How can a function be undefined at one point yet approach a precise value nearby? Direct substitution: real number → found. Nonzero/zero → asymptote. Zero/zero → rewrite via factoring, conjugates, or trig identities, then substitute. Graphs/tables if algebra fails. Limits power derivatives for robot control, ML gradients, and physics. Useful values often hide where the function is silent. Where have you seen a limit resolve what direct calculation could not?

The agent converts a named export to a default export. The old `import { getUser }` now resolves to undefined. No build error. The first caller that actually fires it gets `getUser is not a function` deep in a route handler. Where does your build catch shape drift between export sites?

🚨NEW: The @USOCC and @FDICgov are moving to finalize a rule that would define the term “unsafe or unsound practices” in relation to bank supervision. This term has been undefined for years, and has relied on the broad discretion of bank examiners. The rule would require supervisors to tie alleged unsafe or unsound practices to an actual violation of law or material financial risk, making it harder to use vague reputational or procedural concerns to pressure banks over lawful customers, including crypto companies. It marks another significant step toward unwinding “Operation Choke Point 2.0.”

Phew, Grok Build is really thorough, pretty incredible. Relay feature for PasteLocal is done, pushing to Github now. And if you want to know what this adds, here's a bit more about it, this is a feature I really wanted in there, and honestly didn't really expect to have done this week. • Per-peer E2E encryption: clipboard data is encrypted individually for each paired device using X25519 + HKDF + AES-GCM (no plaintext ever leaves the client) • Durable persistence: relay state is now stored in an atomic state.json with proper TTL handling and compaction. Pending clips survive relay-server restarts • Safe compaction: fixed unsafe map mutation during expiration/compaction that could cause data loss or undefined behavior • Full bidirectional CLI: new commands: pastelocal relay send, inbox, fetch, and status, plus pastelocal-remote --relay --peer --send • Auto-sync: when watch.enabled + are on, meaningful clipboard changes are automatically pushed to paired devices • Improved DX: doctor checks are now only shown when relay is enabled, and the TUI shows basic relay status • Multiple review cycles: went through full implement → review → fix → re-review (effort 4), plus a final targeted regression fix round Try it out and please send any and all feedback!

The Schrödinger Equation Can Fold Phase Into Geometry. Density is only half the story. Here, the quantum phase itself twists into moving helicoidal ribbons, while self-gravity from the Schrödinger-Poisson coupling bends and compresses the wavefield into glowing caustics and vortex singularities. Tiny white pearls mark places where the phase becomes undefined topological defects drifting through a self-generated gravitational landscape. #QuantumPhysics# #WaveFunction# #SchrodingerEquation# #ComputationalPhysics# #ScientificVisualization# #Mathematics#

Hot take on today’s AI framework: these issues are so complex that even a pro-AI administration is deferring the hardest calls to Congress and the courts. This framework signals momentum and kudos to those who did such important work on it. But it still leaves open some thorny questions: -Federal preemption sounds clean, but could the undefined “traditional state police powers” carveout swallow it whole? -LLM copyright? Handed to the courts—leaving massive, open-ended risk on both liability and damages. SCOTUS likely won't take up the issue until there's a circuit split which will take many years. Meanwhile the race is on to file in district courts, as happened again in San Jose just this week (BMG case). Translation: clarity on paper, uncertainty in practice.

# Decision Points for Embedding AI Agents in Enterprise Systems # Pre-verification vs Post-verification 🎯 The Hook Are you applying the same verification policy to every agent output? Irreversible operations demand pre-verification, but applying pre-verification to information-only responses collapses throughput. If you do not design this fork based on the reversibility and impact of side effects, you will sacrifice either safety or speed — unnecessarily 🔑 📋 Overview Pre-verification is the right choice when the agent's operations have irreversible side effects: payment execution, contract signing, data deletion, production deployment. Mistakes directly translate to financial damage, legal liability, or brand harm. Salary changes in Workday, contract amount modifications in Salesforce, and bulk price adjustments in Shopify are textbook examples. Pre-verification is also mandatory when regulatory compliance requires pre-execution approval, or when incorrect outputs cannot be tolerated — medical, financial, or legal advice. Post-verification fits cases where output is informational only with no side effects, or where side effects are reversible and easily undone. Information summaries in Slack, document draft generation in Notion, and ticket classification suggestions in Jira fall into this category 📊 🔍 Decision Points Follow this flow: Does the operation have side effects? → No (information only) means post-verification is sufficient Are the side effects reversible? → Reversible means post-verification + automatic rollback works Are the side effects irreversible? → Irreversible means pre-verification is mandatory What is the blast radius? → Limited to one user vs. affecting all customers determines pre-verification intensity Do regulations mandate pre-approval? → Financial transactions, HR changes, and medical domains may require it Can confidence scores be leveraged? → Route below-threshold outputs to pre-verification, above-threshold to post-verification ⚡ 💡 Key Details The standard production configuration is a dual-track setup combining pre and post verification: Risk-level routing: Classify operations by risk upfront. High-risk operations (irreversible, high-impact) route to the pre-verification track. Low-risk operations (informational, reversible) route to the post-verification track. Routing is automatic. Gradual relaxation: Start with all operations on pre-verification. As trust accumulates for specific categories, progressively migrate them to post-verification. Measure quality continuously and adjust thresholds. Confidence score integration: Attach confidence scores to agent outputs and use threshold-based routing to automatically assign verification tracks. Set initial thresholds conservatively and calibrate with real data. In Zendesk customer support, answer draft generation belongs on the post-verification track (sampling review), while refund processing belongs on the pre-verification track (human approval required) 🔄 ⚖️ Trade-offs Putting irreversible operations on post-verification is the most dangerous design mistake. Bulk-deleting Shopify products and then reviewing the output is a path to unrecoverable disaster 😩 Putting everything on pre-verification is equally problematic. Requiring human approval for search result display drops agent response times to minutes, and users simply stop using the system. Having no actual post-verification mechanism is another overlooked failure mode. Operations are classified as post-verification, but no one actually reviews them, and quality degrades silently. Define sampling rates and quality metric thresholds explicitly. Stale risk classifications are dangerous too. Newly added operations default to post-verification when their risk level is undefined. Make risk classification a mandatory step whenever a new tool or API is added ⚠️ 🛠️ Use Cases Customer support (Zendesk): Customer-facing answer draft generation runs on post-verification (10% sampling review for quality monitoring). Refund and credit processing runs on pre-verification (approver level varies by amount). Product exchange arrangements run on pre-verification (inventory check → approval → execution as a deterministic workflow) 📚 HR systems (Workday): Employee information search and display runs on post-verification (no side effects). Salary changes and transfer procedures run on pre-verification (regulatory requirements mandate approval). Org chart changes run on pre-verification with dual approval (broad impact scope) 🛒 E-commerce operations (Shopify): Product information search and analysis runs on post-verification. Minor inventory quantity adjustments run on pre-verification (reversible but immediately impactful). Bulk price changes and product deletion run on pre-verification with dry-run and dual approval (irreversible, high-impact) 🔧 Practical tip: Make "update the risk classification whenever a new tool or API is added" a mandatory team process. Unclassified operations defaulting to post-verification is not an intentional design — it is an oversight 💪 #AIAgents# #EnterpriseArchitecture#

# Useful but Little-Known Features of ADK 2.0 🌍 What if your agent could dynamically pick the best LLM for each request, balancing cost and quality on the fly? ADK 2.0's model routing uses the RoutedLlm class and LlmRouter function to dynamically select which model handles each request. 📌 Title: Model Routing 🔗 URL: 🧩 Overview The RoutedLlm class enables dynamic model selection from a pool of LLMs on a per-request basis. An LlmRouter function receives the map of available models, the current request, and an error context, then returns the key of the model to use. If a model fails before producing output, the router is called again with the error information, allowing automatic fallback to a different model. Note that you cannot switch models mid-stream once `connect()` has started. 🛠 How to use it Define an LlmRouter function and pass it to RoutedLlm as the agent's model. ```typescript import { BaseLlm, Gemini, LlmRequest, LlmAgent, RoutedLlm } from '@google/adk'; const myRouter = ( models: Readonly>, request: LlmRequest, errorContext?: { failedKeys: ReadonlySet; lastError: unknown }, ) => { if (!errorContext) { return 'primary'; // Try the powerful model first } if (errorContext.failedKeys.has('primary')) { return 'fallback'; // Fall back to the lightweight model on failure } return undefined; // No more options, propagate the error }; const agent = new LlmAgent({ name: 'smart_agent', model: new RoutedLlm({ models: { primary: new Gemini({ model: 'gemini-pro-latest' }), fallback: new Gemini({ model: 'gemini-flash-latest' }), }, router: myRouter, }), instruction: 'Process the task', }); ``` Unlike agent routing (switching between agents), model routing keeps the same agent logic and only changes the underlying model. 🏗 Building it into production ・Configure automatic fallback to a backup model when the primary model fails ・Route based on request complexity to optimize costs between powerful and lightweight models ・Implement A/B testing routers to compare model performance in production ・Log model selection decisions for cost analysis and performance optimization 💡 Use cases 🔄 Automatic failover when the primary model goes down 💰 Cost-optimized routing based on request complexity 🧪 A/B testing new vs. existing models for performance comparison 🌍 Model selection based on request language or region ⚠️ Watch out Model routing is experimental and available in ADK TypeScript v1.0.0 and later. You cannot switch models mid-stream after `connect()` has started. Overly complex router logic becomes hard to debug and maintain — keep your selection criteria simple. Also, verify that your fallback model supports the same capabilities as the primary model before relying on it in production. ✨ Model routing gives you dynamic control over availability, cost, and quality — making agent operations in production far more flexible and resilient. #ADK# #AIAgent#

I’ve built HFT/exchange systems in three languages that sit at very different points on the safety/performance/ergonomics spectrum: OCaml, C++, and Rust. Observations and a practical comparison from production use: OCaml • Strong static typing and algebraic data types make illegal states almost impossible to represent. Protocol parsers, order book models, and risk checks are self-documented by types and function signatures. • The default garbage collector is a non-starter for predictable tail latencies. There are workarounds using disciplined zero-allocation techniques: custom core libraries, careful use of the [@ inline] and [@ unboxed] attributes, and a culture that treats any heap allocation in the hot loop as a bug. • Functional programming forces strategy writers to think in pure transformations of market data to fair values to orders. This style enables multiple forms of unit testing and makes offline model training pipelines easier to implement without major code changes. • The ecosystem for kernel-bypass networking and FPGA offload is thin; performant OCaml requires writing a fair amount of C interop or custom FFI. Compile times and binary size can also become painful at scale. • Engineering effort on type safety is a replacement for future engineering effort on debugging. We used to half-joke, “if it compiles, it works.” C++ • The most commonly used language in HFT because it offers maximum control. The writer can pinpoint every cache line, allocation, and branch. When the last microseconds matter, few languages can compete. • Industry standard for exchange connectivity, FPGA drivers, and shared-memory IPC. Virtually every low-latency NIC vendor’s API is written for it. • The cost is constant vigilance. Use-after-free, data races, and subtle ABI mismatches are permanent time sinks. Even with modern C++ features such as concepts, spans, and std::atomic memory orders, the cognitive load stays high. • Template metaprogramming offers some of the type-level guarantees of OCaml or Rust, but the error messages and compile times can be inscrutable. • Most of the “C++ is faster” advantage narrows when factoring in the engineering time spent hunting undefined behavior. Rust • Ownership and borrowing give the memory-safety guarantees of a garbage-collected language with the performance profile of C++. Zero-cost abstractions allow HFT system authors to write zero-allocation, lock-free, cache-aware code and the compiler will refuse to allow introduction of data races. • Excellent for the modern low-latency stack: DPDK/AF_XDP bindings, io_uring, shared-memory rings, and safe wrappers around exchange binary protocols. • The type system is expressive enough to encode many of the same invariants of OCaml, such as phantom types, newtypes, and state machines, without the garbage-collection tax. • The borrow checker still occasionally forces awkward redesigns of hot-path data structures, async/await is not yet as mature for ultra-low-latency work as plain threads/ busy-polling, and the ecosystem for certain HFT-specific libraries lags C++. • It takes time for the ownership model to click, after which mental bandwidth can be dedicated to strategy and latency. It’s much more difficult to build a high-frequency trading system that retains correctness and readability as it scales than it is to build one that’s fast. Good taste and developer culture can coalesce around a particular language, but the best teams possess these qualities independently, and can adapt freely and agilely to new technologies as they become available.