BY8FfgbrCCwP8gtoDEcG"
            "5AirBqAH+woVCgoKLQutDUESngitBVkGZgdEBn0FmwhGDgsS2RYrCu4HWweWCfUITAncCyUPYhG5FeQLvQiBCO0I0gqfCLML"
            "vwvMDegPCwoGCmMGfwddCrIKjAjjDe0OIBHSDLcI0wZyCMUIXweFCqsMIA4PDxQJfwlnCMUH8gxBFU4MdQjGCOsLxQnnDq4N"
            "mQZ9BjYOPwlwEVUHFgk0BnILnAoBCJ8JPws8CuwKpAhtCikHiAfpB5gF5wSNBbIMzwhNBb0GDwU8E1YPFAzyD2QMdAtGDZYL"
            "bAiRClIUjBfrCTIOOQ3pCbkUMgpwCCEKKAPoAogEwQInBL8KMAVCBeUGhAOXEmkTjBWrD+EMvxEFEYIULwvIHNMPIww5E20N"
            "hwr9DmcPyBBmD4gUMwqgB6sK9wuKCl4MoQ6ODy4Uxg5ACx4M7Qu5Dx8OZQ0TEBsRlBIlEK8GZwajCJsGuwebB4sJuAkNC/IP"
            "TgyNDPAJ6QvSCjMPswoVCTUKMQeEBXUEHQagB9EIxQdBCZ0KrQwDDkkOIAscD+UTkRAID7cOJRJsEgIQdg2VCgYM1Q6LDnwO"
            "jg28DCEQug2CFPsRMBYPDw8LTBTfEM4QsgmIEw=="
        ),
        600: (
            "MA4oEhEQIwxaDWUPfw2lDuILiAzXFMoVHBLoENgSfBnEFR4U3BIeFAoP6RCGDbIQgxOTCfcLoA7yB3IIXQihCSsKwwolDl8H"
            "pAbLCPwLSQnUEX4Y1w+nENUQFBfAEjoQZBCXEcwLIg4BEPMLbQ2AD8MO7w1aClsM9QdOC9IKiQuED3cOYhN7DsQNyg13FCoZ"
            "QBEnEZoRNA4WFEsOyA6kDmUKUwsnCw0Q2RCqCccFkAfKDg0KOwigCZ0KjwuDDvoFLgfFBhYP0hHkB64JSAtvD3wRlQhVCrIJ"
            "MgzjDcAIJgr2CccNLBBPCEYJbwmqDN4MIQliCs4SIAijC18OTAcIDvoQ2AeGCyYJIgzJCvgImQe0BSUHfwicBTgSJA8iDb4M"
            "3QpLFH4LrwyWE88JLQMzBO4F1QQPBS4UnxUgEXESbhhVDygSuQ12D+USRQmLC4EMIg67EIsL6gwoDq8PFxL3Bm4Iigh6CQsO"
            "+AzQChcOagpeCd0EeAcfCH8Jjw00DccSwxCcD1ER+QwGD+wPKg1hD0IVxBWMES8RsBE="
        ),
    }
    # cross-encoder（BAAI/bge-reranker-v2-m3）對「每題 × 每個子塊」的實測分數（logit，int16 ÷1000），CPU 上事先算好
    CE_B64 = (
        "6Ood5JPYeeWs1ujU79Tt1N/U3NT+1tjjVuPp1OXUqNcF2rTWbtbh1OnU5tTi1DXjItZ35uvUCtYP1RPwlO0n9+T/2f3a/e3l"
        "+em75wrk5dQ/1Vvn6dbh1OHU79Th1OTUM9Xh1OjU8tS82zTV5NT91NDm5tT31N/UCtdJ1dzU6NSP1ab17NRO4xDX8NQB1eXU"
        "7NT21LvW3NTn1PHUBNXr1ObU9dTc1OTUGNXo1C3VmOd+3FHV3thk/EbfYtfx12LWz9iE1UrVBNXf1F3cAdnr1BTV99T41H7W"
        "4NR71unU4NRL1cTek9m33zLYvdnm1AjV6NRG19HZ/NoT2a/eotUE253n7tQF1drU2tTh1OLU7NTd1B3Va9vm1OLU7dQA2/zU"
        "5tSx3OnUUNUP1avWj90M3dvU3dTs1O7U7tRS2+vU9tQJ1e7UANXq1OXU8ODe1PfU8NTl1DzV39Td1PfU5dQE30rb4NTO5ePU"
        "3tQx21DbRtxC2PHfqe+t5+TU7tQb4wfktuQk14XVH9Xm1LvVSdX71OrU+9SD1+Lqq+QX5QTe7NS41eTU+dSP2zjl2Nbp1OLU"
        "utow18jV69Th1N3U3tT31PbU3uvm1OjU6NT81O3U7Njn1FrY6tSm1/bU9tQJ1dvU6dTp1B/VANXk1KfV6tTC1+PUAdXj1APV"
        "5dTq1ODU4dQM1enUHdUY1ebUvdY+1XDi6tTl1ODU49Tn1P7U8NQZ2BHhDdx31TnXnNsu2rPWy9Wf7XDaNexd1+LU59St5ujU"
        "9tS/4NPZWtdD2BHgnN/j2AjYRNcd5OjU69SR2SLleNvp1OvUitpr5VTXK9Uy1W7WH9zt1O3UfdW32vjU6NTs1PPVEOMj3jHf"
        "79SY20jXptX21O3U8NTq1OvU59TI1T/Z9NQr1enUCdWQ1gPV7NT+1FLVH9X/1PXUGdUI1aPYNd4n2uPUi9Xk1OLU69T61OrU"
        "4tTB2UHVVtg52HzVCdWS3PjU8tSS2vHYB/jM8s3tM9Uy4NjeTObd1S3XjOMR1WrYM9rl1OvU79Qb2RTb59vG1Yvf89Q71jfW"
        "6NR11d3U8tVN1RXVHtXw1PDU9dSh1xDVFtXB2NHXpuVI3x3k7tRa3rTl59Tp1N/UadXt3JDXh9je1zHiuNXb2+7XP9lr8hnY"
        "7dRl1qzVPuRZ1s/VWtXy1PTez+MZ6Bfbt9dS2eXULdWe1e3U/9SQ1QLc/9Xh1OPU7NTa1OzU/dTc1N3U+9Te1PzU3NTn1N3U"
        "7NT+1PXU79Tp1BnV69RL397U9tTt1ALVJtYN1aHV+tzp1r/sBeOY5d7n4tTg1GfVwdje1N3U2tTk1N/U69Tv1APV39QE1enU"
        "C9X81JDW4tT/1N7UTN7l1NnU5tRb1YPV79Te1eDUA9X11OXU+tTt1N3U69Tv1OnUDdXx1NvUBtXf1N3U4dQD1d7UuNde1dzU"
        "l99R5xbdsdYS1ebU6NTi1OXU5NQD1qPixdrj1OfU3tT11LHa4NTs1F/VDtWa3JPaAtWm1+bUxNeM1jTWENVA4gLYOd2f3eLg"
        "gd3h34DY5dQS1SrYDtXl1OfU7dTe1OfUdNbl1ObU5tQr1e7U6NRC1ajV6dTp1PfU0NoB3ODUXOKW1V/VotWr3ArV69Rh1fTc"
        "7tTr1IHVYNwd4fzU6dRh1ezdU9X31ujUBtWw1av9idiGB3Pi89QD1eXUAtXm1P7U6NTx1PnU5NTc1NzU39Qa1RPV8NTi1ODU"
        "3dT11AfVBdUT1e/UC9X01PnU8dQF1e/UA9Xj1N3UA9Xf1OLUDNXz1PjU9NTi1P7U9dTq1OTU3tTx1ODU6tTm1OjU6tTf1OjU"
        "rNZm7ZHXBtXn1OfU89Ts1BbV7NQU1evU9NTc1PbU89QM1efUE9UM1QPV49To1OrUdOTp1ObUAtXu1CDVAtXr1ODU6dTi1NvU"
        "39TA1YzV/9Yk4UDlgezW6ILVTdXl1uDUuepF1iXV4NR71eLU4tSD/rDwMufP8uHkhgbI2ILsHdWn3+DU7dTh1DPg5dTh1OPU"
        "UtVH2RfV4tQI1dzU7dTk1OTU39oc2uHUKt5N2+XU/t5C3gHi49QD1pPX7NbG1eLU49Tf1NzU5dTl1CzZ6dTk1ODU5tTg1OLU"
        "bt/i1OLU5+vo1PHU+NTt1ObUmN7s1GjlINXs1O7U69Th1OHU5dRN1Vfd5NRp1TLVIdV918nbmds2GrPpYO6a4JrX6dRP5OXU"
        "fNd32BzXzdnh1KXW9tTd1NzU59Rk2ebU59Tp1LjV39Ti1ODV7dRs193U7dVU1u3WF9jj1OPU9dTS7uHU5NQL1f3WxtnP2P/U"
        "7NSG19vV3tTv1OTU5tTd1OjU5tTi1FbWhtjf1qzV89Sy1vDU6NTg1N7UXdX31PfUBtUA1WvV39pE9+nU49Tk1D3V7dTm1N3U"
        "3NSD1eHU39fn1HPVFNf21PHU6NT/1P7UUOI417nW+dTr1HPVr+Ll1P3U8NQD1cnVcNXt1OjU7dQC1YThNNbh1ITk4NQK1efU"
        "+9Ql1erUAtnS2d3U39Tt1O3U39T01GURSeVPAhTV69Tk2cTd69TC3ujU5tTl1OPUbtb11N7U+9Xo1KrZ/tRn1urU7NTo1Bre"
        "TNzf103Vydb61/7U8NTt1OXU8dQE1RbV4NTK5hrb+dTh1ObUtdYo1eLUCdUlFGrW99Qu1Zva3tqu1bvVUOJF147ZQNg821PW"
        "G9a94qPjpdsp1QfVTdrf1HPcFNUY1RHdL95D1dva6NQO1QTV5NQF1ezUy9vW2oraVta61oXWDNdu3enU/NQ72BPWV9W87d7k"
        "+NQi1jTV6dTo1NzU5tRL2ezWM9V63m/c5NT73VDV5tSg3CDVVtcD2RLVdNzi1OzU79Ts1KvWc9aI1eDUPNXi1BLYrd271wTV"
        "4tTd1PHU4dTo1ODU59Th1OHU4dTc1PrU29T71O7U3NT+1N3U3dTd1AHV7NT+1OLU9tTu1OPU5dQI1dba59Tj1N/U49Tg1ODU"
        "+dTc1N7ULtW21eDU39T51PnU4tTn1OPU4tTp1P7U3NTm1OXU5NTi1ODU5dTk1NzU6dTw1NzU6NTm1ObU5NTt1ObU5NTi1IPV"
        "6dTi1OHUjtXu1OTU4dTl1OTUBtX61P7U39Tn1HvkLuAJ1RAY+NQF1d7UHNUq2ozV7tTv1ezUjNbg1HTVQtw54MvbTeCV3jMQ"
        "sv6h3pLb7tTn1OLU+dTe1OHU5NTh1C3e6NTn1GXb4tT52P7V49Qh1RfVQdWL1efU59Rh1UPV6tTv1FrebdUg7VrVX9vl5/He"
        "4dV91jje69Tv1N3UJdXc1NvU59Tt1A3b8tQY5OPU6tTf4IDVU9Ua1eDUytjl1OzU/9Tr1OTUVdaP1RLV4tRp163XfdU71RvV"
        "EtWT2XLaU9kY5SPbzd772aze8N4v4jLV+Oj45KLbot9e3CDgxtdi+vQUGuWu3nraFOv81Drt9ddW6ejU4tTc1Xvm4Nbk1OnU"
        "791L3YPWbddS2TjWb9nh1ODUINWp3+DUeNcy3gDVo+G63t7h6NTV1m/VPN6S1eXU/tTh1NvU3dT51xDfftWk2+PU3dSB1+LU"
        "Yt6Q1eDUMejk1OfU9dTq1FHVI+uO1d3Uptbw1JzV3dTl1N7UbtVu1jfV5NRH3e3U29UV1Tfc8dTe1OPUPuHj1OLU4dTx1OrU"
        "4dSe+iblntej1YLVKOjf1EIRmuZk5PfUC9VH1W7Y8dT51N/U39Ti1OPUB9Y01/fU4NTp1OjU4dRL1eTUO9Xl1OfUQNZM3O/U"
        "69Tj1DTVA9Xn1NzU8tQl1XjV39Q41ebU/9Tf1PLU7dTe1OfUKdXj1ODUqePm1PLUDNX/1BrV2djk1N7Uddbm1OLU4dSA1d/U"
        "39T+1OjU/9QQ2OfU3tTk1OnU7tTp1OvU5dQL1pbX4NTl1OrUBtXe1PfUBNX71ODU4tT61NvUBtUN1eXUKdnu1PjZ5NRV3+3U"
        "49Ty1CLX6NTs1N7U4dTq1OrU7tTk1E/c+9kV1f/UENro1NHh8NRG2enU7tTn1N/UY9Wh2rDcNd+S24vaQNW2AVbjkNxr2G/g"
        "cNob3RHc9drH453oqtqg2xzX3tTe1OLU9tXs6hXY7tQB3HPgZNVQ1eXU6tTv1LfY69Qm1e3U69Tn1N7UB9bB3ejfQNWK2hDV"
        "3taR1enUntbe1EDV49Ti1ObUmNXc1OrULuHe1OXV59Qm1fjU4NT01N/UgtVK1ajV3Nhq1VbVqdbn1OTXMdXr1OzU6NQg1ejU"
        "AtVF1f/UbtVd1d/U6tT045zmCuR57RgGNtxT6W/nn+Bs5jXi7uWO4RbjHOug3kjdmNuV2ifgntWO2bbVxNcz1xDVDtbm1OfU"
        "P9Uk34jaFeJ+3PPU79Ts1ObU5NQD3FzYkN0B2A7b6tT31ETWS9xz1e3UH9vr1aTfJd8S4wjVj9U12DXWD+F34d/hmeGX5V7l"
        "k+Bh4OXgONVQ1SnW5dXz1PPUINUH1dLb99jt1PjUCtjv1Djf69S11wDVqN051enUf9yF3uXglOYN4bbfJNYN6mzeHd1e30rk"
        "veGs/5Xlz98g5XDjxNwH2r/ac97K2T/ZU91E7CPWjtsc4DrZ59T21N7U6dQD1fHU5NTs1O3U6tTf1N/UjdUV6EDoA9Xu1PDU"
        "59Xp1OjU4NTl1OHU5dTk1OHU5dTj1O3UFeLk1ArV4dSP1efU99Tn1OXUoNWY1e7UsNWw1fDVINbm1O/VJtXt1PPU79Th1C7V"
        "8dQL1ejU6Nfy1N/U7NQi5EPnZ+Ia5YHg9NzE6SDmB+Mw5SLkAeOC4/Tli+TqAjLl2ORQ4WTgo9Wn1c7WF9vk4PPU4dYb1fDU"
        "4NTj2efUzdY21+XU4dTi1O/U5NT81N7U4tVs1fLh4dTv1AbV3tji1OvUIdXe1IfVVNb/2eLU6NTe1BvVE9ww3X/a0Ni74MDa"
        "dtWk2JnVNtUH1fTUJNbw1O/UTNXh1BTbnNZA1fPUrNXn1B/c89Tr1e3UPtWx2OLUmdlm273fLuhH3Y3c/dQg6IvZ0tl25WgF"
        "X+Ju3gDjAeCI6UTkGNoL2jPae9qS2SrVSd5O7OvULNUO2jXV7tWz4PfUXtnc2frU7NQd1e/U7NSy4GXWd+kV1WHW69Tz1PTU"
        "TtYo1Q3V19vg1PncYti53ufU8tT51PDVs9Y05A7lzd4l4dzcMtfu2iDYCdXh1QPZo9Xt1O/UC9Ug1QvV99Ts1BPV2tgP1Z/V"
        "AdVE193XMNUo1d7U4dUe2rPfjdzW2pjfw9Ub52jZZ9dz3mbajtkJ3WXeCuBZ2A7e8O6h18/bTtcY2vfUl9UI4QTVpdXG1xjV"
        "Rtn01/LUAtVY1fnU6NQH1fXU8tRK1fbU6tol1frUCtUU1XXYBtYA1oXVb9rh1OnV5dQc2OzU7tTi1K7bLtam1djYINaE3Tjg"
        "UdZB1m7VW9Y5117Xr9Zg1k/WNtXq1BTXE9b+1PLU7NQ61fLU89T81HDWYtXq1sDVItWg29DcjgcS37nbKdge4pbaJ9ou3ujt"
        "mNgb1zPdA9tO7onX7dQy1y7aC9YX3fLU1NVg3xX3rOLr6r3j/dXr4bTV1ttr3QrV79RD1erU69SG10za9d7+1P3U7NQ+1UnX"
        "RtsP2afV4dn41CfbpNec4KDZYtX/1dPV59aM3Ongidz75K/ba9vM2snfYtUG1mfV4dny1PPUjtXy1Cnk0dsG1jXWJNko1YDf"
        "BtVj3ufV99XC3OzUYtny3Dvi/OO04OXgANlb7wjtN/us6UfkZOIK4h7i3N/m4azkIN5Z4BjdIdiF3PfUZNXK68TcndYc3HTX"
        "UtZI4SjV7NZs1ZXVqdb91BvVPNX21ObUj+GY11zVstYv2K7YpNXm1ufU69Tj1DzZ/tSC2SHV/9Xn1BDuct731fvlhtYu2d3g"
        "5Nfe5YjVQBLFBULVReM+5K3kaNZZ1abgINwW5DDVG9Xo1x3a/9Qx3BzV9NR11evUq9gN1Y3VCdU91bnZ79R/1u7U79Q81Vfd"
        "NNzM1r3WUdXv1O/U79QX1erU4NTe1ODUr9X61fvqr9iR1mvZlddm5PPU59Q81mv2yO8x3/7t4PKD1THXsNlG1d7U5dbf1JjX"
        "9tdQ1uPU6NXj1OfW3tT61PLU+9V71prW4NRL11vXAtVS2XDY29Qz1gzVCPrYBmvVXtXy1PTU0daX1QXV6tR+1ebU6dTB1ufU"
        "avV61zbVB9mA3O3UidX11N/U29Tl1OPU99QB2KTV4tQw1uDU8tTh1PPUVdXb1N/U59Tj1I3a3NTi1ObUBNV51yvXK9Vf2fPU"
        "1N3P7Rzdh+RR4kjaF9hL3APVqdYX63LokutB1oLV89us2S7jr9/X4OzZ1N6S28fpUOIK6tHkduAC3Z7XcNay4rvtTeja4Afe"
        "XeB36QPmC9pm1/PdCAXH1qLW79dv1rbml9o32tPgouay4bTgTtXo5oHfVuEY50XfH9741ZzWKtXk1tvX8dTy4lvV4NWq4FXW"
        "7dac16Pd+dft1BrV+tSO1YTYMNXy3AnWvtZ/4f3dqtUU5OXU69eD2NvU5tT02XnZJdWc2PbVyePz1N3UKdvg1OHUyNrq1JnW"
        "9NRj2pfW3tTg1HvV3dTq1FfX2dXk1PXU5tQG1crZ6tQr1eDU3tT71HPVnNUG2FzVBNVB36P82tZM1T3aB9VZ1fXU7dQS2PTU"
        "Ytfa1uvU+tRM2QPX9NTz1OPUGdXu1O/U+NRR2uzU9dQ71QDVMdXr1OvUjNX11PbUCdXr1PDU4dTd1ObU6tQ42ZLcUdV31uLU"
        "Q/Xr4snX9tSo2lPXC9hg1bLnqdUh5pTZWegy1d3UQNUV1eHUTdVO2RDVD9Wk1gvi+NTj1wXhiuMs4lrYBdbuELvZztvP11TV"
        "59QT1djVHd663CgXdNn41PzUTNXg4gHV5tT21O3URtY03e3U7tQo2uXUm9Zg1ePUGNac4Z3Z/dRF1enU7tSV1ePU7dQW1enU"
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    # ── DATA END ──
    return (
        CE_B64,
        C_B64,
        C_SCALES,
        HDR_B64,
        QUESTIONS,
        Q_B64,
        Q_SCALES,
        SECTIONS,
        WINDOWS,
        WIN_B64,
        WIN_SIZES,
    )


@app.cell
def _(
    CE_B64,
    C_B64,
    C_SCALES,
    HDR_B64,
    QUESTIONS,
    Q_B64,
    Q_SCALES,
    SECTIONS,
    WIN_B64,
    WIN_SIZES,
    base64,
    np,
):
    # 攤平手冊：單位（unit）＝章節標題行或一句；子塊＝一句；父塊＝一整節
    UNITS, CHILDREN, CHILD_UNIT, CHILD_SEC, SEC_UNITS = [], [], [], [], []
    for _s, (_title, _sents) in enumerate(SECTIONS):
        _ids = [len(UNITS)]
        UNITS.append(f"【{_title}】")
        for _t in _sents:
            CHILD_UNIT.append(len(UNITS))
            CHILD_SEC.append(_s)
            CHILDREN.append(_t)
            _ids.append(len(UNITS))
            UNITS.append(_t)
        SEC_UNITS.append(_ids)
    TITLES = [_t for _t, _ in SECTIONS]
    Q_TEXT = [_q for _q, _, _ in QUESTIONS]
    Q_TYPE = [_ty for _, _ty, _ in QUESTIONS]
    Q_GOLD = [_g for _, _, _g in QUESTIONS]

    def _i8(b64, scales, n):
        _v = np.frombuffer(base64.b64decode(b64), dtype=np.int8).reshape(n, -1)
        _v = _v.astype(np.float32) * np.array(scales, dtype=np.float32)[:, None]
        return _v / np.linalg.norm(_v, axis=1, keepdims=True)

    def _i16(b64, n, scale):
        return np.frombuffer(base64.b64decode(b64), dtype=np.int16).reshape(n, -1).astype(np.float64) / scale

    # 向量檢索的相似度＝問題向量 · 子塊向量（都已單位化，所以內積就是 cosine）——現場算
    DENSE = _i8(Q_B64, Q_SCALES, len(Q_TEXT)) @ _i8(C_B64, C_SCALES, len(CHILDREN)).T
    HDR = _i16(HDR_B64, len(Q_TEXT), 10000)
    WIN_SIM = {_w: _i16(WIN_B64[_w], len(Q_TEXT), 10000) for _w in WIN_SIZES}
    CE = _i16(CE_B64, len(Q_TEXT), 1000)
    return (
        CE,
        CHILDREN,
        CHILD_SEC,
        CHILD_UNIT,
        DENSE,
        HDR,
        Q_GOLD,
        Q_TEXT,
        Q_TYPE,
        SEC_UNITS,
        TITLES,
        UNITS,
        WIN_SIM,
    )


@app.cell
def _(CHILD_SEC, CHILD_UNIT, Q_GOLD, Q_TYPE, SEC_UNITS, UNITS, WINDOWS, np, re):
    # ── 本課全部的檢索零件（跟實測 spike 同一份邏輯）──
    _TOKEN_RE = re.compile(r"[a-z0-9]+(?:[-.][a-z0-9]+)*|[一-鿿]+")
    TYPES = [("proc", "步驟題"), ("pin", "單點題"), ("kw", "型號／故障碼"), ("para", "換句話說")]
    TYPE_NAME = dict(TYPES)

    def tokenize(text):
        """BM25 的切詞：英數整詞（e07、wf-12）＋中文字元 bigram（Lucene CJK 的切法）。"""
        _toks = []
        for _m in _TOKEN_RE.findall(text.lower()):
            if "一" <= _m[0] <= "鿿":
                _toks += [_m] if len(_m) == 1 else [_m[_i : _i + 2] for _i in range(len(_m) - 1)]
            else:
                _toks.append(_m)
        return _toks

    def bm25_fit(docs, k1=1.5, b=0.75):
        _dt = [tokenize(_d) for _d in docs]
        _vocab = {_t: _i for _i, _t in enumerate(sorted({_t for _d in _dt for _t in _d}))}
        _tf = np.zeros((len(docs), len(_vocab)), dtype=np.float32)
        for _i, _d in enumerate(_dt):
            for _t in _d:
                _tf[_i, _vocab[_t]] += 1
        _dl = _tf.sum(1)
        _df = (_tf > 0).sum(0)
        _idf = np.log(1 + (len(docs) - _df + 0.5) / (_df + 0.5))
        _w = _tf / (_tf + k1 * (1 - b + b * _dl[:, None] / _dl.mean()))
        return _vocab, _w, _idf

    def bm25_query(model, query):
        _vocab, _w, _idf = model
        _ids = [_vocab[_t] for _t in tokenize(query) if _t in _vocab]
        if not _ids:
            return np.zeros(_w.shape[0], dtype=np.float32)
        return (_w[:, _ids] * _idf[_ids]).sum(1).astype(np.float32)

    def dense_lists(sim):
        return [[int(_i) for _i in np.argsort(-_row, kind="stable")] for _row in sim]

    def bm25_lists(bm):
        """BM25 只列出「至少命中一個詞」的文件——分數 0 的不算被檢索到。"""
        return [[int(_i) for _i in np.argsort(-_row, kind="stable") if _row[_i] > 0] for _row in bm]

    def rrf_lists(a, b, k=60, wa=1.0, wb=1.0):
        """Reciprocal Rank Fusion：score(d) = Σ w / (k + 名次)；沒出現在某張清單就不拿那一份。"""
        _out = []
        for _la, _lb in zip(a, b):
            _sc = {}
            for _w, _lst in ((wa, _la), (wb, _lb)):
                for _r, _d in enumerate(_lst, 1):
                    _sc[_d] = _sc.get(_d, 0.0) + _w / (k + _r)
            _out.append(sorted(_sc, key=lambda _d, _s=_sc: -_s[_d]))
        return _out

    def rerank_lists(lists, ce, n):
        """第一階段的前 n 名交給 cross-encoder 重排，其餘照原順序接在後面。"""
        return [sorted(_l[:n], key=lambda _d, _q=_qi: -ce[_q][_d]) + _l[n:] for _qi, _l in enumerate(lists)]

    def list_metrics(lists, k=3):
        _rows = []
        for _qi, _lst in enumerate(lists):
            _g = set(Q_GOLD[_qi])
            _r = next((_n for _n, _i in enumerate(_lst, 1) if _i in _g), None)
            _rows.append({"hit1": int(bool(_lst) and _lst[0] in _g), "reck": len(_g & set(_lst[:k])) / len(_g),
                          "mrr": 1.0 / _r if _r else 0.0, "rank": _r})
        return _rows

    def score(lists, k=3):
        """依題型彙總：第一名就對幾題、recall@k、MRR。"""
        _rows = list_metrics(lists, k)
        _out = {}
        for _t in ["proc", "pin", "kw", "para", "all"]:
            _sel = [_r for _r, _qt in zip(_rows, Q_TYPE) if _t == "all" or _qt == _t]
            _out[_t] = {"n": len(_sel), "hit1": sum(_r["hit1"] for _r in _sel),
                        "reck": float(np.mean([_r["reck"] for _r in _sel])),
                        "mrr": float(np.mean([_r["mrr"] for _r in _sel]))}
        return _out, _rows

    def context_units(kind, lst, k, win_size=None):
        """塞進 prompt 的單位：child＝前 k 句；parent＝前 k 句所在的整節（去重）；win＝前 k 個固定大小切塊。"""
        if kind == "child":
            return {CHILD_UNIT[_i] for _i in lst[:k]}
        if kind == "parent":
            return {_u for _i in lst[:k] for _u in SEC_UNITS[CHILD_SEC[_i]]}
        return {_u for _i in lst[:k] for _u in WINDOWS[win_size][_i]}

    def coverage(kind, lists, k, win_size=None):
        """每題：標準答案句有幾成進了 prompt、是否全部進去、prompt 幾個字。"""
        _rows = []
        for _qi, _lst in enumerate(lists):
            _u = context_units(kind, _lst, k, win_size)
            _g = [CHILD_UNIT[_c] for _c in Q_GOLD[_qi]]
            _c = sum(_x in _u for _x in _g) / len(_g)
            _rows.append({"cov": _c, "full": int(_c == 1.0), "chars": sum(len(UNITS[_x]) for _x in _u)})
        _proc = [_r["full"] for _r, _t in zip(_rows, Q_TYPE) if _t == "proc"]
        _single = [_r["full"] for _r, _t in zip(_rows, Q_TYPE) if _t != "proc"]
        return {"proc_full": sum(_proc), "n_proc": len(_proc), "single": sum(_single), "n_single": len(_single),
                "chars": float(np.mean([_r["chars"] for _r in _rows])), "rows": _rows}

    return (
        TYPES,
        TYPE_NAME,
        bm25_fit,
        bm25_lists,
        bm25_query,
        coverage,
        dense_lists,
        rerank_lists,
        rrf_lists,
        score,
        tokenize,
    )


@app.cell
def _(CHILDREN, DENSE, HDR, Q_TEXT, bm25_fit, bm25_lists, bm25_query, dense_lists, np):
    # 三張「第一階段」清單：向量、向量（子塊加章節標題）、BM25
    BM25_MODEL = bm25_fit(CHILDREN)
    BM25 = np.stack([bm25_query(BM25_MODEL, _q) for _q in Q_TEXT])
    L_DENSE = dense_lists(DENSE)
    L_HDR = dense_lists(HDR)
    L_BM25 = bm25_lists(BM25)
    return BM25_MODEL, L_BM25, L_DENSE, L_HDR


@app.cell(hide_code=True)
def _(mo):
    mo.md(
        r"""
    ## 1️⃣ 考卷：41 題，每題都有標準答案

    每一招進階手法都有代價，所以動手前先出考卷。41 題分四型，每題標好「答案在手冊哪幾句」：

    - **步驟題**（8 題）：答案橫跨同一節好幾句，例如「除垢的完整步驟」——少一句就是錯的操作
    - **單點題**（8 題）：答案就一句，例如「單份濃縮放幾公克粉」
    - **型號／故障碼**（15 題）：問題裡有 `E07`、`WF-21` 這種代碼，差一個字就是另一回事
    - **換句話說**（10 題）：使用者的用詞跟手冊不一樣，例如「摔到地上」vs 手冊的「摔落」

    打分用三個指標：**第一名就對**（hit@1：排第一的那句就是標準答案）、
    **recall@3**（標準答案句有幾成進了前 3 名）、**MRR**（第一個對的排第 r 名就得 1/r 分，再平均）。
    選一型，看天真版——只用向量、一句一塊——把每題的答案排在第幾名：
    """
    )
    return


@app.cell
def _(TYPES, mo):
    q_filter = mo.ui.dropdown(
        options={"全部 41 題": "all", **{f"{_n}": _t for _t, _n in TYPES}},
        value="全部 41 題",
        label="看哪一型",
    )
    q_filter
    return (q_filter,)


@app.cell
def _(CHILDREN, L_DENSE, Q_GOLD, Q_TEXT, Q_TYPE, TYPES, TYPE_NAME, mo, q_filter, score):
    _sc, _rows = score(L_DENSE)
    _lines = []
    for _qi, _q in enumerate(Q_TEXT):
        if q_filter.value not in ("all", Q_TYPE[_qi]):
            continue
        _r = _rows[_qi]["rank"]
        _mark = "✅ 第 1 名" if _r == 1 else f"⚠️ 第 {_r} 名"
        _gold = "／".join(CHILDREN[_g][:18] + "…" for _g in Q_GOLD[_qi])
        _lines.append(f"| {_q} | {TYPE_NAME[Q_TYPE[_qi]]} | {_gold} | {_mark} |")
    _table = "\n    ".join(_lines)
    _sum = "\n    ".join(
        f"| {_n} | {_sc[_t]['hit1']}/{_sc[_t]['n']} | {_sc[_t]['reck']:.2f} | {_sc[_t]['mrr']:.2f} |"
        for _t, _n in TYPES + [("all", "**全部**")]
    )
    mo.md(
        f"""
    | 問題 | 題型 | 標準答案句 | 向量檢索把它排第幾 |
    | --- | --- | --- | --- |
    {_table}

    **天真版（向量、一句一塊）的成績單：**

    | 題型 | 第一名就對 | recall@3 | MRR |
    | --- | --- | --- | --- |
    {_sum}

    看起來不差——但「第一名就對」不等於「答案完整」：步驟題的答案有好幾句，
    排第一的那句對了，其他步驟可能根本沒進 prompt。這就是 2️⃣ 要處理的事。
    """
    )
    return


@app.cell(hide_code=True)
def _(mo):
    mo.md(
        r"""
    ## 2️⃣ 父子檢索：用小塊找、用大塊給

    切塊的兩難：**切小**（一句一塊），向量很「尖」、找得準，但步驟題只撈到零碎幾句；
    **切大**（幾百字一塊），步驟湊齊了，但一塊裡混了好幾個主題，向量被稀釋、單點題反而找不準，
    prompt 還一路變胖。**父子檢索**（parent-child／small-to-big）拆開兩件事：
    用**子塊**（一句）去比對，找到之後把它所在的**父塊**（整節）交給模型。

    拉「取前幾名」，比較五種固定大小的切法和父子檢索（★）：
    """
    )
    return


@app.cell
def _(mo):
    pc_k = mo.ui.slider(start=1, stop=5, step=1, value=3, label="取前幾名（top-k）", show_value=True)
    pc_k
    return (pc_k,)


@app.cell
def _(L_DENSE, WIN_SIM, WIN_SIZES, coverage, dense_lists, np, pc_k, plt):
    _k = pc_k.value
    _res = [coverage("child", L_DENSE, _k)] + [
        coverage("win", dense_lists(WIN_SIM[_w]), _k, _w) for _w in WIN_SIZES
    ]
    _pc = coverage("parent", L_DENSE, _k)
    _labels = ["1 sentence"] + [f"{_w} chars" for _w in WIN_SIZES]
    _x = np.arange(len(_labels))
    _xp = len(_labels) + 0.5
    _proc = [_r["proc_full"] / _r["n_proc"] for _r in _res]
    _single = [_r["single"] / _r["n_single"] for _r in _res]
    _fig, (_a1, _a2) = plt.subplots(
        2, 1, figsize=(6.4, 5.6), sharex=True, gridspec_kw={"height_ratios": [3, 2]}
    )
    _a1.plot(_x, _proc, "o-", color="#4C72B0", lw=2, label="multi-step Qs: every step in prompt")
    _a1.plot(_x, _single, "s-", color="#DD8452", lw=2, label="other Qs: answer fully in prompt")
    _a1.scatter([_xp - 0.12], [_pc["proc_full"] / _pc["n_proc"]], marker="*", s=260, color="#4C72B0", zorder=5,
                edgecolor="#1C2B33")
    _a1.scatter([_xp + 0.12], [_pc["single"] / _pc["n_single"]], marker="*", s=260, color="#DD8452", zorder=5,
                edgecolor="#1C2B33")
    _a1.axvline(len(_labels) - 0.25, color="#8A9AA3", ls=":", lw=1)
    _a1.set_ylim(0, 1.08)
    _a1.set_ylabel("share of questions")
    _a1.set_title(f"The chunking dilemma (top-{_k})  -  stars = parent-child")
    _a1.legend(loc="lower right", fontsize=8)
    _a1.grid(alpha=0.3)
    _a2.bar(_x, [_r["chars"] for _r in _res], color="#C9D2D8", edgecolor="#1C2B33")
    _a2.bar([_xp], [_pc["chars"]], color="#55A868", edgecolor="#1C2B33")
    _a2.set_ylabel("avg prompt chars")
    _a2.set_xticks(list(_x) + [_xp])
    _a2.set_xticklabels(_labels + ["parent-\nchild"], fontsize=8)
    _a2.grid(axis="y", alpha=0.3)
    _fig.tight_layout()
    _fig
    return


@app.cell
def _(L_DENSE, WIN_SIM, WIN_SIZES, coverage, dense_lists, mo, pc_k):
    _k = pc_k.value
    _named = [("一句一塊（子塊）", coverage("child", L_DENSE, _k))]
    _named += [(f"固定 {_w} 字", coverage("win", dense_lists(WIN_SIM[_w]), _k, _w)) for _w in WIN_SIZES]
    _named += [("**★ 父子檢索**", coverage("parent", L_DENSE, _k))]
    _rows = "\n    ".join(
        f"| {_n} | {_r['proc_full']}/{_r['n_proc']} | {_r['single']}/{_r['n_single']} | "
        f"{_r['chars']:.0f} 字（≈{_r['chars'] * 1.14:.0f} tokens） |"
        for _n, _r in _named
    )
    mo.md(
        f"""
    **top-{_k} 的實際數字**（步驟題 8 題；其他 33 題的答案只有一兩句）：

    | 切法 | 步驟題：步驟全進 prompt | 其他題：答案全進 prompt | prompt 平均長度 |
    | --- | --- | --- | --- |
    {_rows}

    固定大小的切法只能在「湊齊步驟」和「prompt 變胖、其他題找不準」之間二選一；
    父子檢索用一句一塊去找（找得準），交出去的是整節（步驟齊）。
    token 粗估：中文 1 字 ≈ 1.14 token（主線第 1 課實測的刀工）。
    """
    )
    return


@app.cell(hide_code=True)
def _(mo):
    mo.md(
        r"""
    ## 3️⃣ 混合搜尋：向量＋BM25，用 RRF 融合

    向量檢索懂「意思」，但對 `E07` 這種代碼很鈍——它覺得 `E07` 跟 `E17` 長得差不多。
    **BM25** 是老派的關鍵字檢索：數「問題裡的詞在這句出現幾次、這個詞在全手冊有多稀有」，
    `e07` 只出現在一句裡，所以一命中就排第一。中文沒有空格，這裡用**字元 bigram** 切詞
    （「除垢燈」→「除垢」「垢燈」），英數代碼整個當一個詞。

    兩張排名怎麼合？**RRF（Reciprocal Rank Fusion）**：每張清單的第 r 名得 `w/(k+r)` 分，加總再排。
    只看名次、不看原始分數——因為 cosine 落在 0–1、BM25 可以到十幾，直接相加會被 BM25 綁架。
    拉 BM25 的權重，看哪些題型變好、哪些變差：
    """
    )
    return


@app.cell
def _(mo):
    hy_w = mo.ui.slider(start=0.0, stop=1.0, step=0.05, value=1.0, label="BM25 權重 w（向量固定 1）", show_value=True)
    hy_k = mo.ui.slider(start=1, stop=100, step=1, value=60, label="RRF 的 k", show_value=True)
    mo.hstack([hy_w, hy_k], wrap=True, justify="start", gap=2)
    return hy_k, hy_w


@app.cell
def _(L_BM25, L_DENSE, hy_k, hy_w, rrf_lists):
    L_HYBRID = rrf_lists(L_DENSE, L_BM25, k=hy_k.value, wb=hy_w.value)
    return (L_HYBRID,)


@app.cell
def _(L_BM25, L_DENSE, L_HYBRID, TYPES, np, plt, score):
    _names = ["dense (vector)", "BM25 (keyword)", "hybrid (RRF)"]
    _colors = ["#4C72B0", "#DD8452", "#8172B2"]
    _scores = [score(_l)[0] for _l in (L_DENSE, L_BM25, L_HYBRID)]
    _cats = [_t for _t, _ in TYPES] + ["all"]
    _xt = ["multi-step", "single-fact", "code / part no.", "paraphrase", "ALL 41"]
    _x = np.arange(len(_cats))
    _fig, _ax = plt.subplots(figsize=(6.4, 3.8))
    for _j, (_n, _c, _s) in enumerate(zip(_names, _colors, _scores)):
        _v = [_s[_t]["hit1"] / _s[_t]["n"] for _t in _cats]
        _ax.bar(_x + (_j - 1) * 0.27, _v, width=0.27, color=_c, edgecolor="#1C2B33", label=_n, zorder=3)
    _ax.set_xticks(_x)
    _ax.set_xticklabels(_xt, fontsize=9)
    _ax.set_ylim(0, 1.12)
    _ax.set_ylabel("hit@1 (share of questions)")
    _ax.set_title("Which retriever puts the right sentence first?")
    _ax.legend(fontsize=8, ncol=3, loc="upper center")
    _ax.grid(axis="y", alpha=0.3)
    _fig.tight_layout()
    _fig
    return


@app.cell
def _(L_BM25, L_DENSE, L_HYBRID, Q_TEXT, Q_TYPE, TYPE_NAME, hy_k, hy_w, mo, score):
    _sd, _rd = score(L_DENSE)
    _sb, _rb = score(L_BM25)
    _sh, _rh = score(L_HYBRID)

    def _fmt(r):
        return "—（沒命中任何詞）" if r is None else f"第 {r} 名"

    _chg = []
    for _qi, _q in enumerate(Q_TEXT):
        _a, _b = _rd[_qi]["rank"], _rh[_qi]["rank"]
        if (_a == 1) != (_b == 1):
            _tag = "🟢 救回來" if _b == 1 else "🔴 被拖下水"
            _chg.append(f"| {_tag} | {_q} | {TYPE_NAME[Q_TYPE[_qi]]} | {_fmt(_a)} | {_fmt(_rb[_qi]['rank'])} | {_fmt(_b)} |")
    _tbl = "\n    ".join(_chg) if _chg else "| — | 這組設定跟純向量的第一名完全一樣 | | | | |"
    mo.md(
        f"""
    **目前設定（w={hy_w.value:.2f}、k={hy_k.value}）**：第一名就對——
    向量 {_sd['all']['hit1']}/41、BM25 {_sb['all']['hit1']}/41、**混合 {_sh['all']['hit1']}/41**
    （型號題 {_sd['kw']['hit1']} → {_sh['kw']['hit1']}／15，換句話說 {_sd['para']['hit1']} → {_sh['para']['hit1']}／10）。

    跟純向量比，「第一名對不對」有變的題目：

    | 變化 | 問題 | 題型 | 向量 | BM25 | 混合 |
    | --- | --- | --- | --- | --- | --- |
    {_tbl}

    BM25 對換句話說題幾乎是瞎的——「摔到地上」跟手冊的「摔落」bigram 一個都對不上，
    它只撈得到剛好共用「可以」這種虛詞的句子；權重給太大，它就把向量原本排對的題目拖下水。
    """
    )
    return


@app.cell(hide_code=True)
def _(mo):
    mo.md(
        r"""
    **BM25 試打區**——BM25 不需要任何模型，所以任何字都能現場查。試試 `E07`、`E17`、`GS-54`，
    再試一句換句話說（例如「摔到地上」），看它什麼時候準、什麼時候交白卷：
    """
    )
    return


@app.cell
def _(mo):
    bm_q = mo.ui.text(value="螢幕顯示 E07 怎麼辦？", label="查詢", full_width=True)
    bm_q
    return (bm_q,)


@app.cell
def _(BM25_MODEL, CHILDREN, bm25_query, bm_q, html_mod, mo, np, tokenize):
    _toks = tokenize(bm_q.value)
    _s = bm25_query(BM25_MODEL, bm_q.value)
    _order = [int(_i) for _i in np.argsort(-_s, kind="stable")[:5] if _s[_i] > 0]
    _vocab = BM25_MODEL[0]
    _hit = [_t for _t in _toks if _t in _vocab]
    _items = "".join(
        f'<li style="margin:4px 0"><b style="font-family:monospace">{_s[_i]:.2f}</b>　{html_mod.escape(CHILDREN[_i])}</li>'
        for _i in _order
    ) or '<li style="color:#C44E52">一句都沒命中——BM25 在這題交白卷（向量檢索還是會給你「最像的」幾句）</li>'
    mo.Html(
        '<div style="font-size:13.5px;line-height:1.7">'
        f'<div>切出來的詞：<span style="font-family:monospace">{html_mod.escape(" · ".join(_toks)) or "（空）"}</span></div>'
        f'<div>在手冊裡出現過的：<span style="font-family:monospace;color:#DD8452">{html_mod.escape(" · ".join(_hit)) or "（沒有）"}</span></div>'
        f'<ol style="margin:6px 0 0 18px;padding:0">{_items}</ol></div>'
    )
    return


@app.cell(hide_code=True)
def _(mo):
    mo.md(
        r"""
    ## 4️⃣ Rerank：讓 cross-encoder 把前 N 名重排

    前面的向量檢索是 **bi-encoder**：問題、句子**各自**變成向量再比，所以句子的向量可以事先算好存起來，
    查詢時只算一次問題向量——快，但兩邊從頭到尾沒「見過面」。
    **cross-encoder** 把「問題＋一句」**一起**讀進模型、直接輸出相關度——準得多，
    但每一對都要跑一次模型，沒辦法事先算。所以標準做法是兩段式：
    第一階段（向量或混合）撈前 N 名，cross-encoder 只重排這 N 個。

    本機實測（bge-reranker-v2-m3、CPU 14 執行緒）：**約 45 ms 一對**，重排 20 個候選 ≈ 0.9 秒。
    拉 N，看分數和代價怎麼變：
    """
    )
    return


@app.cell
def _(mo):
    rr_first = mo.ui.dropdown(
        options={"向量（dense）": "dense", "混合（沿用 3️⃣ 的設定）": "hybrid"},
        value="向量（dense）",
        label="第一階段",
    )
    rr_n = mo.ui.slider(start=1, stop=40, step=1, value=20, label="交給 reranker 的候選數 N", show_value=True)
    mo.hstack([rr_first, rr_n], wrap=True, justify="start", gap=2)
    return rr_first, rr_n


@app.cell
def _(CE, L_DENSE, L_HYBRID, np, plt, rerank_lists, rr_n, score):
    _ns = list(range(1, 41))
    _fig, _ax = plt.subplots(figsize=(6.4, 3.8))
    for _l, _name, _c in ((L_DENSE, "dense -> rerank", "#4C72B0"), (L_HYBRID, "hybrid -> rerank", "#8172B2")):
        _base = score(_l)[0]["all"]["hit1"]
        _curve = [score(rerank_lists(_l, CE, _n))[0]["all"]["hit1"] for _n in _ns]
        _ax.plot(_ns, _curve, "-", color=_c, lw=2, label=_name)
        _ax.axhline(_base, color=_c, ls="--", lw=1, alpha=0.7)
    _ax.axvline(rr_n.value, color="#2A7F8E", lw=1.5, ls=":")
    _ax.text(rr_n.value + 0.5, 27.3, f"N={rr_n.value}", color="#2A7F8E", fontsize=9)
    _ax.set_xlabel("N = candidates handed to the cross-encoder")
    _ax.set_ylabel("hit@1 (out of 41)")
    _ax.set_ylim(27, 41)
    _ax.set_yticks(np.arange(28, 42, 2))
    _ax.set_title("Rerank: dashed = before rerank, solid = after")
    _ax.legend(fontsize=8, loc="lower right")
    _ax.grid(alpha=0.3)
    _fig.tight_layout()
    _fig
    return


@app.cell
def _(CE, CHILDREN, L_DENSE, L_HYBRID, Q_TEXT, np, rerank_lists, rr_first, rr_n, mo, score):
    _base = L_DENSE if rr_first.value == "dense" else L_HYBRID
    _after = rerank_lists(_base, CE, rr_n.value)
    _s0, _r0 = score(_base)
    _s1, _r1 = score(_after)

    def _p(x):
        return 1 / (1 + np.exp(-x))

    _chg = []
    for _qi, _q in enumerate(Q_TEXT):
        _a, _b = _r0[_qi]["rank"], _r1[_qi]["rank"]
        if (_a == 1) != (_b == 1):
            _tag = "🟢 救回來" if _b == 1 else "🔴 排錯了"
            _top = _after[_qi][0]
            _chg.append(
                f"| {_tag} | {_q} | 第 {_a} 名 → 第 {_b} 名 | {CHILDREN[_top][:16]}…（{_p(CE[_qi][_top]):.2f}） |"
            )
    _tbl = "\n    ".join(_chg) if _chg else "| — | 沒有任何一題的第一名改變 | | |"
    mo.md(
        f"""
    **{'向量' if rr_first.value == 'dense' else '混合'} → rerank（N={rr_n.value}）**：
    第一名就對 {_s0['all']['hit1']} → **{_s1['all']['hit1']}**／41，MRR {_s0['all']['mrr']:.3f} → {_s1['all']['mrr']:.3f}；
    型號題 {_s0['kw']['hit1']} → {_s1['kw']['hit1']}／15，換句話說 {_s0['para']['hit1']} → {_s1['para']['hit1']}／10。
    這一步在 CPU 上約多花 **{rr_n.value * 45 / 1000:.1f} 秒**／每次查詢（N × 45 ms，本機實測）。

    | 變化 | 問題 | 標準答案名次 | rerank 後的第一名（相關度） |
    | --- | --- | --- | --- |
    {_tbl}

    reranker 不是神：它也會把原本排對的題目排錯（🔴），而且**只能重排第一階段撈到的 N 個**——
    正確答案不在前 N 名，它就無能為力。
    """
    )
    return


@app.cell(hide_code=True)
def _(mo):
    mo.md(
        r"""
    ## 5️⃣ 組你自己的管線

    三招可以疊起來用。每個開關都會用同一份考卷重新打分，跟「天真版」（向量、一句一塊、同樣的 k）並排比較。
    多一個開關：**子塊加章節標題**——算向量前把「除垢｜」這種章節名貼在每句前面
    （Anthropic 叫它 contextual retrieval 的最簡版），讓「最後裝回濾水芯」這種句子知道自己在講除垢。
    """
    )
    return


@app.cell
def _(mo):
    pl_ret = mo.ui.dropdown(
        options={"向量（dense）": "dense", "BM25": "bm25", "混合（沿用 3️⃣ 的權重）": "hybrid"},
        value="向量（dense）",
        label="第一階段檢索",
    )
    pl_hdr = mo.ui.switch(value=False, label="子塊加章節標題")
    pl_rr = mo.ui.switch(value=False, label="Rerank")
    pl_n = mo.ui.slider(start=1, stop=40, step=1, value=20, label="rerank 候選數 N", show_value=True)
    pl_ctx = mo.ui.dropdown(
        options={"一句一塊（子塊）": "child", "父子（展開成整節）": "parent"},
        value="一句一塊（子塊）",
        label="交給模型的是",
    )
    pl_k = mo.ui.slider(start=1, stop=5, step=1, value=3, label="取前幾名 k", show_value=True)
    mo.vstack(
        [
            mo.hstack([pl_ret, pl_hdr], wrap=True, justify="start", gap=2),
            mo.hstack([pl_rr, pl_n], wrap=True, justify="start", gap=2),
            mo.hstack([pl_ctx, pl_k], wrap=True, justify="start", gap=2),
        ]
    )
    return pl_ctx, pl_hdr, pl_k, pl_n, pl_ret, pl_rr


@app.cell
def _(CE, L_BM25, L_DENSE, L_HDR, hy_k, hy_w, pl_hdr, pl_n, pl_ret, pl_rr, rerank_lists, rrf_lists):
    _d = L_HDR if pl_hdr.value else L_DENSE
    _base = {"dense": _d, "bm25": L_BM25, "hybrid": rrf_lists(_d, L_BM25, k=hy_k.value, wb=hy_w.value)}[pl_ret.value]
    L_MINE = rerank_lists(_base, CE, pl_n.value) if pl_rr.value else _base
    return (L_MINE,)


@app.cell
def _(L_DENSE, L_MINE, TYPES, coverage, np, pl_ctx, pl_k, plt, Q_TYPE):
    _k = pl_k.value
    _base = coverage("child", L_DENSE, _k)["rows"]
    _mine = coverage(pl_ctx.value, L_MINE, _k)["rows"]
    _cats = [_t for _t, _ in TYPES] + ["all"]
    _xt = ["multi-step", "single-fact", "code / part no.", "paraphrase", "ALL 41"]

    def _rate(rows, t):
        _sel = [_r["full"] for _r, _qt in zip(rows, Q_TYPE) if t == "all" or _qt == t]
        return sum(_sel) / len(_sel)

    _x = np.arange(len(_cats))
    _fig, _ax = plt.subplots(figsize=(6.4, 3.8))
    _ax.bar(_x - 0.2, [_rate(_base, _t) for _t in _cats], width=0.4, color="#C9D2D8", edgecolor="#1C2B33",
            label="naive: dense, 1 sentence per chunk", zorder=3)
    _ax.bar(_x + 0.2, [_rate(_mine, _t) for _t in _cats], width=0.4, color="#55A868", edgecolor="#1C2B33",
            label="your pipeline", zorder=3)
    _ax.set_xticks(_x)
    _ax.set_xticklabels(_xt, fontsize=9)
    _ax.set_ylim(0, 1.15)
    _ax.set_ylabel("answer fully in prompt")
    _ax.set_title(f"Did every needed sentence reach the model? (top-{_k})")
    _ax.legend(fontsize=8, loc="upper center", ncol=2)
    _ax.grid(axis="y", alpha=0.3)
    _fig.tight_layout()
    _fig
    return


@app.cell
def _(L_DENSE, L_MINE, coverage, mo, pl_ctx, pl_k, score):
    _k = pl_k.value
    _s0, _ = score(L_DENSE, _k)
    _s1, _ = score(L_MINE, _k)
    _c0 = coverage("child", L_DENSE, _k)
    _c1 = coverage(pl_ctx.value, L_MINE, _k)
    mo.md(
        f"""
    | 指標（top-{_k}） | 天真版 | **你的管線** |
    | --- | --- | --- |
    | 第一名就對（41 題） | {_s0['all']['hit1']} | **{_s1['all']['hit1']}** |
    | recall@{_k} | {_s0['all']['reck']:.2f} | **{_s1['all']['reck']:.2f}** |
    | MRR | {_s0['all']['mrr']:.3f} | **{_s1['all']['mrr']:.3f}** |
    | 步驟題：步驟全進 prompt（8 題） | {_c0['proc_full']} | **{_c1['proc_full']}** |
    | 其他題：答案全進 prompt（33 題） | {_c0['single']} | **{_c1['single']}** |
    | prompt 平均長度 | {_c0['chars']:.0f} 字 | **{_c1['chars']:.0f} 字** |

    前三列看**排序**（跟交給模型的是子塊還是父塊無關），後三列看**模型實際拿到什麼**。
    挑一題，看你的管線把什麼送進 prompt：
    """
    )
    return


@app.cell
def _(Q_TEXT, mo):
    pl_q = mo.ui.dropdown(options=Q_TEXT, value=Q_TEXT[0], label="逐題檢視")
    pl_q
    return (pl_q,)


@app.cell
def _(CHILDREN, CHILD_SEC, CHILD_UNIT, L_MINE, Q_GOLD, Q_TEXT, SEC_UNITS, TITLES, UNITS, html_mod, mo, pl_ctx, pl_k, pl_q):
    _qi = Q_TEXT.index(pl_q.value)
    _lst = L_MINE[_qi][: pl_k.value]
    _gold = set(Q_GOLD[_qi])
    _gold_units = {CHILD_UNIT[_g] for _g in _gold}

    def _li(text, ok):
        _c = "#2E7042" if ok else "#1C2B33"
        _bg = "#E4F2E7" if ok else "transparent"
        return (f'<li style="margin:3px 0;padding:2px 6px;border-radius:6px;background:{_bg};color:{_c}">'
                f'{"✅ " if ok else ""}{html_mod.escape(text)}</li>')

    if pl_ctx.value == "child":
        _body = "".join(_li(CHILDREN[_i], _i in _gold) for _i in _lst)
    else:
        _secs = []
        for _i in _lst:
            if CHILD_SEC[_i] not in _secs:
                _secs.append(CHILD_SEC[_i])
        _body = "".join(
            f'<li style="margin:6px 0"><b>【{html_mod.escape(TITLES[_s])}】</b><ul style="margin:2px 0 0 14px;padding:0">'
            + "".join(_li(UNITS[_u], _u in _gold_units) for _u in SEC_UNITS[_s][1:])
            + "</ul></li>"
            for _s in _secs
        )
    _got = sum(1 for _g in _gold if (_g in _lst) or (pl_ctx.value == "parent" and CHILD_SEC[_g] in {CHILD_SEC[_i] for _i in _lst}))
    mo.Html(
        '<div style="font-size:13.5px;line-height:1.7;border:2px solid #C9D2D8;border-radius:12px;padding:10px 14px">'
        f'<div style="font-weight:800;margin-bottom:4px">送進 prompt 的內容（標準答案句 {_got}/{len(_gold)} 句在裡面，綠色）</div>'
        f'<ol style="margin:0 0 0 18px;padding:0">{_body}</ol></div>'
    )
    return


@app.cell(hide_code=True)
def _(mo):
    mo.md(
        r"""
    ## 6️⃣ 換你動手

    挑戰題在教學頁的「換你動手」，全部用上面的拉桿和開關就做得到。做完再打開解答對照：
    """
    )
    return


@app.cell(hide_code=True)
def _(mo):
    mo.accordion(
        {
            "💡 LEVEL 1 參考解答（2️⃣ 把 k 拉到 1）": mo.md(
                r"""
    k=1 時，「其他題：答案全進 prompt」一句一塊是 **25/33**，固定 150 與 300 字都掉到 **18/33**，
    600 字回到 23/33，父子檢索最高 **28/33**。

    為什麼切大塊反而找不準：一塊 300 字裡可能同時講除垢、清潔、耗材——它的向量是這些主題的「平均」，
    跟任何一個具體問題都只有中等相似度；一句一塊的向量只講一件事，對上了就很尖。
    父子檢索的分數用的就是一句一塊的向量，所以它繼承了「找得準」；交出去的卻是整節，所以步驟也齊
    （k=1 時步驟題 5/8 全進——排第一的那句剛好在正確的那一節，就整節帶走）。
    """
            ),
            "💡 LEVEL 2 參考解答（3️⃣ 找 BM25 權重）": mo.md(
                r"""
    把 w 從 1 往下拉：w=1.00 時型號題 15/15、換句話說只剩 5/10，全部 33/41；
    **w=0.25～0.30** 是「型號題還保得住 15/15」的最低權重，這時換句話說回到 7/10，全部 **35/41**——
    跟純向量（35/41）**一樣多**，只是錯的題目不同：型號題全對了，換句話說題錯了 3 題。

    這就是這份手冊的真相：**單靠混合搜尋，並沒有比純向量好**，只是把錯誤從一型搬到另一型。
    混合真正的價值在第一階段「撈得全」——它要配 4️⃣ 的 reranker 才完整。
    （別的語料結果會不同：代碼越多、越像，BM25 的權重越值得給高。這正是要有考卷的原因。）
    """
            ),
            "💡 LEVEL 3 參考解答（5️⃣ 組出最好的管線）": mo.md(
                r"""
    目標：第一名就對 ≥ 38/41、步驟題 8/8 全進、其他題 ≥ 31/33、prompt 越短越好。

    一組做得到的設定：**向量 → Rerank N=3 → 父子 → k=2**：38/41、8/8、31/33，平均約 **242 字**。
    再打開「子塊加章節標題」、N 改 5：38/41、8/8、**32/33**，約 **237 字**——這是實測格點搜尋裡
    符合條件、字數最少的一組（全部組合的搜尋在本課 spike 裡）。

    怎麼確認自己做對了：表格的「第一名就對」≥ 38、步驟題欄是 8、其他題 ≥ 31。
    注意 N 拉大（20、40）反而掉到 37——候選越多，reranker 越有機會把干擾句排上來。
    （天真版 k=3 是 35/41、步驟題只有 **1/8** 全進、94 字；多花約 150 字，換來每一題步驟都完整。）
    """
            ),
        }
    )
    return


if __name__ == "__main__":
    app.run()