[{"data":1,"prerenderedAt":2146},["ShallowReactive",2],{"site-info":3,"post-eth-refuted-not-p-np":99,"related-zh-TW-eth-refuted-not-p-np":771},{"id":4,"company":5,"extension":16,"meta":17,"services":18,"social":96,"stem":97,"__hash__":98},"site\u002Fsite.yml",{"name":6,"nameEn":7,"email":8,"address":9,"addressEn":10,"lineUrl":11,"lineId":12,"duns":13,"youtube":14,"youtubeId":15},"銡策數位有限公司","Jecision Digital Co., Ltd.","contact@jecision.com","231 新北市新店區北新路二段 262 號 3 樓之 3","3F.-3, No. 262, Sec. 2, Beixin Rd., Xindian Dist., New Taipei City 231, Taiwan","https:\u002F\u002Fline.me\u002FR\u002Fti\u002Fp\u002F@374qnumi","@374qnumi","963905705","https:\u002F\u002Fwww.youtube.com\u002Fshorts\u002F6UE0WTmyjsg","6UE0WTmyjsg","yml",{},[19,43,69],{"key":20,"zh":21,"en":32},"audit",{"title":22,"tagline":23,"summary":24,"points":25,"deliverable":29,"detail":30,"duration":31},"企業 AI 導入健檢","先看清楚，再花錢","60 分鐘線上訪談，盤點最耗時、最依賴人力的營運環節；我們會告訴你哪些工作現在就能交給 AI、哪些還不成熟。",[26,27,28],"現況盤點：梳理日常營運中最耗時、最依賴人力的環節","痛點診斷：判斷哪些工作現在就能交給 AI，哪些建議先保留人力","可行性評估：依你的業務特性與預算，篩選適合的模型與工具","《企業 AI 導入建議報告書》（PDF）","含 1–2 個「開發成本最低、成效最明顯」的優先項目、技術棧建議、預期節省的人力時間與下一步","訪談 60 分鐘，報告書 3 個工作天內交付",{"title":33,"tagline":34,"summary":35,"points":36,"deliverable":40,"detail":41,"duration":42},"AI Readiness Audit","Look before you spend","A 60-minute remote audit of the workflows that eat the most time and people-power — and an honest answer on what AI can take over today, and what it cannot.",[37,38,39],"Audit the daily workflows that consume the most time and headcount","Triage which tasks AI can own today, and which should stay human","Shortlist the models and tools that fit your budget and constraints","AI Adoption Recommendation Report (PDF)","One or two highest-ROI entry points, a recommended tech stack, expected hours saved, and the concrete next step","60-minute call, report delivered within 3 business days",{"key":44,"zh":45,"en":56},"prompt",{"title":46,"tagline":47,"summary":48,"points":49,"deliverable":53,"detail":54,"duration":55},"提示詞工程","讓 AI 穩定產出，而不是碰運氣","針對你的實際任務設計提示詞與多步驟工作流，並做極限測試，確保換了資料、換了人操作也不會走鐘。",[50,51,52],"客製提示詞：ChatGPT、Claude、Gemini、Midjourney 等主流工具的專屬模板","除錯與優化：修掉幻覺、格式跑掉、時好時壞的問題","工作流建置：把複雜任務拆成多步驟提示詞與可重複的 SOP","提示詞文件或設定檔","附使用說明與範例，並提供 1 對 1 教學，確保你與團隊能自己維護","依任務複雜度報價，通常 3–7 個工作天",{"title":57,"tagline":58,"summary":59,"points":60,"deliverable":66,"detail":67,"duration":68},"Prompt Engineering","Make AI produce reliably, not by luck","Prompt sets and multi-step workflows designed for your actual tasks, stress-tested so they keep working when the data or the operator changes.",[61,62,64],"Custom prompts for ChatGPT, Claude, Gemini, Midjourney and friends",{"Debugging and tuning":63},"kill hallucinations, broken formats and flaky output",{"Workflow design":65},"break complex work into repeatable multi-step SOPs","Prompt library or exportable config","Ships with usage notes and examples, plus a 1:1 walkthrough so your team can maintain it","Quoted by complexity, typically 3–7 business days",{"key":70,"zh":71,"en":82},"poc",{"title":72,"tagline":73,"summary":74,"points":75,"deliverable":79,"detail":80,"duration":81},"極速 PoC","五天，看到能跑的東西","不談架構藍圖，直接做一個能動的雛形。五個工作天內交付線上可操作的智能體，用你真實的資料驗證。",[76,77,78],"Day 1：15 分鐘對焦，鎖定單一痛點與資料盤點","Day 2–4：模型串接、邏輯設計與雛形開發","Day 5：Demo 展示與 AI 擴展建議書","可線上操作的智能體雛形","交付範圍為概念驗證與展示，不含後續維運或大規模伺服器部署；要進階成完整系統會另行報價","5 個工作天",{"title":83,"tagline":84,"summary":85,"points":86,"deliverable":93,"detail":94,"duration":95},"Rapid PoC","Five days to something that runs","No architecture decks — a working prototype built in five business days, validated against your real data.",[87,89,91],{"Day 1":88},"15-minute scoping call, one pain point, data inventory",{"Day 2–4":90},"model integration, logic design, prototype build",{"Day 5":92},"live demo plus an AI expansion recommendation","A runnable online agent prototype","Proof of concept and demo scope only; ongoing operations and large-scale deployment are quoted separately","5 business days",[],"site","XTwARfVAOcrXNiKehsM6V6cdkd2HXy4d5yZVrSWrI3Q",{"zh":100,"en":447},{"id":101,"title":102,"author":103,"body":104,"cover":428,"coverAlt":429,"date":430,"description":431,"draft":432,"extension":433,"featured":432,"lang":434,"meta":435,"navigation":225,"ogImage":436,"path":437,"seo":438,"slug":439,"stem":440,"tags":441,"translationKey":439,"updated":445,"__hash__":446},"blog\u002Fblog\u002Fzh-TW\u002Feth-refuted-not-p-np.md","朋友問我：P=NP 被攻破了嗎？","Jecision",{"type":105,"value":106,"toc":417},"minimark",[107,111,114,117,120,124,127,130,133,136,144,147,153,164,167,170,173,176,179,185,188,195,198,201,204,211,214,231,235,242,245,248,251,254,257,260,263,266,269,272,283,286,289,292,295,298,301,304,307,310,313,316,327,330,333,336,345,348,351,354,357,360,363,366,369,372,375,378,381,384,387,390,393,396,399,402],[108,109,110],"p",{},"星期二晚上，朋友在群組丟來一張新聞截圖，問我：「這是說 P=NP 被攻破了嗎？」",[108,112,113],{},"我說：「不是 P=NP，是 ETH。」",[108,115,116],{},"他問：「那不是一樣嗎？」",[108,118,119],{},"那個當下我其實沒有好答案。隔天中午我們碰面，我花了半小時把這件事從頭講一次。這篇就是那次講的內容，加上後來我自己去讀原始手稿補上的細節。",[121,122,123],"h2",{"id":123},"那天到底發生了什麼",[108,125,126],{},"OpenAI 在十月六日先把七百多篇數學手稿放上 GitHub。十月二十六日又加了兩篇，其中一篇是目錄上的第 378 號：〈Disproof of the Exponential Time Hypothesis〉，論文自己的標題則是〈The Exponential Time Hypothesis is False〉。",[108,128,129],{},"整個庫現在是 721 篇手稿、373 個家族。家族編號有跳號，所以編號到 378，不代表真的有 378 個家族。",[108,131,132],{},"幾小時後，Anthropic 也說他們的模型在 10 月 16 日獨立找到核心想法，並稱 OpenAI 的模型「獨立且同時」證明了類似的結果。",[108,134,135],{},"朋友打斷我：「所以是誰先的？」",[108,137,138,139,143],{},"「不知道，也不重要。」我跟他說，真正值得看的地方，是",[140,141,142],"strong",{},"這些東西還不是論文","。",[108,145,146],{},"OpenAI 自己在 README 裡寫得很白：這些是「原始研究資料」，不是打磨過的學術論文，而且「部分沒有形式化的結果可能有問題」。整個庫大約 42% 的頂層結果有 Lean 形式化，這篇第 378 號是其中之一，核心的時間上界有被機器檢查過。",[108,148,149,150,143],{},"學界沒有急著下結論。Impagliazzo、Paturi（1999 年提出 ETH，期刊版 2001）跟 MIT 的 Williams 組了工作組、發公開信，特別強調一件事：",[140,151,152],{},"參與，不等於認證",[108,154,155,156,163],{},"到 10 月 28 日，",[157,158,162],"a",{"href":159,"rel":160},"https:\u002F\u002Fmathworld.wolfram.com\u002FExponentialTimeHypothesis.html",[161],"nofollow","MathWorld"," 的紀錄寫得很清楚：還沒有獨立驗證。",[121,165,166],{"id":166},"先從數獨開始",[108,168,169],{},"要講清楚這件事，得先講一個看起來完全不相關的東西：數獨。",[108,171,172],{},"朋友點頭，他玩數獨。",[108,174,175],{},"「你先想像一個填好的盤面。我拿給你看，你大概十秒就能確認對不對。但如果我給你一張空白盤，你要找到那組解，可能要半小時。」",[108,177,178],{},"這就是 P 與 NP 的差別。P 是「可以快速解」的問題，NP 是「答案可以快速驗證」的問題。",[108,180,181,182],{},"而 P 等於 NP 這句話的意思是：",[140,183,184],{},"所有能快速驗證的答案，都能快速找到。",[108,186,187],{},"學界幾乎所有人都覺得這句話是錯的，但沒有人證明過。",[108,189,190,191,194],{},"ETH 比這句話更強。它不只是說「3SAT 不在 P 裡」，而是說：",[140,192,193],{},"存在一個常數 c，使得 3SAT 至少要 2 的 cn 次方步。"," 3SAT 是這一類問題裡最標準的那一個，跟數獨同樣是 NP-完全。",[108,196,197],{},"打個比方。P 不等於 NP 只說「兩者不是同一個位置」；ETH 說的是「兩者至少相距兩千公里」——後者資訊多得多。",[121,199,200],{"id":200},"為什麼有人要假設這種東西",[108,202,203],{},"「假設一個沒人證明的東西，有什麼用？」朋友問。",[108,205,206,207,210],{},"用處在於：",[140,208,209],{},"如果你知道兩地至少相距兩千公里，就可以推論沒有人能在一小時內開車到。"," 距離的下界，直接排除掉一整類「很快」的解法。",[108,212,213],{},"過去二十年，「細粒度複雜度」這個領域就是這樣運作的：先假設 ETH 成立，再證明「如果這個問題有快速演算法，那 3SAT 就有快速演算法，矛盾」。所以 ETH 不是課本上的名詞，它是一整批論文的地基。",[215,216,219,220,219,227],"figure",{"className":217},[218],"article-figure","\n  ",[221,222],"video",{"src":223,"poster":224,"autoPlay":225,"loop":225,"muted":225,"playsInline":225,"ariaLabel":226},"\u002Fimages\u002Fblog\u002Feth-refuted-not-p-np\u002F03-ladder.mp4","\u002Fimages\u002Fblog\u002Feth-refuted-not-p-np\u002F03-ladder-poster.jpg",true,"複雜度階梯：多項式、次指數、指數三層",[228,229,230],"figcaption",{},"複雜度階梯。ETH 主張最上層不能更低；這次的結果把「上界」壓到中間那層。",[121,232,234],{"id":233},"那-openai-到底做了什麼","那 OpenAI 到底做了什麼",[108,236,237,238,241],{},"他們的模型找到一個演算法，可以",[140,239,240],{},"算出","一個邏輯公式有幾組解——是「算出有幾組」，不是「判斷有沒有解」，比原本的要求更強。時間是 2 的 n 除以根號（自然對數 n）次方，空間則是多項式。",[108,243,244],{},"朋友指著我在紙上寫的那串式子：「這是什麼意思？」",[108,246,247],{},"「意思是指數還在，只是除以一個會慢慢變大的數字。n 越大，除得越多。」",[108,249,250],{},"「那不是變快了？」",[108,252,253],{},"「是。但要看跟誰比。」",[108,255,256],{},"目前最好的 3SAT 演算法（隨機化）大約是 1.307 的 n 次方。",[108,258,259],{},"假設 n 等於一千。那個等級的演算法，大約是 2 的 386 次方；這次的結果，大約是 2 的 380 次方。",[108,261,262],{},"只快了大約 60 倍。",[108,264,265],{},"60 倍聽起來不少，但 2 的 380 次方還是 10 的 114 次方。宇宙年齡以秒計，也只有 4 乘 10 的 17 次方。",[108,267,268],{},"真正的差別在 n 很大的時候。n 等於一百萬，一個是 2 的 269000 次方，一個是 2 的 386000 次方——差距拉開，但兩個都還是天文數字。",[108,270,271],{},"所以這次的重點不是「快多少」，而是「快過那條下界」。",[215,273,219,275,219,280],{"className":274},[218],[221,276],{"src":277,"poster":278,"autoPlay":225,"loop":225,"muted":225,"playsInline":225,"ariaLabel":279},"\u002Fimages\u002Fblog\u002Feth-refuted-not-p-np\u002F05-magnitude.mp4","\u002Fimages\u002Fblog\u002Feth-refuted-not-p-np\u002F05-magnitude-poster.jpg","n=1000 時的量級比較：已知最快 2^386，這次 2^380",[228,281,282],{},"n = 1000 的對照。這次不是從 2^n 降到 2^380，而是從 2^386 降到 2^380——快 64 倍，仍然不可行。",[121,284,285],{"id":285},"上下界要分清楚",[108,287,288],{},"這裡有個容易搞混的地方。",[108,290,291],{},"演算法是一種「上界」：它告訴我們，這件事最多需要多少時間就能做到。",[108,293,294],{},"ETH 是一種「下界」：它說，這件事至少需要多少時間。",[108,296,297],{},"這次的結果，把上界壓到次指數。對足夠大的 n，這個上界會低於 ETH 宣稱的下界——所以 ETH 被推翻。",[108,299,300],{},"朋友問：「所以反過來也成立嗎？」",[108,302,303],{},"「你說的『反過來』有兩種。」",[108,305,306],{},"P 等於 NP 確實會讓 ETH 不成立——但那是同一個箭頭的逆否命題，不是新的推論。",[108,308,309],{},"真正不成立的是另一種反推：手上只有「ETH 被推翻」，推不出「P 等於 NP」。這個箭頭，不成立。",[108,311,312],{},"用回距離的比喻：原本大家以為至少兩千公里，現在證明只有八百公里。距離變短了，但你手上那台車還是太慢，一小時內到不了。",[108,314,315],{},"所以 P 是否等於 NP，到今天為止，完全開放。",[215,317,219,319,219,324],{"className":318},[218],[221,320],{"src":321,"poster":322,"autoPlay":225,"loop":225,"muted":225,"playsInline":225,"ariaLabel":323},"\u002Fimages\u002Fblog\u002Feth-refuted-not-p-np\u002F04-implication.mp4","\u002Fimages\u002Fblog\u002Feth-refuted-not-p-np\u002F04-implication-poster.jpg","兩個箭頭：上面成立、下面打叉",[228,325,326],{},"上面那個箭頭成立，下面那個不成立。這是整件事最常被誤讀的地方。",[121,328,329],{"id":329},"那為什麼還是大事",[108,331,332],{},"「既然 P 等於 NP 沒有被動到，那大家在興奮什麼？」",[108,334,335],{},"「因為它拆掉了很多人的直覺。」",[108,337,338,339,344],{},"Ryan Williams ",[157,340,343],{"href":341,"rel":342},"https:\u002F\u002Ftechcrunch.com\u002F2026\u002F10\u002F27\u002Ffrontier-ai-labs-say-their-models-refuted-the-exponential-time-hypothesis-what-does-that-mean\u002F",[161],"對媒體說","，證明的有些部分也許算例行公事，但確實有兩三個「看起來很外星人」的部分，正是這些部分讓他覺得，這是整個社群要一起處理的課題。",[108,346,347],{},"他也說了一句很誠實的話：「每一位電腦科學家大概都該把 P 等於 NP 的可能性權重調高一點，但調整多少因人而異。」",[108,349,350],{},"「所以有人檢查過了嗎？」朋友問。",[108,352,353],{},"「有，但還沒檢查完。」",[108,355,356],{},"手稿裡大約 42% 的頂層結果有 Lean 形式化。Lean 是一套能讓電腦逐步檢查證明的工具。可是電腦檢查過，不等於結論成立——它確認推導沒有漏洞，卻不能保證題目定義是大家想的那一題，也不能保證這個定理有用。",[108,358,359],{},"實際影響大概三塊。",[108,361,362],{},"第一，細粒度複雜度要重看一批論文。那些「假設 ETH 成立，則某問題不能低於某個複雜度」的條件句，前提沒了；結論不一定變假，但不能再拿來推無條件下界。",[108,364,365],{},"第二，密碼學沒有因此被破。現行系統依賴的是因數分解、離散對數、格問題這幾類特定問題，不是 3SAT 這個家族；而且這次的演算法還是指數時間。",[108,367,368],{},"第三，工程上短期完全無感。任何拿這件事說「AI 推論要變快了」的說法，都是把理論上界當成執行時間。",[121,370,371],{"id":371},"回到那個群組",[108,373,374],{},"隔天吃完午飯，朋友問我最後一個問題：「所以這是假新聞嗎？」",[108,376,377],{},"「不是。」我說，「它有真東西。錯的是把它講成『攻破 P=NP』。」",[108,379,380],{},"「那我以後要怎麼看這種新聞？」",[108,382,383],{},"我想了一下，伸出三根手指。",[108,385,386],{},"「第一，看它是宣稱還是證明。發在 GitHub 上的手稿，跟期刊論文不是同一個等級的東西——更何況 OpenAI 自己就寫了『這是原始研究資料』。",[108,388,389],{},"第二，看它形式化到哪裡。Lean 能檢查推導，但不能保證題目是大家想的那一題。",[108,391,392],{},"第三，看它推翻了什麼、又沒推翻什麼。這次推翻的是『3SAT 至少要 2 的 cn 次方』這個下界的宣稱；它沒有推翻 P 不等於 NP，也沒有給出任何能用的演算法。」",[108,394,395],{},"他聽完，把手機收起來，說了一句：「所以那則新聞，是把『距離沒那麼遠』寫成『已經到了』。」",[108,397,398],{},"對。就是這樣。",[400,401],"hr",{},[108,403,404],{},[405,406,407,408,413,414,143],"em",{},"這篇寫在 2026-10-29，學界審查還在進行中。如果後續出現獨立驗證、或證明被找出問題，我會回來更新。原始資料在 ",[157,409,412],{"href":410,"rel":411},"https:\u002F\u002Fgithub.com\u002Fopenai\u002Fmath",[161],"openai\u002Fmath"," 的第 378 號家族；ETH 的定義與推論可以看 ",[157,415,162],{"href":159,"rel":416},[161],{"title":418,"searchDepth":419,"depth":419,"links":420},"",2,[421,422,423,424,425,426,427],{"id":123,"depth":419,"text":123},{"id":166,"depth":419,"text":166},{"id":200,"depth":419,"text":200},{"id":233,"depth":419,"text":234},{"id":285,"depth":419,"text":285},{"id":329,"depth":419,"text":329},{"id":371,"depth":419,"text":371},"\u002Fimages\u002Fblog\u002Feth-refuted-not-p-np.svg","複雜度階梯圖，標出這次把上界從指數推到次指數，但還沒到多項式","2026-10-29","朋友在群組丟來一則新聞，問我「P=NP 是不是被攻破了」。這則新聞是真的有東西，但朋友把兩件事混在一起了：被推翻的是 ETH，不是 P=NP。而且這次改善的是「上界」，不是「我們終於有快演算法」。這篇是把話講清楚的版本。",false,"md","zh-TW",{},"\u002Fimages\u002Fblog\u002Feth-refuted-not-p-np.jpg","\u002Fblog\u002Fzh-tw\u002Feth-refuted-not-p-np",{"title":102,"description":431},"eth-refuted-not-p-np","blog\u002Fzh-TW\u002Feth-refuted-not-p-np",[442,443,444],"complexity","ai-research","mathematics",null,"NMrlp3rpEa3JWDfQNgon-vgHLEx-iVcVc5fiZjvqrAk",{"id":448,"title":449,"author":103,"body":450,"cover":760,"coverAlt":761,"date":430,"description":762,"draft":432,"extension":433,"featured":432,"lang":763,"meta":764,"navigation":225,"ogImage":765,"path":766,"seo":767,"slug":439,"stem":768,"tags":769,"translationKey":439,"updated":445,"__hash__":770},"blog\u002Fblog\u002Fen\u002Feth-refuted-not-p-np.md","My friend asked: has P=NP been broken?",{"type":105,"value":451,"toc":751},[452,455,458,461,464,468,471,474,477,480,487,490,496,503,507,510,513,516,519,525,528,535,538,542,545,552,555,564,568,575,578,581,584,587,590,593,596,599,602,605,614,618,621,628,635,638,641,644,647,650,653,656,665,669,672,675,682,685,688,691,694,697,700,703,706,710,713,716,719,722,725,728,731,734,737,739],[108,453,454],{},"On Tuesday night, a friend dropped a news screenshot into our group chat and asked: \"Does this mean P=NP has been broken?\"",[108,456,457],{},"I said: \"It's not P=NP. It's ETH.\"",[108,459,460],{},"He asked: \"Isn't that the same thing?\"",[108,462,463],{},"At that moment I didn't have a good answer. We met for lunch the next day, and I spent half an hour walking him through it. This is what I said, plus the details I filled in later from reading the original manuscripts.",[121,465,467],{"id":466},"what-actually-happened","What actually happened",[108,469,470],{},"On October 6, OpenAI put several hundred mathematical manuscripts on GitHub. On October 26 it added two more. One of them is catalogue entry 378: 〈Disproof of the Exponential Time Hypothesis〉 — the paper's own title is 〈The Exponential Time Hypothesis is False〉.",[108,472,473],{},"The repository now holds 721 manuscripts across 373 families. The family numbers skip around, so \"number 378\" does not mean there are 378 families.",[108,475,476],{},"The same day, Anthropic said its model had found the core idea independently on October 16, and described OpenAI's model as having \"independently and concurrently\" proven a similar result.",[108,478,479],{},"My friend cut in: \"So who got there first?\"",[108,481,482,483,486],{},"\"I don't know, and it doesn't matter.\" What matters, I told him, is that ",[140,484,485],{},"these are not papers yet",".",[108,488,489],{},"OpenAI says so itself in the README: these are \"raw research data, rather than polished academic papers\", and \"some of the unformalized results could have issues\". About 42% of the top-line results in the repository have Lean formalizations; entry 378 is one of them, and its core time bound has been machine-checked.",[108,491,492,493,486],{},"The academic response was not slow. Impagliazzo and Paturi (who formulated ETH in 1999; journal version 2001) and MIT's Ryan Williams formed a working group and published an open letter. They stressed one thing: ",[140,494,495],{},"involvement is not certification",[108,497,498,499,502],{},"As of October 28, ",[157,500,162],{"href":159,"rel":501},[161]," records that no independent verification had been reported.",[121,504,506],{"id":505},"start-with-sudoku","Start with Sudoku",[108,508,509],{},"To explain this properly, we have to start with something that looks unrelated: Sudoku.",[108,511,512],{},"My friend nodded. He plays Sudoku.",[108,514,515],{},"\"Imagine a filled-in grid. I show it to you, and you can check it in about ten seconds. Now imagine an empty grid. Finding that solution might take you half an hour.\"",[108,517,518],{},"That is the difference between P and NP. P is the class of problems you can solve quickly. NP is the class you can verify quickly.",[108,520,521,522],{},"And P = NP means: ",[140,523,524],{},"every answer you can verify quickly, you can also find quickly.",[108,526,527],{},"Almost everyone believes that is false, but nobody has proven it.",[108,529,530,531,534],{},"ETH is a stronger claim. It does not just say \"3SAT is not in P\". It says: ",[140,532,533],{},"there is a constant c such that 3SAT requires at least 2 to the cn steps."," 3SAT is the most standard problem in that family — like Sudoku, it is NP-complete.",[108,536,537],{},"Here is an analogy. P ≠ NP only says \"these two are not in the same place\". ETH says \"they are at least two thousand kilometers apart\" — much more information.",[121,539,541],{"id":540},"why-would-anyone-assume-such-a-thing","Why would anyone assume such a thing",[108,543,544],{},"\"What's the use of assuming something nobody has proven?\" my friend asked.",[108,546,547,548,551],{},"The use is this: ",[140,549,550],{},"if you know two places are at least two thousand kilometers apart, you can rule out anyone driving there in an hour."," A lower bound on distance eliminates an entire class of \"fast\" solutions.",[108,553,554],{},"That is how fine-grained complexity has worked for the past twenty years: assume ETH, then prove \"if this problem had a fast algorithm, 3SAT would too, contradiction\". So ETH is not a textbook term. It is the foundation under a whole shelf of papers.",[215,556,219,558,219,561],{"className":557},[218],[221,559],{"src":223,"poster":224,"autoPlay":225,"loop":225,"muted":225,"playsInline":225,"ariaLabel":560},"Complexity ladder: polynomial, sub-exponential, exponential",[228,562,563],{},"The complexity ladder. ETH claimed the top rung could not be lower; this result pushes the upper bound down to the middle rung.",[121,565,567],{"id":566},"what-did-openai-actually-do","What did OpenAI actually do",[108,569,570,571,574],{},"Their model found an algorithm that ",[140,572,573],{},"counts"," the satisfying assignments of a logical formula — counting them, not just deciding whether one exists, which is a stronger requirement. The running time is 2 to the n divided by the square root of the natural log of n, using polynomial space.",[108,576,577],{},"My friend pointed at the expression I had scribbled on a piece of paper: \"What does that mean?\"",[108,579,580],{},"\"It means the exponent is still there, but divided by a number that grows slowly. The bigger n is, the more it gets divided.\"",[108,582,583],{},"\"So it's faster?\"",[108,585,586],{},"\"It is. But faster than what?\"",[108,588,589],{},"The best known 3SAT algorithm runs in roughly 1.307 to the n.",[108,591,592],{},"Take n = 1,000. That algorithm takes about 2 to the 386. This new one takes about 2 to the 380.",[108,594,595],{},"It is only about 60 times faster.",[108,597,598],{},"Sixty times sounds like a lot, until you notice that 2 to the 380 is still 10 to the 114. The age of the universe in seconds is only 4 × 10 to the 17.",[108,600,601],{},"The real difference appears when n gets large. Take n = 1,000,000: one is 2 to the 269,000, the other is 2 to the 386,000. The gap widens, but both remain astronomical.",[108,603,604],{},"So the point here is not \"how much faster\". It is \"faster than that lower bound\".",[215,606,219,608,219,611],{"className":607},[218],[221,609],{"src":277,"poster":278,"autoPlay":225,"loop":225,"muted":225,"playsInline":225,"ariaLabel":610},"Magnitude comparison at n=1000: 2^386 versus 2^380",[228,612,613],{},"At n = 1,000. This is not 2^n dropping to 2^380 — it is 2^386 dropping to 2^380. Sixty times faster, still infeasible.",[121,615,617],{"id":616},"keep-upper-and-lower-bounds-straight","Keep upper and lower bounds straight",[108,619,620],{},"This is where people get confused.",[108,622,623,624,627],{},"An algorithm is an ",[140,625,626],{},"upper bound",": it tells you the most time you need to get something done.",[108,629,630,631,634],{},"ETH is a ",[140,632,633],{},"lower bound",": it says the least time anything must take.",[108,636,637],{},"This result pushes the upper bound down to sub-exponential. For large enough n, that upper bound falls below the lower bound ETH claimed — so ETH is refuted.",[108,639,640],{},"My friend asked: \"Does that work in reverse too?\"",[108,642,643],{},"\"There are two kinds of 'reverse'.\"",[108,645,646],{},"P = NP would indeed imply ETH is false — but that is just the contrapositive of the same arrow, not a new deduction.",[108,648,649],{},"What does not hold is the other reverse: from \"ETH has been refuted\" you cannot conclude \"P = NP\". That arrow fails.",[108,651,652],{},"Back to the distance analogy: everyone thought it was at least two thousand kilometers; now someone proves it is only eight hundred. The distance got shorter, but your car is still too slow to arrive within an hour.",[108,654,655],{},"So whether P equals NP remains completely open today.",[215,657,219,659,219,662],{"className":658},[218],[221,660],{"src":321,"poster":322,"autoPlay":225,"loop":225,"muted":225,"playsInline":225,"ariaLabel":661},"Two arrows: the top one holds, the bottom one is crossed out",[228,663,664],{},"The top arrow holds. The bottom one does not. This is the most commonly misread part of the story.",[121,666,668],{"id":667},"then-why-does-it-matter","Then why does it matter",[108,670,671],{},"\"If P = NP is untouched, why is everyone excited?\"",[108,673,674],{},"\"Because it knocks out a lot of intuitions.\"",[108,676,338,677,681],{},[157,678,680],{"href":341,"rel":679},[161],"told reporters"," that some parts of the proof are, you might say, routine — but there are two or three \"alien-looking\" parts, and those are exactly what make this something the whole community needs to work through.",[108,683,684],{},"He also said something honest: \"Every computer scientist should probably put a little more weight on the plausibility of P = NP, but one's weight may vary.\"",[108,686,687],{},"\"So has anyone checked it?\" my friend asked.",[108,689,690],{},"\"Yes, but they are not done.\"",[108,692,693],{},"About 42% of the top-line results carry Lean formalizations. Lean is a tool that lets a computer check a proof step by step. But a machine check is not the same as the result being true — it confirms the derivation has no gaps, not that the statement is the one everyone cares about, and not that the theorem is useful.",[108,695,696],{},"Three practical effects.",[108,698,699],{},"First, fine-grained complexity has papers to re-read. Those \"assuming ETH, problem X cannot be solved below Y\" conditionals lost their premise. The conclusions are not necessarily false, but they can no longer be used to derive unconditional lower bounds.",[108,701,702],{},"Second, cryptography is not broken. Today's systems rely on specific problems — factoring, discrete logarithms, lattices — not on the 3SAT family; and this algorithm is still exponential.",[108,704,705],{},"Third, engineering feels nothing in the short term. Anyone telling you this means \"AI inference is about to get faster\" is confusing a theoretical bound with a wall-clock time.",[121,707,709],{"id":708},"back-to-the-group-chat","Back to the group chat",[108,711,712],{},"After lunch the next day, my friend asked one last question: \"So is it fake news?\"",[108,714,715],{},"\"No,\" I said. \"There is something real in it. What's wrong is turning it into 'P=NP has fallen'.\"",[108,717,718],{},"\"How should I read stories like this in the future?\"",[108,720,721],{},"I held up three fingers.",[108,723,724],{},"\"First, is it a claim or a proof? A manuscript on GitHub is not the same class of object as a journal paper — especially when OpenAI itself writes 'this is raw research data'.",[108,726,727],{},"Second, how far did the formalization go? Lean can check a derivation, but it cannot guarantee the problem is the one everyone thinks it is.",[108,729,730],{},"Third, what does it refute, and what does it not? This refutes the claim that 3SAT requires at least 2 to the cn steps. It does not refute P ≠ NP, and it does not hand anyone a usable algorithm.\"",[108,732,733],{},"He put his phone away and said: \"So the headline turned 'not that far' into 'we're there'.\"",[108,735,736],{},"Yes. That is exactly it.",[400,738],{},[108,740,741],{},[405,742,743,744,747,748,486],{},"Written on 2026-10-29, while academic review is still in progress. If independent verification appears, or the proof is found to have problems, I will come back and update this. The source material is family 378 in ",[157,745,412],{"href":410,"rel":746},[161],"; the definition of ETH and its implications are on ",[157,749,162],{"href":159,"rel":750},[161],{"title":418,"searchDepth":419,"depth":419,"links":752},[753,754,755,756,757,758,759],{"id":466,"depth":419,"text":467},{"id":505,"depth":419,"text":506},{"id":540,"depth":419,"text":541},{"id":566,"depth":419,"text":567},{"id":616,"depth":419,"text":617},{"id":667,"depth":419,"text":668},{"id":708,"depth":419,"text":709},"\u002Fimages\u002Fblog\u002Fen\u002Feth-refuted-not-p-np.svg","A complexity ladder showing the upper bound pushed down to sub-exponential, not yet to polynomial","A friend sent me a news story and asked whether P=NP had fallen. The story is real, but it mixes up two things: it was ETH that was refuted, not P=NP. Here is the explanation I gave him.","en",{},"\u002Fimages\u002Fblog\u002Fen\u002Feth-refuted-not-p-np.jpg","\u002Fblog\u002Fen\u002Feth-refuted-not-p-np",{"title":449,"description":762},"blog\u002Fen\u002Feth-refuted-not-p-np",[442,443,444],"wq5KMOvcqergp4H5bMBJJNK9LUMe3vqhM8PeTxKhMLw",[772,1646],{"id":773,"title":774,"author":103,"body":775,"cover":1631,"coverAlt":1632,"date":1633,"description":1634,"draft":432,"extension":433,"featured":432,"lang":434,"meta":1635,"navigation":225,"ogImage":1636,"path":1637,"seo":1638,"slug":1639,"stem":1640,"tags":1641,"translationKey":1639,"updated":445,"__hash__":1645},"blog\u002Fblog\u002Fzh-TW\u002Flogic-folding-fpga-cgra.md","FPGA 的死胡同，邏輯折疊可能是出口",{"type":105,"value":776,"toc":1618},[777,783,786,789,792,798,801,805,808,830,833,836,839,898,901,944,953,956,960,963,980,990,1002,1014,1018,1021,1027,1033,1039,1045,1052,1056,1059,1065,1071,1077,1089,1092,1096,1150,1154,1157,1365,1368,1417,1420,1423,1426,1498,1501,1504,1556,1559,1562,1568,1574,1580,1586,1589,1597,1603,1609,1615],[778,779,780],"blockquote",{},[108,781,782],{},"這篇沒有我們的實測。已發生的事實都有連結；預測與機率是我們的判斷，會標明。我們對這個方向是樂觀的，但會把「要看到什麼才算成立」寫清楚。",[121,784,785],{"id":785},"先講結論",[108,787,788],{},"2026 年 9 月，麒麟 2026 出貨。它是第一顆把邏輯折疊帶進量產的 SoC。拆機之後的數字是：密度從 1.55 億顆\u002Fmm² 升到 2.38 億（+55%），同效能下 NPU 功耗降 66%、CPU 大核降 41%。",[108,790,791],{},"這不是路線圖，是已經在手上的手機晶片。",[108,793,794,795],{},"所以真正的問題不是「華為行不行」。是：",[140,796,797],{},"同一個槓桿，能不能把 FPGA 與 CGRA 從二十年的死胡同裡拉出來？",[108,799,800],{},"我的答案：有望。但理由不是「數字變大」，而是它同時鬆開三個卡點，而這三個卡點剛好是 AI 時代最痛的地方。",[121,802,804],{"id":803},"死胡同fpga-卡在什麼地方","死胡同：FPGA 卡在什麼地方",[108,806,807],{},"FPGA 不是不強，是三個體質問題讓它一直停在「膠合與原型」：",[809,810,811,818,824],"ol",{},[812,813,814,817],"li",{},[140,815,816],{},"面積。"," 配置 SRAM 與可程式開關吃掉一大塊面積，同樣功能比 ASIC 大一個數量級。",[812,819,820,823],{},[140,821,822],{},"記憶體牆。"," 可程式織體換不到 HBM 級的頻寬，只能外掛 DRAM；推論一進入大模型，就先輸在搬資料。",[812,825,826,829],{},[140,827,828],{},"靜態性。"," 權重與路由在合成時就固定，模型一改就得重新走一次工具鏈。這件事在模型每季改版的年代，變成最大的成本。",[108,831,832],{},"第三點最少被討論，但它其實是 FPGA 在 AI 時代最應該贏的地方。只是過去的硬體做不到「改得夠快、改得夠便宜」。",[121,834,835],{"id":835},"折疊給了三把鑰匙",[108,837,838],{},"邏輯折疊在 2026 年指兩件不同的事，而它們解的是不同的鎖：",[840,841,842,855],"table",{},[843,844,845],"thead",{},[846,847,848,852],"tr",{},[849,850,851],"th",{},"華為 LogicFolding（折 Z 軸）",[849,853,854],{},"學術 temporal logic folding（折 T 軸）",[856,857,858,872,885],"tbody",{},[846,859,860,867],{},[861,862,863,866],"td",{},[140,864,865],{},"做法","：一個邏輯區塊拆成上下兩層、面對面鍵合",[861,868,869,871],{},[140,870,865],{},"：同一組 LUT 每隔幾個 cycle 重配置一次",[846,873,874,880],{},[861,875,876,879],{},[140,877,878],{},"解鎖","：密度、頻率、更短的路徑",[861,881,882,884],{},[140,883,878],{},"：用時間換面積，重配置變成常態",[846,886,887,893],{},[861,888,889,892],{},[140,890,891],{},"實證","：麒麟 2026（已量產）",[861,894,895,897],{},[140,896,891],{},"：NATURE／NanoMap、Tabula Spacetime",[108,899,900],{},"三把鑰匙分別對應三個卡點：",[902,903,904,916,932],"ul",{},[812,905,906,909,910,915],{},[140,907,908],{},"密度","：把配置記憶體搬出邏輯層（BEOL 配置記憶體，",[157,911,914],{"href":912,"rel":913},"https:\u002F\u002Fdoi.org\u002F10.1109\u002FDAC63849.2025.11132615",[161],"M3D FPGA，DAC 2025","），面積稅就有機會打折。",[812,917,918,921,922,927,928,143],{},[140,919,920],{},"頻寬","：把 SRAM 或 DRAM 貼上去。28nm 3D logic-on-SRAM CGRA 已經做出 ",[157,923,926],{"href":924,"rel":925},"https:\u002F\u002Fieeexplore.ieee.org\u002Fdocument\u002F11509617",[161],"4TB\u002Fs 垂直頻寬","，51.19mm²、",[157,929,931],{"href":930},"mailto:1GHz@0.9V","1GHz@0.9V",[812,933,934,937,938,943],{},[140,935,936],{},"重配置速度","：混合鍵合把重配置延遲壓到 sub-10ns（",[157,939,942],{"href":940,"rel":941},"https:\u002F\u002Fdoi.org\u002F10.1145\u002F3748173.3779206",[161],"vFPGA，2026","），時間折疊第一次在成本上說得通。",[108,945,946,947,952],{},"再加一項：面對面鍵合讓線變短。",[157,948,951],{"href":949,"rel":950},"https:\u002F\u002Farxiv.org\u002Fabs\u002F2505.05579",[161],"LaZagna（ICCAD 2025）","在 VTR 模擬裡量到臨界路徑最多縮短 6.7%、總線長 22.9%。",[108,954,955],{},"單看每一項都不算革命。放在一起，是 FPGA 二十年來第一次有機會把三個稅同時往下壓。",[121,957,959],{"id":958},"已經發生的事不是預測","已經發生的事，不是預測",[108,961,962],{},"這一節全部是可以查證的。它重要，因為它把「折疊」從論文搬到商品。",[108,964,965,968,969,143,974,979],{},[140,966,967],{},"密度與功耗。"," 麒麟 2026 對比前代平面架構的麒麟 9030 Pro：密度 +55%，同效能下 NPU 功耗 −66%、CPU 大核 −41%，",[157,970,973],{"href":971,"rel":972},"https:\u002F\u002Fwww.ithome.com\u002F0\u002F998\u002F598.htm",[161],"GPU 的數字各家報導落在 45–58%",[157,975,978],{"href":976,"rel":977},"https:\u002F\u002Fm.cena.com.cn\u002Fsemi\u002F20261021\u002F129796.html",[161],"華為的說法","是：晶片能耗大半花在金屬走線搬資料。折疊縮短路徑、降低互連電容，所以同效能可以用更低的頻率與電壓。",[108,981,982,985,986,143],{},[140,983,984],{},"做得比預期細。"," 華為強調這是「選擇性折疊」：只折關鍵路徑與關鍵時序。再配合熱感知布局，讓冷熱電路交錯、避免熱點垂直重疊。垂直互連已經超過 1 億根，",[157,987,989],{"href":971,"rel":988},[161],"目標三年內做到 720nm 頂層金屬節距、2 億根以上",[108,991,992,995,996,1001],{},[140,993,994],{},"製程也不再是藉口。"," SMIC 的 N+3 已經進入 5nm 級量產（",[157,997,1000],{"href":998,"rel":999},"https:\u002F\u002Fwww.techpowerup.com\u002F344000\u002Fchinese-smic-achieves-5-nm-production-on-n-3-node-without-euv-tools",[161],"TechPowerUp","）。也就是說，折疊不是在「沒有先進製程」時的替代品，而是「有製程之後仍然值得做」的架構選項。這一點改變了整件事的性質。",[108,1003,1004,1007,1008,1013],{},[140,1005,1006],{},"官方路線圖把它排進 AI 加速器。"," 依韜定律論文 V2，2025 年的昇騰 910C、2026 年的 950 仍用 Chiplet 與 2.5D；",[157,1009,1012],{"href":1010,"rel":1011},"https:\u002F\u002Fwww.trendforce.com\u002Fnews\u002F2026\u002F07\u002F06\u002Fnews-huawei-expands-tau-scaling-law-v2-paper-highlighting-logicfolding-path-to-ascend-ai-chips-around-2030\u002F",[161],"約 2030 年的昇騰 990 會把邏輯折疊引進 AI 加速器","，此後 3D 折疊成為主要載體。",[121,1015,1017],{"id":1016},"往前看折疊真正解鎖的是什麼","往前看：折疊真正解鎖的是什麼",[108,1019,1020],{},"如果折疊成立，FPGA／CGRA 在 AI 推論的位置會從「膠合」變成「可重構的推理引擎」。有四件事會因此變得可行：",[108,1022,1023,1026],{},[140,1024,1025],{},"一、持續學習。"," 權重與路由可以隨資料更新，不必為每一版模型重投片。ASIC 的結構弱點正好在這裡：模型一改，它就過期。",[108,1028,1029,1032],{},[140,1030,1031],{},"二、動態路由。"," MoE 的 expert routing 本質上是「每個 token 走不同的路徑」。這件事在硬體層可變，比在軟體層用快取模擬更省。FPGA 與 CGRA 天生就在做路由。",[108,1034,1035,1038],{},[140,1036,1037],{},"三、動態權重與精度。"," 同一顆晶片可以今天跑 INT4、明天跑 FP8，或在長上下文時切換 KV 的存放層級。GPU 靠軟體排程，可重構硬體可以直接改電路。",[108,1040,1041,1044],{},[140,1042,1043],{},"四、邊緣與現場。"," 不能連網、不能大聲散熱、不能被斷料的場景，需要的是「買得到、改得動、十年供貨」。這一段 GPU 進不去，ASIC 的出貨量養不活。",[108,1046,1047,1048,1051],{},"把這四件事放在一起，就會看到一個和過去不同的結論：",[140,1049,1050],{},"FPGA 賣的不是算力，是面對不確定性的能力。"," 而 AI 的下一段，剛好充滿不確定性。",[121,1053,1055],{"id":1054},"但要小心求證四個還沒到","但要小心求證：四個還沒到",[108,1057,1058],{},"樂觀不等於盲目。以下四件事如果沒解決，折疊就只是漂亮的原型：",[108,1060,1061,1064],{},[140,1062,1063],{},"一、2026 的實作是保守版。"," 麒麟用的是微凸塊與標準間距鍵合，不是最細的間距；TSV 的禁置區還會吃掉標準元件的位置。真正的密度紅利要等間距往下走。",[108,1066,1067,1070],{},[140,1068,1069],{},"二、工具鏈。"," 3D 要跨 die 做 P&R、時序、熱、SI 簽核，把多顆晶粒當成一個連續的設計實體。對 FPGA 來說，這等於整個編譯流程要重寫。這件事比晶圓鍵合難。",[108,1072,1073,1076],{},[140,1074,1075],{},"三、散熱與良率。"," 兩層主動邏輯把功率密度翻倍。華為用手機證明「密度高不等於更熱」。但 FPGA 長期跑在無風扇、工業、基地台環境，考驗的是十年可靠度，不是跑分。",[108,1078,1079,1082,1083,1088],{},[140,1080,1081],{},"四、成本。"," 混合鍵合連 HBM4 都還在",[157,1084,1087],{"href":1085,"rel":1086},"https:\u002F\u002Ftechnews.tw\u002Fai-agent\u002Fhuaweis-chip-law-looks-less-like-moore-and-more-like-marketing\u002F11265\u002F",[161],"觀望","。良率相乘、成本相加，誰來付溢價，目前沒有答案。",[108,1090,1091],{},"這四點不是反對理由，是「什麼時候知道它成立」的清單。",[121,1093,1095],{"id":1094},"檢查點未來三年要看什麼","檢查點：未來三年要看什麼",[840,1097,1098,1108],{},[843,1099,1100],{},[846,1101,1102,1105],{},[849,1103,1104],{},"訊號",[849,1106,1107],{},"為什麼重要",[856,1109,1110,1118,1126,1134,1142],{},[846,1111,1112,1115],{},[861,1113,1114],{},"鍵合節距往 720nm 以下走、互連數破 2 億",[861,1116,1117],{},"密度紅利能不能延續",[846,1119,1120,1123],{},[861,1121,1122],{},"昇騰 990 如期在 2030 前導入折疊",[861,1124,1125],{},"AI 加速器真的採用，不只是手機",[846,1127,1128,1131],{},[861,1129,1130],{},"出現第一顆商用的 3D logic-on-logic FPGA",[861,1132,1133],{},"從「華為的 SoC」變成「產業的選項」",[846,1135,1136,1139],{},[861,1137,1138],{},"3D-aware 的 EDA 與編譯器能把利用率拉高",[861,1140,1141],{},"沒有工具鏈，硬體只是樣品",[846,1143,1144,1147],{},[861,1145,1146],{},"邊緣裝置的 tokens\u002FJ 明顯優於 2026 年的 GPU",[861,1148,1149],{},"商業價值最終要落在每瓦推論",[121,1151,1153],{"id":1152},"_2030-的樂觀情境","2030 的樂觀情境",[108,1155,1156],{},"推論速度的關係很簡單：",[1158,1159,1162],"span",{"className":1160},[1161],"katex-display",[1158,1163,1166,1211],{"className":1164},[1165],"katex",[1158,1167,1170],{"className":1168},[1169],"katex-mathml",[1171,1172,1175],"math",{"xmlns":1173,"display":1174},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML","block",[1176,1177,1178,1206],"semantics",{},[1179,1180,1181,1185,1189],"mrow",{},[1182,1183,1184],"mtext",{},"tok\u002Fs",[1186,1187,1188],"mo",{},"≈",[1190,1191,1192,1203],"mfrac",{},[1179,1193,1194,1197,1200],{},[1182,1195,1196],{},"記憶體頻寬",[1186,1198,1199],{},"×",[1182,1201,1202],{},"頻寬效率",[1182,1204,1205],{},"每 token 要讀的權重",[1207,1208,1210],"annotation",{"encoding":1209},"application\u002Fx-tex","\\text{tok\u002Fs} \\approx \\frac{\\text{記憶體頻寬} \\times \\text{頻寬效率}}{\\text{每 token 要讀的權重}}",[1158,1212,1216,1245],{"className":1213,"ariaHidden":1215},[1214],"katex-html","true",[1158,1217,1220,1225,1233,1238,1242],{"className":1218},[1219],"base",[1158,1221],{"className":1222,"style":1224},[1223],"strut","height:1em;vertical-align:-0.25em;",[1158,1226,1230],{"className":1227},[1228,1229],"mord","text",[1158,1231,1184],{"className":1232},[1228],[1158,1234],{"className":1235,"style":1237},[1236],"mspace","margin-right:0.2778em;",[1158,1239,1188],{"className":1240},[1241],"mrel",[1158,1243],{"className":1244,"style":1237},[1236],[1158,1246,1248,1252],{"className":1247},[1219],[1158,1249],{"className":1250,"style":1251},[1223],"height:2.0463em;vertical-align:-0.686em;",[1158,1253,1255,1260,1361],{"className":1254},[1228],[1158,1256],{"className":1257},[1258,1259],"mopen","nulldelimiter",[1158,1261,1263],{"className":1262},[1190],[1158,1264,1268,1352],{"className":1265},[1266,1267],"vlist-t","vlist-t2",[1158,1269,1272,1347],{"className":1270},[1271],"vlist-r",[1158,1273,1277,1304,1315],{"className":1274,"style":1276},[1275],"vlist","height:1.3603em;",[1158,1278,1280,1285],{"style":1279},"top:-2.314em;",[1158,1281],{"className":1282,"style":1284},[1283],"pstrut","height:3em;",[1158,1286,1288],{"className":1287},[1228],[1158,1289,1291,1296,1300],{"className":1290},[1228,1229],[1158,1292,1295],{"className":1293},[1228,1294],"cjk_fallback","每",[1158,1297,1299],{"className":1298},[1228]," token ",[1158,1301,1303],{"className":1302},[1228,1294],"要讀的權重",[1158,1305,1307,1310],{"style":1306},"top:-3.23em;",[1158,1308],{"className":1309,"style":1284},[1283],[1158,1311],{"className":1312,"style":1314},[1313],"frac-line","border-bottom-width:0.04em;",[1158,1316,1318,1321],{"style":1317},"top:-3.677em;",[1158,1319],{"className":1320,"style":1284},[1283],[1158,1322,1324,1330,1334,1338,1341],{"className":1323},[1228],[1158,1325,1327],{"className":1326},[1228,1229],[1158,1328,1196],{"className":1329},[1228,1294],[1158,1331],{"className":1332,"style":1333},[1236],"margin-right:0.2222em;",[1158,1335,1199],{"className":1336},[1337],"mbin",[1158,1339],{"className":1340,"style":1333},[1236],[1158,1342,1344],{"className":1343},[1228,1229],[1158,1345,1202],{"className":1346},[1228,1294],[1158,1348,1351],{"className":1349},[1350],"vlist-s","​",[1158,1353,1355],{"className":1354},[1271],[1158,1356,1359],{"className":1357,"style":1358},[1275],"height:0.686em;",[1158,1360],{},[1158,1362],{"className":1363},[1364,1259],"mclose",[108,1366,1367],{},"以 7B 模型、INT4、batch 1、頻寬效率 0.6 估算（權重約 3.5 GB）：",[840,1369,1370,1382],{},[843,1371,1372],{},[846,1373,1374,1377,1379],{},[849,1375,1376],{},"機器",[849,1378,920],{},[849,1380,1381],{},"推論速度",[856,1383,1384,1395,1406],{},[846,1385,1386,1389,1392],{},[861,1387,1388],{},"2026 邊緣 FPGA（LPDDR5）",[861,1390,1391],{},"25 GB\u002Fs",[861,1393,1394],{},"約 4 tok\u002Fs",[846,1396,1397,1400,1403],{},[861,1398,1399],{},"2030 3D FPGA（3D DRAM）",[861,1401,1402],{},"2 TB\u002Fs",[861,1404,1405],{},"約 340 tok\u002Fs",[846,1407,1408,1411,1414],{},[861,1409,1410],{},"2030 GPU（HBM4）",[861,1412,1413],{},"8 TB\u002Fs",[861,1415,1416],{},"約 1,370 tok\u002Fs",[108,1418,1419],{},"從 4 到 340 是 85 倍。這 85 倍跨了兩個產品級別，不能直接當成「同級比較」。",[108,1421,1422],{},"跟同年的 GPU 比，3D FPGA 仍然慢約四倍。但這個比較只在「大模型、批次、頻寬受限」時才決定勝負。在延遲敏感、模型碎片化、每瓦 token 被寫進規格書的場景，基準換了，答案也會換。",[108,1424,1425],{},"相對 2026 年同級 FPGA，我們的推估分佈是：",[840,1427,1428,1441],{},[843,1429,1430],{},[846,1431,1432,1435,1438],{},[849,1433,1434],{},"倍數",[849,1436,1437],{},"機率",[849,1439,1440],{},"情境",[856,1442,1443,1454,1465,1476,1487],{},[846,1444,1445,1448,1451],{},[861,1446,1447],{},"\u003C3×",[861,1449,1450],{},"15%",[861,1452,1453],{},"只做到 2-tier 邏輯，記憶體照舊",[846,1455,1456,1459,1462],{},[861,1457,1458],{},"3–10×",[861,1460,1461],{},"25%",[861,1463,1464],{},"3D DRAM 到位，編譯器仍弱",[846,1466,1467,1470,1473],{},[861,1468,1469],{},"10–30×",[861,1471,1472],{},"35%",[861,1474,1475],{},"邏輯、記憶體、工具鏈三者同時到位",[846,1477,1478,1481,1484],{},[861,1479,1480],{},"30–80×",[861,1482,1483],{},"20%",[861,1485,1486],{},"窄門：3B 以下模型、全 SRAM、邊緣對邊緣",[846,1488,1489,1492,1495],{},[861,1490,1491],{},">80×",[861,1493,1494],{},"5%",[861,1496,1497],{},"需要 CIM 或類比，或者基準作弊",[108,1499,1500],{},"中位數大約 15 倍，期望值大約 22 倍。這組數字偏樂觀，理由是麒麟已經把密度與功耗同時做出來。那是三把鑰匙裡最難的一把。",[121,1502,1503],{"id":1503},"我的判斷",[840,1505,1506,1515],{},[843,1507,1508],{},[846,1509,1510,1513],{},[849,1511,1512],{},"情境（未來 5 年）",[849,1514,1437],{},[856,1516,1517,1525,1533,1541,1548],{},[846,1518,1519,1522],{},[861,1520,1521],{},"折疊成為某一家 FPGA 旗艦的標準微架構",[861,1523,1524],{},"60%",[846,1526,1527,1530],{},[861,1528,1529],{},"中國 3D 路線在 AI 加速器落地（昇騰 990 如期）",[861,1531,1532],{},"65%",[846,1534,1535,1538],{},[861,1536,1537],{},"FPGA／CGRA 在邊緣推論拿下可觀市佔",[861,1539,1540],{},"40%",[846,1542,1543,1546],{},[861,1544,1545],{},"出現以折疊為核心賣點、年營收逾 10 億美元的新公司",[861,1547,1450],{},[846,1549,1550,1553],{},[861,1551,1552],{},"折疊讓 FPGA 在資料中心推論取代 GPU 的一部分",[861,1554,1555],{},"10%",[108,1557,1558],{},"這些是判斷，不是預測模型。它們的共同前提是：工具鏈要在 2028 年前追上硬體。追不上，上面全部往下修。",[121,1560,1561],{"id":1561},"這篇的限制",[108,1563,1564,1567],{},[140,1565,1566],{},"一、我們沒有實測。"," 所有數字來自公開報導、論文與廠商說法；麒麟那組功耗數字是華為自行量測。",[108,1569,1570,1573],{},[140,1571,1572],{},"二、樂觀有來源，也有偏誤。"," 麒麟是個案，而且是華為在特定條件下（選擇性折疊、手機功耗預算）調出來的結果。換到 600mm² 的 FPGA，散熱與良率的帳要重算。",[108,1575,1576,1579],{},[140,1577,1578],{},"三、機率是判斷。"," 沒有統計模型，請當成「我們的看法」。",[108,1581,1582,1585],{},[140,1583,1584],{},"四、未來的推估建立在三個假設上。"," 混合鍵合的良率與成本在 2030 年前達標、3D-aware 工具鏈成熟、2030 年的 GPU 沒有進步得比預期快。",[121,1587,1588],{"id":1588},"如果你要下注",[108,1590,1591,1592,1596],{},"三個問題，比記住任何數字有用。這是我們做",[157,1593,1595],{"href":1594},"\u002Fservices","概念驗證","時的前三題。",[108,1598,1599,1602],{},[140,1600,1601],{},"一、你的模型還會不會變？"," 會變，可重構的價值就成立；已經定型、出貨量又大，去開 ASIC。",[108,1604,1605,1608],{},[140,1606,1607],{},"二、你的瓶頸是頻寬還是延遲？"," 大模型批次推論，頻寬決定一切，FPGA 不會贏；延遲、離線、每瓦 token，這些是它的地盤。",[108,1610,1611,1614],{},[140,1612,1613],{},"三、你的比較基準是 die，還是板子？"," 只要競品是「2–4 顆離散元件加一塊板子」，折疊就有帳可算。",[108,1616,1617],{},"至於要不要現在押注——我們的經驗是，硬體路線的賭注通常輸在「太早下注」，而不是「太晚跟上」。但這一次，值得把它放進 2027 年的選項清單裡。",{"title":418,"searchDepth":419,"depth":419,"links":1619},[1620,1621,1622,1623,1624,1625,1626,1627,1628,1629,1630],{"id":785,"depth":419,"text":785},{"id":803,"depth":419,"text":804},{"id":835,"depth":419,"text":835},{"id":958,"depth":419,"text":959},{"id":1016,"depth":419,"text":1017},{"id":1054,"depth":419,"text":1055},{"id":1094,"depth":419,"text":1095},{"id":1152,"depth":419,"text":1153},{"id":1503,"depth":419,"text":1503},{"id":1561,"depth":419,"text":1561},{"id":1588,"depth":419,"text":1588},"\u002Fimages\u002Fblog\u002Flogic-folding-fpga-cgra.svg","邏輯折疊把邏輯區塊拆成上下兩層堆疊的示意圖","2026-10-25","麒麟 2026 已經把邏輯折疊帶進量產，密度 +55%、同效能功耗大降。同一個槓桿，能不能把 FPGA／CGRA 從二十年的死胡同裡拉出來？這篇看它解鎖什麼、還缺什麼、以及 2030 年前要盯哪些檢查點。",{},"\u002Fimages\u002Fblog\u002Flogic-folding-fpga-cgra.jpg","\u002Fblog\u002Fzh-tw\u002Flogic-folding-fpga-cgra",{"title":774,"description":1634},"logic-folding-fpga-cgra","blog\u002Fzh-TW\u002Flogic-folding-fpga-cgra",[1642,1643,1644],"fpga","cgra","hardware","ZLO0bnOuzLOnC9C4wZH-KP3lBPxf7NcvEuwfvwTfbhc",{"id":1647,"title":1648,"author":103,"body":1649,"cover":2131,"coverAlt":2132,"date":2133,"description":2134,"draft":432,"extension":433,"featured":432,"lang":434,"meta":2135,"navigation":225,"ogImage":2136,"path":2137,"seo":2138,"slug":2139,"stem":2140,"tags":2141,"translationKey":2139,"updated":445,"__hash__":2145},"blog\u002Fblog\u002Fzh-TW\u002Fstrata-125b-on-12gb.md","125B 模型，12GB 顯卡，94 tok\u002Fs",{"type":105,"value":1650,"toc":2119},[1651,1668,1671,1674,1677,1680,1686,1693,1697,1700,1714,1717,1721,1728,1731,1734,1738,1744,1747,1797,1800,1803,1809,1816,1820,1823,1826,1829,1832,1893,1900,1905,1912,1915,1921,1927,1933,1936,1939,1945,1952,1959,1963,1966,1973,1976,2024,2027,2034,2042,2045,2065,2068,2071,2074,2081,2093,2096,2116],[778,1652,1653],{},[108,1654,1655,1656,1661,1662,1667],{},"這篇沒有我們的實測。數據來自 Qwen 官方發布、",[157,1657,1660],{"href":1658,"rel":1659},"https:\u002F\u002Fgithub.com\u002FBlockYugaLabs\u002FStrata",[161],"Strata 開源專案"," 的說明，以及一位對岸開發者的",[157,1663,1666],{"href":1664,"rel":1665},"https:\u002F\u002Fwww.bilibili.com\u002Fvideo\u002FBV1WwJy6EEuN\u002F",[161],"公開實測影片","。文中會標明哪個數字是誰給的。",[121,1669,1670],{"id":1670},"三個數字",[108,1672,1673],{},"125B 的模型。12GB 的顯示卡。94 tok\u002Fs。",[108,1675,1676],{},"半年前，這三個數字放在一起是笑話。當時想在家用電腦跑 27B 的模型，量化後 20GB，加上 KV cache，你得有 24GB 的卡才勉強開到 128K 上下文。",[108,1678,1679],{},"現在 125B 跑在 12GB 上，而且不是「能跑」，是「比你讀字還快」。",[108,1681,1682,1683,143],{},"真正變的不是模型變聰明，是",[140,1684,1685],{},"模型有多大，和硬體要多好，已經開始脫鉤",[108,1687,1688,1689,1692],{},"先講清楚前提：94 tok\u002Fs 是 RTX 5070（12GB）搭配 ",[140,1690,1691],{},"64GB 系統記憶體","的成績。只有 32GB 記憶體的話，只能跑砍半的 Coder 版本。這不是「插一張卡就好」的故事。",[121,1694,1696],{"id":1695},"兩個限制被分別繞過","兩個限制，被分別繞過",[108,1698,1699],{},"大模型跑不動，卡在兩件事：",[809,1701,1702,1708],{},[812,1703,1704,1707],{},[140,1705,1706],{},"裝不下","：權重是硬的。這顆模型加上 51B 的 n-gram 查表，量化後檔案還是 70–80GB。",[812,1709,1710,1713],{},[140,1711,1712],{},"算不動","：每個 token 都要讓所有參數參與計算。",[108,1715,1716],{},"Qwen3.8-Flash-Next 處理了第二個，Strata 處理了第一個。",[121,1718,1720],{"id":1719},"第一個限制不是每個專家都要上班","第一個限制：不是每個專家都要上班",[108,1722,1723,1724,1727],{},"Flash-Next 是 MoE（混合專家）架構。官方數字是 125B 總參數、",[140,1725,1726],{},"6B 激活","：每個 token 的計算量，大約等於一個 6B 模型。",[108,1729,1730],{},"打個比方：傳統稠密模型是「公司裡每個部門都得參與每一個案子」，MoE 是「只叫相關的幾個部門進來開會」。",[108,1732,1733],{},"所以「算不動」這件事，先解決了一半。",[121,1735,1737],{"id":1736},"第二個限制把整台電腦當成一台機器","第二個限制：把整台電腦當成一台機器",[108,1739,1740,1741,143],{},"但 6B 的計算量，不代表 6B 的記憶體——",[140,1742,1743],{},"125B 的權重還是得存在某個地方",[108,1745,1746],{},"Strata 的做法是不要全部塞進顯存，按「多常用」分三層放（見圖 1）：",[840,1748,1749,1762],{},[843,1750,1751],{},[846,1752,1753,1756,1759],{},[849,1754,1755],{},"層",[849,1757,1758],{},"放什麼",[849,1760,1761],{},"佔用",[856,1763,1764,1775,1786],{},[846,1765,1766,1769,1772],{},[861,1767,1768],{},"顯存 VRAM",[861,1770,1771],{},"最常命中的專家",[861,1773,1774],{},"12–24 GB",[846,1776,1777,1780,1783],{},[861,1778,1779],{},"系統記憶體",[861,1781,1782],{},"全部專家（開機時載入）",[861,1784,1785],{},"約 47 GB",[846,1787,1788,1791,1794],{},[861,1789,1790],{},"SSD",[861,1792,1793],{},"其餘權重與 n-gram 查表",[861,1795,1796],{},"檔案總量 70–80 GB",[108,1798,1799],{},"（47GB 是那位開發者在 IQ3_S 量化下的實測；官方建議 64GB 記憶體就是為了裝下這一層。）",[108,1801,1802],{},"跑起來的時候，GPU 算它手上的專家；沒命中的，要嘛走 PCIe 搬進顯存，要嘛直接讓 CPU 用記憶體裡的權重算。",[108,1804,1805,1806,143],{},"這就是為什麼 12GB 的卡能跑——",[140,1807,1808],{},"顯存不再是「裝不裝得下」的容器，而是「快取多大」的問題",[108,1810,1811],{},[1812,1813],"img",{"alt":1814,"src":1815},"如圖 1：三層記憶體階層——顯存放熱門專家、記憶體放全部專家、SSD 放冷門權重與 n-gram 查表","\u002Fimages\u002Fblog\u002Fstrata-125b-on-12gb\u002F01-memory-tiers.svg",[121,1817,1819],{"id":1818},"還有一個加速器猜然後驗證","還有一個加速器：猜，然後驗證",[108,1821,1822],{},"除了省記憶體，Strata 還用了投機解碼：小模型先猜接下來幾個 token，大模型一次驗證。",[108,1824,1825],{},"猜對就省下好幾步，官方數字大約快 1.6–1.8 倍。",[121,1827,1828],{"id":1828},"實際多快",[108,1830,1831],{},"官方在 RTX 5070（12GB 顯存、64GB RAM）上測到的：",[840,1833,1834,1847],{},[843,1835,1836],{},[846,1837,1838,1841,1844],{},[849,1839,1840],{},"量化",[849,1842,1843],{},"寫答案",[849,1845,1846],{},"讀 prompt（32K）",[856,1848,1849,1860,1871,1882],{},[846,1850,1851,1854,1857],{},[861,1852,1853],{},"Q2_0",[861,1855,1856],{},"94 tok\u002Fs",[861,1858,1859],{},"2,650 tok\u002Fs",[846,1861,1862,1865,1868],{},[861,1863,1864],{},"IQ2_XS",[861,1866,1867],{},"79 tok\u002Fs",[861,1869,1870],{},"2,090 tok\u002Fs",[846,1872,1873,1876,1879],{},[861,1874,1875],{},"IQ3_XXS",[861,1877,1878],{},"62 tok\u002Fs",[861,1880,1881],{},"1,750 tok\u002Fs",[846,1883,1884,1887,1890],{},[861,1885,1886],{},"IQ3_S",[861,1888,1889],{},"53 tok\u002Fs",[861,1891,1892],{},"1,620 tok\u002Fs",[108,1894,1895,1896,1899],{},"24GB 的卡更快。那位開發者在他的 4090 + 64GB RAM 上實測：",[140,1897,1898],{},"解碼約 140 tok\u002Fs、prefill 約 4,400 tok\u002Fs","，256K 上下文開滿也還跑得動。",[778,1901,1902],{},[108,1903,1904],{},"他第一次測到 203 tok\u002Fs，後來發現是 benchmark 沒把 reasoning 時間與快取命中算進去。修正後才是 140。這種「先懷疑自己的量測」比數字本身更有價值。",[108,1906,1907,1908,1911],{},"要注意上面那張表的「讀 prompt 2,650 tok\u002Fs」是快取熱起來之後的數字。",[140,1909,1910],{},"冷啟動第一次讀長文會慢很多","——官方文件寫的是每 30,000 tokens 約一分鐘，大約 500 tok\u002Fs。",[121,1913,1914],{"id":1914},"代價",[108,1916,1917,1920],{},[140,1918,1919],{},"一、量化到 2-bit。"," 94 tok\u002Fs 是 Q2_0 的數字，那是很兇的壓縮。要品質就得犧牲速度——IQ3_S 剩 53 tok\u002Fs。這是取捨，不是免費的。",[108,1922,1923,1926],{},[140,1924,1925],{},"二、記憶體與啟動。"," 開機要把 35–55GB 載進記憶體，電腦會卡 1–3 分鐘；整個程序佔用超過 50GB。32GB 的機器只能跑 Coder 變體（砍掉一半專家），官方也提醒它在中文本表現較弱。",[108,1928,1929,1932],{},[140,1930,1931],{},"三、一次一個請求。"," 預設不支援併發，第二個請求要排隊。開併發得調參數，12GB 的卡上會讓每個回答變慢。",[121,1934,1935],{"id":1935},"調參的迷思",[108,1937,1938],{},"Strata 有不少參數可調：PCIE_FRAC（GPU 與 CPU 怎麼分攤計算）、CPU Workers、MTP 深度、KVGROW。",[108,1940,1941,1942,143],{},"那位開發者花了大量時間做矩陣測試，他的結論是：",[140,1943,1944],{},"官方自動校準就夠了",[108,1946,1947,1948,1951],{},"他自己測出的「快 5%、快 9%」，多跑幾輪就消失，有時候還反過來。原因是速度受當下生成的內容、專家路由狀態、MTP 命中率、GPU 快取影響——這些變異比參數本身還大。這是",[140,1949,1950],{},"在他那台機器上","的結論，換硬體要重新驗證。",[108,1953,1954,1955,1958],{},"有一個參數值得單獨提：",[140,1956,1957],{},"KVGROW","。預設開 256K 上下文時，引擎會先把整段 KV cache 的顯存預留起來，結果短對話也沒位置放熱專家，速度掉到最慢檔。KVGROW 讓 cache 跟著實際用量長大：短對話快，長對話才讓位。",[121,1960,1962],{"id":1961},"所以該不該自架","所以，該不該自架？",[108,1964,1965],{},"先把興奮放一邊，算一算。匯率抓 1 美元 ≈ NT$31.5。",[108,1967,1968,1969,1972],{},"Qwen3.8-Flash 的 API 價格是 ",[140,1970,1971],{},"$0.16 \u002F 百萬 input token、$0.47 \u002F 百萬 output","——output 是 input 的三倍，這段先只算 input，方便比較。",[108,1974,1975],{},"一台跑得舒服的機器（4090 或同級 + 64GB RAM）大約台幣 8–10 萬。",[840,1977,1978,1991],{},[843,1979,1980],{},[846,1981,1982,1985,1988],{},[849,1983,1984],{},"每月 input 用量",[849,1986,1987],{},"API 成本",[849,1989,1990],{},"自架電費",[856,1992,1993,2004,2014],{},[846,1994,1995,1998,2001],{},[861,1996,1997],{},"1,000 萬 token",[861,1999,2000],{},"約 NT$50",[861,2002,2003],{},"NT$250–370",[846,2005,2006,2009,2012],{},[861,2007,2008],{},"1 億 token",[861,2010,2011],{},"約 NT$500",[861,2013,2003],{},[846,2015,2016,2019,2022],{},[861,2017,2018],{},"10 億 token",[861,2020,2021],{},"約 NT$5,000",[861,2023,2003],{},[108,2025,2026],{},"電費怎麼算的：推論時約 350W，每天用兩小時、其餘時間閒置 80W，一個月約 74 度；台電累進電價抓每度 NT$3–5，就是每個月 250–370 元。24 小時滿載的話是 250 度左右，大約 NT$750–1,250。",[108,2028,2029,2030,2033],{},"看表就知道結論：",[140,2031,2032],{},"每月十億 token 以下，API 連電費都比較便宜","，還沒算機器折舊。",[108,2035,2036,2037,2041],{},"粗算回本點：",[2038,2039,2040],"code",{},"10 萬 ÷ (5,000 − 370) ≈ 22 個月","——那是每月十億 token 的量才成立。對絕大多數中小企業，這個量級不會出現。",[108,2043,2044],{},"那自架還有什麼意義？三個：",[902,2046,2047,2053,2059],{},[812,2048,2049,2052],{},[140,2050,2051],{},"隱私","：資料不出門。這是最難用錢換的",[812,2054,2055,2058],{},[140,2056,2057],{},"離線","：工廠、船上、沒有網路的現場",[812,2060,2061,2064],{},[140,2062,2063],{},"不受限","：不用擔心費率調整、政策變更、API 下架",[108,2066,2067],{},"如果你不屬於這三種，用 API 就好，而且會用得比自架開心。",[121,2069,2070],{"id":2070},"真正的重點",[108,2072,2073],{},"這篇想說的不是「125B 好強」。",[108,2075,2076,2077,2080],{},"是",[140,2078,2079],{},"模型大小已經不能拿來判斷硬體需求了","。同樣 125B，你可以用 360GB 的伺服器跑，也可以用 12GB 的遊戲卡跑——差別只在於有沒有人幫你把記憶體階層調度好。",[108,2082,2083,2084,2087,2088,2092],{},"這也是我們做",[157,2085,2086],{"href":1594},"地端部署","時真正在處理的問題：不是「這顆模型跑不跑得動」，而是「你的瓶頸在哪一層」。我們在",[157,2089,2091],{"href":2090},"\u002Fwork\u002Fembedded-vision-background","資源受限裝置","上累積的經驗，換到 LLM 上其實是同一件事。",[108,2094,2095],{},"如果你正在評估要不要自架，先問三個問題：",[809,2097,2098,2104,2110],{},[812,2099,2100,2103],{},[140,2101,2102],{},"每月 token 量有沒有到億級？"," 沒有，API 幾乎一定更划算。",[812,2105,2106,2109],{},[140,2107,2108],{},"資料能不能出門？"," 不能，才輪到自架。",[812,2111,2112,2115],{},[140,2113,2114],{},"有沒有 64GB 記憶體與一張 12GB 以上的卡？"," 沒有，連門檻都不到。",[108,2117,2118],{},"三題有兩題是「否」，答案就是 API。",{"title":418,"searchDepth":419,"depth":419,"links":2120},[2121,2122,2123,2124,2125,2126,2127,2128,2129,2130],{"id":1670,"depth":419,"text":1670},{"id":1695,"depth":419,"text":1696},{"id":1719,"depth":419,"text":1720},{"id":1736,"depth":419,"text":1737},{"id":1818,"depth":419,"text":1819},{"id":1828,"depth":419,"text":1828},{"id":1914,"depth":419,"text":1914},{"id":1935,"depth":419,"text":1935},{"id":1961,"depth":419,"text":1962},{"id":2070,"depth":419,"text":2070},"\u002Fimages\u002Fblog\u002Fstrata-125b-on-12gb.svg","125B 模型跑在 12GB 顯卡上的示意圖","2026-10-24","Strata 讓 125B 的 Qwen3.8-Flash-Next 跑在 12GB 顯卡的遊戲機上，解碼 94 tok\u002Fs。拆解它靠什麼做到、代價在哪裡，以及中小企業該不該自架。",{},"\u002Fimages\u002Fblog\u002Fstrata-125b-on-12gb.jpg","\u002Fblog\u002Fzh-tw\u002Fstrata-125b-on-12gb",{"title":1648,"description":2134},"strata-125b-on-12gb","blog\u002Fzh-TW\u002Fstrata-125b-on-12gb",[2142,2143,2144],"local-llm","qwen","inference","AzAFYoV9JKM6X1-qHOAhv64-PaZVkfvITS_J8_39_Oc",1793255763659]