Python Code (NumPy) '''Python import numpy as np # ==================================== # E8 Weyl Group - Simple Reflection Matrices # ==================================== # Simple roots for E8 (standard realization, ||alpha_i||^2 = 2) # Chain: alpha1 to alpha7 # Branched root: alpha8 (adjust last coordinate if needed for exact Cartan matrix) simple_roots = np.array([ [ 1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0], # alpha1 [ 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 0.0, 0.0], # alpha2 [ 0.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 0.0], # alpha3 [ 0.0, 0.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0], # alpha4 [ 0.0, 0.0, 0.0, 0.0, 1.0, -1.0, 0.0, 0.0], # alpha5 [ 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0, 0.0], # alpha6 [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 1.0, -1.0], # alpha7 [-0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5, -0.5], # alpha8 (branched) ], dtype=float) # Reflection matrix: s_i = I - alpha_i @ alpha_i^T (since ||alpha||^2 = 2) def reflection_matrix(alpha): return np.eye(8) - np.outer(alpha, alpha) # Generate all 8 reflection matrices reflection_matrices = [reflection_matrix(alpha) for alpha in simple_roots] # ==================================== # Verification # ==================================== print("=== E8 Simple Reflection Matrices (s1 to s8) ===\n") for i, mat in enumerate(reflection_matrices, 1): print(f"s{i} =") print(np.round(mat, decimals=6)) # rounded for readability print() # Quick sanity check: s_i @ s_i should be close to Identity print("=== Sanity Check: s_i @ s_i ≈ I (max error) ===") for i, mat in enumerate(reflection_matrices, 1): err = np.max(np.abs(mat @ mat - np.eye(8))) print(f"s{i} error: {err:.2e}") print("\nCode ready. These 8 matrices generate W(E8) of order 696729600.") print("They seed the finite exceptional symmetry that participates in the E_∞ attractor across layers.") ''' === E8 Simple Reflection Matrices (s1 to s8) === s1 = [[0. 1. 0. 0. 0. 0. 0. 0.] [1. 0. 0. 0. 0. 0. 0. 0.] [0. 0. 1. 0. 0. 0. 0. 0.] [0. 0. 0. 1. 0. 0. 0. 0.] [0. 0. 0. 0. 1. 0. 0. 0.] [0. 0. 0. 0. 0. 1. 0. 0.] [0. 0. 0. 0. 0. 0. 1. 0.] [0. 0. 0. 0. 0. 0. 0. 1.]] s2 = [[1. 0. 0. 0. 0. 0. 0. 0.] [0. 0. 1. 0. 0. 0. 0. 0.] [0. 1. 0. 0. 0. 0. 0. 0.] [0. 0. 0. 1. 0. 0. 0. 0.] [0. 0. 0. 0. 1. 0. 0. 0.] [0. 0. 0. 0. 0. 1. 0. 0.] [0. 0. 0. 0. 0. 0. 1. 0.] [0. 0. 0. 0. 0. 0. 0. 1.]] s3 = [[1. 0. 0. 0. 0. 0. 0. 0.] [0. 1. 0. 0. 0. 0. 0. 0.] [0. 0. 0. 1. 0. 0. 0. 0.] [0. 0. 1. 0. 0. 0. 0. 0.] [0. 0. 0. 0. 1. 0. 0. 0.] [0. 0. 0. 0. 0. 1. 0. 0.] [0. 0. 0. 0. 0. 0. 1. 0.] [0. 0. 0. 0. 0. 0. 0. 1.]] s4 = [[1. 0. 0. 0. 0. 0. 0. 0.] [0. 1. 0. 0. 0. 0. 0. 0.] [0. 0. 1. 0. 0. 0. 0. 0.] [0. 0. 0. 0. 1. 0. 0. 0.] [0. 0. 0. 1. 0. 0. 0. 0.] [0. 0. 0. 0. 0. 1. 0. 0.] [0. 0. 0. 0. 0. 0. 1. 0.] [0. 0. 0. 0. 0. 0. 0. 1.]] s5 = [[1. 0. 0. 0. 0. 0. 0. 0.] [0. 1. 0. 0. 0. 0. 0. 0.] [0. 0. 1. 0. 0. 0. 0. 0.] [0. 0. 0. 1. 0. 0. 0. 0.] [0. 0. 0. 0. 0. 1. 0. 0.] [0. 0. 0. 0. 1. 0. 0. 0.] [0. 0. 0. 0. 0. 0. 1. 0.] [0. 0. 0. 0. 0. 0. 0. 1.]] s6 = [[1. 0. 0. 0. 0. 0. 0. 0.] [0. 1. 0. 0. 0. 0. 0. 0.] [0. 0. 1. 0. 0. 0. 0. 0.] [0. 0. 0. 1. 0. 0. 0. 0.] [0. 0. 0. 0. 1. 0. 0. 0.] [0. 0. 0. 0. 0. 0. 1. 0.] [0. 0. 0. 0. 0. 1. 0. 0.] [0. 0. 0. 0. 0. 0. 0. 1.]] s7 = [[1. 0. 0. 0. 0. 0. 0. 0.] [0. 1. 0. 0. 0. 0. 0. 0.] [0. 0. 1. 0. 0. 0. 0. 0.] [0. 0. 0. 1. 0. 0. 0. 0.] [0. 0. 0. 0. 1. 0. 0. 0.] [0. 0. 0. 0. 0. 1. 0. 0.] [0. 0. 0. 0. 0. 0. 0. 1.] [0. 0. 0. 0. 0. 0. 1. 0.]] s8 = [[ 0.75 -0.25 -0.25 -0.25 -0.25 -0.25 -0.25 -0.25] [-0.25 0.75 -0.25 -0.25 -0.25 -0.25 -0.25 -0.25] [-0.25 -0.25 0.75 -0.25 -0.25 -0.25 -0.25 -0.25] [-0.25 -0.25 -0.25 0.75 -0.25 -0.25 -0.25 -0.25] [-0.25 -0.25 -0.25 -0.25 0.75 -0.25 -0.25 -0.25] [-0.25 -0.25 -0.25 -0.25 -0.25 0.75 -0.25 -0.25] [-0.25 -0.25 -0.25 -0.25 -0.25 -0.25 0.75 -0.25] [-0.25 -0.25 -0.25 -0.25 -0.25 -0.25 -0.25 0.75]] === Sanity Check: s_i @ s_i ≈ I (max error) === s1 error: 0.00e 00 s2 error: 0.00e 00 s3 error: 0.00e 00 s4 error: 0.00e 00 s5 error: 0.00e 00 s6 error: 0.00e 00 s7 error: 0.00e 00 s8 error: 0.00e 00 Code ready. These 8 matrices generate W(E8) of order 696729600. They seed the finite exceptional symmetry that participates in the E_∞ attractor across layers.

(avec le code Alpha5 bien sur)

お疲れ様です！ 奈良の銘酒「風の森 ALPHA5」をいただきました✨ ひと口呑んだ瞬間、 「え？これ本当に日本酒！？」ってなるくらいフレッシュ。 シュワっとしたガス感と、 お米の甘みが口いっぱいに広がってめちゃくちゃ呑みやすい😳 ブチうまでした👍🏻 #風の森 #ALPHA5 #日本酒

The Alpha5 is a sleek EV sedan penned by ItalDesign—whose founder, Giorgetto Giugiaro, created the origami form of the original DMC-12. motortrend.com/news/delorean…

alpha5/15号を全部読めたら、またニュースで学ぶ現代英語を聴きはじめようかな。伊藤サム先生のだけ、とか。 全部手を出すとまた「どれだけ頑張ったら、いつになったら、私は英語を理解できるようになるのか」という暗黒モードに入ってしまいそうなので…

币安alpha5积分活动 📅 活动时间：2026年5月14日 08:00 - 5月28日 07:59 ✅ 参与方式： 1⃣下载币安钱包插件 🔗chromewebstore.google.com/de… 2⃣单笔购买任意Alpha代币 ≥50美元

If you're looking to buy something nostalgic with a real history, then @DeloreanLabs $DMC will definitely catch your eye. This token connects the iconic car brand to a Web3/RWA-style ecosystem. What I'm keeping an eye on: • DeLorean brand awareness • Blockchain-based car reservations • Potential for a construction slot market • Potential for Alpha5 use • Solana expansion will attract more attention from retailers • And now even the fun AI-powered "Doodles x DeLorean Labs" contest -time travel vibes are back 🚗⚡🌀 $DMC is still highly speculative, having fallen significantly from its all-time high, and the main question is whether the token can meet real demand from the DeLorean ecosystem, rather than simply exploiting nostalgia. For me, this is more of an investment idea for small-cap stocks than an all-or-nothing deal. If real trading volumes emerge, utility for vehicles, and demand for tokens emerge, the upside potential could be interesting. Otherwise, it will remain an interesting token with a legendary name. I'm keeping a close eye on it. #DMC #DeLorean #Doodles #RWA #Web3 #Crypto #Solana #Ethereum #RealWorldAssets #Tokenization #Alpha5

K-Shoot Editor v2.0.0-alpha5とかいうゲーム飽きた🫠

DeLorean $DMC going live on @solana through @sunrisedefi is a fun one • real global brand • originally launched on SUI • Alpha5 reservation slots (new DeLorean EV) • ownership and vehicle data onchain • now available across Solana apps (@solflare included) The teaser had plenty of culture nods: @bonk_inu, @pudgypenguins, @moonbirds and @doodles And with Solana Accelerate references in the video, it feels like there may be more to watch during the event Another one @DeLoreanlabs Bullish. x.com/solana/status/20513030…

Stephen Wynne herhalde hala haklarına sahip. İşin en temizi satması. alpha5 de çıkmadı.

MATCH DAY 🔥 B.Times 2. gün başlıyor! Bu akşam sahne bizim. 🆚 Alpha5 ⏰ 19:00 🎯 BO3 Hedefimiz net: galibiyet. Desteklerinizi bekliyoruz! 💪 #WeAreFuture #MatchDay #FORZATG #TGWİN

Time travel isn’t sci-fi anymore — it’s being rebuilt in real life, one on-chain mile at a time. ⚡🚗 That’s why I keep my eyes on $DMC. Not just hype — real machines, real ownership, real future. While others simulate value, DeLorean Motor Company is putting it on-chain with the DeLorean Alpha5 powered by Sui Network. Feels less like speculation… and more like stepping into Back to the Future — but this time it’s real. $DMC 🫡

【CrossTie 1.0.0-Alpha5 has released】 github.com/suzumiyatrainer/C…

亀泉 大那夢ささら 田酒純米大吟醸 風の森ALPHA5 流石に飲みすぎた🤣お酒のラインナップ良すぎて怖い🥰 お店出る時、店員さんにこんだけ呑んで正常な状態で帰るグループはなかなかすごい…って驚かれた🤣🤣 お店来る前からすでに呑んでたっていえなかった🤣🤣1日付き合ってくれてありがとう🫶

Im pretty sure this story has been floated before but im sorry this just looks like a reskinned Alpha5

ALPHA5周年お祝いパーティーなうですが私はほぼヤケ酒です🤣🤣🤣

My problem with the movie is that it kinda took itself too seriously, like "Oh we're not THOSE Power Rangers, we're your big brothers Power Rangers." The best bit was when Alpha5 shouted "Go go Power Rangers!" and the theme song played.

【α版エディタ】K-Shoot Editor v2.0.0-alpha5を試験公開しました bbs.kshootmania.com/thread/1… ＜主な変更点＞ ・音声ファイルへのレンダリング機能を追加 ・音声エフェクト定義をテキストで編集する機能を追加 ・各種オプションを次回起動時にも記憶するかどうかを設定可能に ・その他バグ修正

ALPHA 5 IS LIVE ✨🔥 - With combat (😎) - With bugs fixed - With Google login - With spring props on your planets - With Character Customization Time to play 📌 play.google.com/store/apps/d… #alpha5 #indiegamedev

Remember the DeLorean Alpha5 concept? Hot Wheels did. And Italdesign won a 4.) million dollar judgment against DeLorean for unpaid work on this piece of vaporware.