Looking for the most recent regular Connections answers? Click here for today’s Connections hints, as well as our daily answers and hints for The New York Times Mini Crossword, Wordle and Strands puzzles.

Today’s Connections: Sports Edition is a tough one. The purple category requires you to mentally add some letters to four words to turn them into sports-related words. If you’re struggling with the puzzle but still want to solve it, read on for hints and the answers.

Connections: Sports Edition is published by The Athletic, the subscription-based sports journalism site owned by The Times. It doesn’t appear in the NYT Games app, but it does in The Athletic’s own app. Or you can play it for free online.

Read more: NYT Connections: Sports Edition Puzzle Comes Out of Beta

Hints for today’s Connections: Sports Edition groups

Here are four hints for the groupings in today’s Connections: Sports Edition puzzle, ranked from the easiest yellow group to the tough (and sometimes bizarre) purple group.

Yellow group hint: Not going up.

Green group hint: Gridiron plan.

Blue group hint: Pacific Northwest teams.

Purple group hint: Add two letters to form a baseball team’s name.

Answers for today’s Connections: Sports Edition groups

Yellow group: Slide.

Green group: Football running plays.

Blue group: An Oregon athlete.

Purple group: MLB teams, minus the last two letters.

Read more: Wordle Cheat Sheet: Here Are the Most Popular Letters Used in English Words

What are today’s Connections: Sports Edition answers?

The yellow words in today’s Connections

The theme is slide. The four answers are decline, dip, downturn and slump.

The green words in today’s Connections

The theme is football running plays. The four answers are counter, dive, draw and sweep.

The blue words in today’s Connections

The theme is an Oregon athlete. The four answers are Beaver, Duck, Thorn and Timber.

The purple words in today’s Connections

The theme is MLB teams, minus the last two letters. The four answers are ange (Angels), dodge (Dodgers), marine (Mariners) and range (Rangers)

Lately, Kegel has been steadily improving its automation, to the point where today’s machines do the entire job without any human intervention.

The lanes you and I bowl on as amateurs are oiled very differently from the ones pros use.

At your local bowling center, public lanes are oiled in what’s referred to as a “high” ratio: The level of oil present in the middle of a lane is eight to 10 times higher than what’s on the outside. At the far left and right of the lane, many public bowling alleys have no oil at all.

“On a normal pattern at your normal bowling center, there is some autocorrect,” Tackett says. Because the edges of the lane have very little oil, shots that drift to either side will slow down; if the ball has been thrown with the proper spin to guide it back toward the middle of the lane, it will curl more effectively on the drier surface. “It makes it easier to hit the pocket.”

(By “the pocket,” Tacket means that sweet spot at the front corner of the standard 10-pin configuration. For right-handed bowlers that’s the space between the first and third pins slightly right of center; for lefties, it’s on the left side.)

In the pros, though, the patterns are far tougher. Instead of 8:1 or even 10:1 ratios of oil in the middle of the lane to the outside, the PBA uses ratios of 3:1 and under—even as low as nearly 1:1 in some cases. Learning how each board is oiled at the start of a match allows the pros to map their ideal shots. “You have to be a lot more precise, not only with where you’re placing the ball on the lane, but with your speed that you’re throwing it and the revolutions that you’re applying to the ball,” Tackett says.

Oil patterns also vary in terms of their length up the 60-foot lane. Many common patterns run for the first 40 feet before the oil tapers off near the pins, but several variations exist.

As lane oil technology has improved, understanding and adjusting to lane oil patterns and ratios has become an outsize tactical element for professional bowlers. Tackett likens it in some ways to golf.

“An oil pattern basically adds water and trees and bunkers,” he says. “It’s adding obstacles to the lane.”

The PBA, the sport’s governing body, likes those comparisons. Rather than using the latest advances in lane oil tech to standardize lanes across every PBA competition, the organization takes the opposite approach, intentionally using varying conditions across different events to challenge top bowlers.

“It forces players to think, adapt, and create, which is how we test greatness,” says Tom Clark, PBA commissioner, via email. “It’s what makes the sport more exciting, interesting, and entertaining every single week.”

The PBA has a library of 20 lane oil patterns for the 2026 season from Kegel, which use varying ratios, lengths, and even specific oil formulations, each of which has its own character. A different pattern is used at virtually every event through the season. For instance, the PBA Tournament of Champions on the week of April 20 used the “Don Johnson 40” pattern, named for famed bowler Don Johnson, with the “40” signifying the length of the pattern in feet.

• Report finds five island nations depend entirely on one vulnerable underwater internet cable
• Accidental ship anchoring causes most global undersea cable failures every year
• Smaller island nations remain dangerously exposed to complete nationwide internet blackouts

A new report has highlighted how all 48 island nations worldwide, including major economies such as the United Kingdom, Japan, and Indonesia, rely on just 126 undersea cables for their internet connectivity.

These cables are often no thicker than a garden hose, making them surprisingly vulnerable to accidental damage or deliberate sabotage.

Amazon’s decision to cut support for older Kindles has pushed some longtime owners toward jailbreaking, a route many never expected to consider.

From May 20, 2026, Kindle devices released in 2012 or earlier will no longer be able to buy, borrow, or download new books directly from Amazon. Books already downloaded will still work, but the store experience is basically being switched off for these devices. Reports now suggest that some users are looking at jailbreaks as a way to keep older Kindles useful instead of replacing hardware that still works.

Why are Kindle owners turning to jailbreaks?

The frustration is not just about losing store access. On Reddit, many users are treating this as another “buying isn’t owning” moment. Several owners say their old Kindles still work perfectly for reading, which makes the shutdown feel unnecessary. Many users see this as a right-to-repair and ownership issue. If an old Kindle still turns on, has a working screen, battery, and buttons, they argue it should not be pushed toward retirement because Amazon has ended software support.

A Kindle jailbreak means removing some of Amazon’s software restrictions so users can install community-made tools and manage the device more freely. In this case, owners are mainly interested in keeping older Kindles useful for reading, sideloading books, and avoiding forced updates that could close those workarounds.

Advertisement

What are the risks of jailbreaking a Kindle?

Jailbreaking is not a clean fix for everyone. The process can fail if users install the wrong files, follow bad instructions, or use a method that does not match their Kindle model or firmware version. In the worst case, the device can become unstable or stop working properly.

In many places, modifying a device for personal use may not automatically be treated as illegal. But using it to break DRM, remove copy protection, or sell modified Kindles can create legal trouble.

Even if Amazon’s decision makes sense from a support and maintenance perspective, it has landed badly with many users. People are tired of electronics being treated as disposable once official support ends. For some older Kindle owners, Jailbreaking is one way to keep those devices out of the e-waste pile.

Retrieval-augmented generation (RAG) has become the de facto standard for grounding large language models (LLMs) in private data. The standard architecture — chunking documents, embedding them into a vector database, and retrieving top-k results via cosine similarity — is effective for unstructured semantic search.

However, for enterprise domains characterized by highly interconnected data (supply chain, financial compliance, fraud detection), vector-only RAG often fails. It captures similarity but misses structure. It struggles with multi-hop reasoning questions like, “How will the delay in Component X impact our Q3 deliverable for Client Y?” because the vector store doesn’t “know” that Component X is part of Client Y’s deliverable.

This article explores the graph-enhanced RAG pattern. Drawing on my experience building high-throughput logging systems at Meta and private data infrastructure at Cognee, we will walk through a reference architecture that combines the semantic flexibility of vector search with the structural determinism of graph databases.

The problem: When vector search loses context

Vector databases excel at capturing meaning but discard topology. When a document is chunked and embedded, explicit relationships (hierarchy, dependency, ownership) are often flattened or lost entirely.

Consider a supply chain risk scenario. While this is a hypothetical example, it represents the exact class of structural problems we see constantly in enterprise data architectures:

• Structured data: A SQL database defining that Supplier A provides Component X to Factory Y.

• Unstructured data: A news report stating, “Flooding in Thailand has halted production at Supplier A’s facility.”

A standard vector search for “production risks” will retrieve the news report. However, it likely lacks the context to link that report to Factory Y’s output. The LLM receives the news but cannot answer the critical business question: “Which downstream factories are at risk?”

In production, this manifests as hallucination. The LLM attempts to bridge the gap between the news report and the factory but lacks the explicit link, leading it to either guess relationships or return an “I don’t know” response despite the data being present in the system.

The pattern: Hybrid retrieval

To solve this, we move from a “Flat RAG” to a “Graph RAG” architecture. This involves a three-layer stack:

1. Ingestion (The “Meta” Lesson): At Meta, working on the Shops logging infrastructure, we learned that structure must be enforced at ingestion. You cannot guarantee reliable analytics if you try to reconstruct structure from messy logs later. Similarly, in RAG, we must extract entities (nodes) and relationships (edges) during ingestion. We can use an LLM or named entity recognition (NER) model to extract entities from text chunks and link them to existing records in the graph.

2. Storage: We use a graph database (like Neo4j) to store the structural graph. Vector embeddings are stored as properties on specific nodes (e.g., a RiskEvent node).

3. Retrieval: We execute a hybrid query:

Reference implementation

Let’s build a simplified implementation of this supply chain risk analyzer using Python, Neo4j, and OpenAI.

1. Modeling the graph

We need a schema that connects our unstructured “risk events” to our structured “supply chain” entities.

2. Ingestion: Linking structure and semantics

In this step, we assume the structural graph (suppliers -> factories) already exists. We ingest a new unstructured “risk event” and link it to the graph.

3. The hybrid retrieval query

This is the core differentiator. Instead of just returning the top-k chunks, we use Cypher to perform a vector search to find the event, and then traverse to find the downstream impact.

The output: Instead of a generic text chunk, the LLM receives a structured payload:

[{‘issue’: ‘Severe flooding…’, ‘impacted_supplier’: ‘TechChip Inc’, ‘risk_to_factory’: ‘Assembly Plant Alpha’}]

This allows the LLM to generate a precise answer: “The flooding at TechChip Inc puts Assembly Plant Alpha at risk.”

Production lessons: Latency and consistency

Moving this architecture from a notebook to production requires handling trade-offs.

1. The latency tax

Graph traversals are more expensive than simple vector lookups. In my work on product image experimentation at Meta, we dealt with strict latency budgets where every millisecond impacted user experience. While the domain was different, the architectural lesson applies directly to Graph RAG: You cannot afford to compute everything on the fly.

Mitigation: We use semantic caching. If a user asks a question similar (cosine similarity > 0.85) to a previous query, we serve the cached graph result. This reduces the “graph tax” for common queries.

2. The “stale edge” problem

In vector databases, data is independent. In a graph, data is dependent. If Supplier A stops supplying Factory Y, but the edge remains in the graph, the RAG system will confidently hallucinate a relationship that no longer exists.

Mitigation: Graph relationships must have Time-To-Live (TTL) or be synced via Change Data Capture (CDC) pipelines from the source of truth (the ERP system).

Infrastructure decision framework

Should you adopt Graph RAG? Here is the framework we use at Cognee:

1. Use vector-only RAG if:

   • The corpus is flat (e.g., a chaotic Wiki or Slack dump).

   • Questions are broad (“How do I reset my VPN?”).

   • Latency < 200ms is a hard requirement.

2. Use graph-enhanced RAG if:

   • The domain is regulated (finance, healthcare).

   • “Explainability” is required (you need to show the traversal path).

   • The answer depends on multi-hop relationships (“Which indirect subsidiaries are affected?”).

Conclusion

Graph-enhanced RAG is not a replacement for vector search, but a necessary evolution for complex domains. By treating your infrastructure as a knowledge graph, you provide the LLM with the one thing it cannot hallucinate: The structural truth of your business.

Daulet Amirkhanov is a software engineer at UseBead.

Welcome to the VentureBeat community!

Our guest posting program is where technical experts share insights and provide neutral, non-vested deep dives on AI, data infrastructure, cybersecurity and other cutting-edge technologies shaping the future of enterprise.

Read more from our guest post program — and check out our guidelines if you’re interested in contributing an article of your own!

Apps for budgeting and personal finance do a good job of tracking your money as you earn and spend it. Some also have excellent debt calculators that help you figure out how to pay off your debts.

Each debt calculator is a little different. Some suggest a specific method for paying down debt, while others are simulators that let you see how your total amount paid will decrease if you increase your monthly payment.

Here are a few useful calculators and some guidance about what makes them different.

A Straightforward Plan: Bankrate

Bankrate’s free debt payoff calculator gives you a timetable for paying off each of your debts. You enter as many debts as you want to include, their interest rates, total loan amounts, and other details. You also enter any new income you expect to receive, such as an annual salary increase or windfall, and the amount that you can put toward your debts. The calculator then generates one payment table for each debt showing how much to pay each month until the debt is cleared.

Bankrate prioritizes paying off the debt with the highest interest rate first. Once your first debt is paid off, the money you would have put toward it is diverted to your other monthly payments. In other words, as you eliminate debts, the monthly payments on your other debts increase until they, too, are paid off.

Who should use it? Bankrate’s calculator works for people who have multiple debts, and the total monthly minimum payments are within their financial reach. If that’s you, then you’ll get a crystal clear plan—with a timeline—for getting rid of all your debts.

Where it comes up short. This calculator assumes that paying off your debts by clearing the one with the highest interest rate first is in your best interest. That’s not true for everyone. You might have other options, such as consolidating credit card debt to a new card with a 0 percent introductory rate or filing for bankruptcy. Bankrate also doesn’t take into account other personal finance concerns, like other uses of monthly funds that free up once you pay off your first debt—Bankrate tells you to put that money toward your next-highest-interest debt. You might be better off putting it toward retirement savings or an emergency fund.

Big-Picture Guidance: NerdWallet

NerdWallet’s free debt load calculator determines your debt load as a percentage of your income. The resulting debt load is classified as smaller (less than 36 percent), larger (37–42), or overwhelming (43 percent or more). Based on the outcome, NerdWallet suggests a method for eliminating your debt, which you read about in an educational article below the results.

Who should use it? This calculator helps you get a big-picture sense of your debt. If you have a lot of debt, it’s useful for ruling out (or ruling in) the option of declaring bankruptcy.

Where it comes up short. It’s not great at analyzing the finer details of your debt. For example, in the setup, there’s no line item for student loans or a mortgage, much less the exact interest rate you pay on loans. The results are a rough guide rather than a personalized strategy.

Automated Inputs: WalletHub

When you sign up for WalletHub (free) and connect your financial accounts, the app pulls real information about how much money you owe and your payment history. Its debt payoff plan is a calculator that lets you play with the numbers to see what would happen if you increased your monthly payment. How much faster can you clear the debt? How much will you save in interest? You can quickly see the difference between increasing your monthly payment by, say, $50 versus $150.

Who should use it? This calculator is for WalletHub users who have connected their financial accounts. It’s most useful for people who can afford to pay more than the monthly minimum on their debts.