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Let $f(x) = \sqrt{1 - x ^ 2}$, $f^{(n)}(x)$ be the n-th derivative of $f$.

Based on the Taylor series expansion (around 0), we have:

$$ f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(0)}{n!} x^n $$

So,

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Attempting to migrate his key from a single vulnerable USB, the author realized he had exposed their master secret key for several years. Forced to generate a new one, he added enhanced features like a second identity with their personal domain and Web Key Directory. This ordeal highlights the importance of careful key management while exploring the fun of a mysterious digital identity.

I was chatting in the MCBBS group about ways to prevent your Minecraft account from being stolen. Someone suggested a solution based on logging into players' Microsoft accounts through a third-party service, which would periodically check whether the account still belonged to the same person. You could also actively report that your account had been hacked, and then your account would become unavailable on all servers that had installed his plugin.

That's not a good idea, though, because by doing that, the third party could literally log into any server using your account.

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Okay, welcome back. In this video (It's too long and I didn't publish it, but some later questions are done in live streams), I'm going to go through the Bronze group contest of the U-Cycle, the first contest in 2026. I didn't perform well during the actual contest, so I'm going to review the problems and see if I can solve them all now.

For this video, I’m trying out speech-to-text and might use some AI to summarize it for my blog later. I want to keep the recording short, just to remember the experience. If a video is two hours long, who would watch it, right? It’s more convenient for me to just record my thoughts and let the software handle the transcription. I don't care too much about the post-processing.

I may post separate videos for the three contest questions. This is the first one: "Chip Exchange."

I glanced at the solution earlier and it seemed like there were no loops—just pure math. I thought it wouldn't be too difficult. During the actual contest, I didn't perform well. It was late, I had jus

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Entity ID Wireless Redstone Documentation

Note: This guide assumes basic familiarity with entity-ID-based wireless redstone mechanics.
It consolidates existing knowledge to prevent redundant design work.
For detailed discussions, visit the TickLink Discord.

---

Definition

Each channel has an address, typically set using repeater / comparator chains.

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Frequently Asked Questions

Q: What about stability?
A: Very high on the server, though not 100%. I haven't experienced a false signal caused by that reason in my life yet. For local (integrated) servers, stability is moderate, but a fix can be applied.
As the machine loaded, there's nearly always a false signal, which is easy to prevent.

Q: Can it transmit signals between dimensions?
A: No.

Q: Does it work in the Nether or the End?

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The author details recent technical maintenance, addressing a React security patch, deprecating old APIs, and resolving Vercel timeouts by enabling Fluid Computing. Faced with static site generation needs, they migrated from React/Next.js to Nuxt, optimizing caching for performance. They also implemented a custom email domain via Mailgun and updated site copyrights to 2026. Additionally, they discuss efficiency improvements in a Minecraft datapack (riscvmc) and plans for a RISC-V precompiler.

There's a new critical remote code execution bug in React,
so it took me a while to upgrade all the projects.
And since the IN site is deprecated, the domestic API is useless now.
It still requires a lot of effort to maintain them,
so I just shut them down.

For security reasons, I removed all the tokens and JWKS from the database.

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Facing slow load times with Next.js caching for dynamic blogs, the author designed a custom caching system that serves content instantly, updates in the background, and forces a refresh after a month of inactivity. The blog's storage was also migrated to an S3 proxy and miniserve for efficient file distribution, with edge caching set to six hours. After initial concerns, the system has been running smoothly for two weeks. The author also notes progress on the riscv-mc emulator project.

Continuing from #7, the built-in caching in NextJS wasn't a good fit for my dynamic blogs, pages are loading painfully slowl. So I stayed up late, designed and implemented my own version. It avoids making requests for a certain period of time, and then starts making background requests as visits, so we can still see the content without delay. Finally, it forces a request when nobody has visited it for about a month. I also added the last updated feature from Gist, so it’s even faster.

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Full environment setup (linker script, stubs, startup code) to eliminate initialization problems which lead to subtle and mysterious failures.

Based on riscv GNU toolchain.
I suggest you to use the default link script, and add your memory & stack & heap defination.
But remember, add a ".other: { (.) }", in case of there's some of the sections are not defined in the default script.
This is an example:

/* Copyright (C) 2014-2025 Free Software Foundation, Inc.
   Copying and distribution of this script, with or without modification,
   are permitted in any medium without royalty provided the copyright

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The author developed a custom blog platform to support multi-account blogging and address aesthetic preferences. This post details various technical challenges, including fixing HTML standards for site navigation, resolving caching issues with Next.js, and managing site monitoring. It also covers ongoing website refactoring plans, academic pressures, and side projects like updating riscv-mc content and integrating a music tokenization library.

Well, I wrote this thing over the weekend: https://github.com/JwbFut/simple-gistblog
Mainly because nothing on the market really fits my needs. "JwbFut" is theoretically an organization, so there might be blogs from more than one account, but not many platforms support that.
Also, aesthetics are a bit of an issue with some others.

Then there's SEO stuff. I replaced the icons for all active sites (the main API site and the gistblog) with SVGs.
It's pretty bad, actually. Because the resolution was too low, the left and right halves of the "J" are different thickn

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The author reflects on their summer projects, including a decision to forgo supporting the new FMJ v2. Their primary achievement is creating an optimized RISC-V simulator within Minecraft, capable of running compiled programs like Snake, though they note concerns over its performance with heavy computations. They also discuss refactoring a website with Rust and a large-number calculation datapack.

Alright, um, on topic: there's still no news about Fabric mod JSON v2, so Noglerr isn't adding support. I think even if v2 comes out, I might not bother with cross-version support. I don’t feel like writing Java anymore, not many people use the mods anyway, and I haven’t been working on survival technical Minecraft lately.

This summer break has been pretty unproductive; I haven’t done much, mostly just playing games. BV1gFVLz1ESY got 73,000 views, which is pretty good.

I’ve done a bit of web development. I’m refactoring the entire website, turning the GUI into a CLI program. This whole thing is based on Rust and