Help Wanted

AI Summary: This issue is a "good first issue" that asks contributors to add a new cultural fact about Japan to a JSON file. The fact to be added is the versatile Japanese phrase 'yoroshiku onegaishimasu'. The instructions are clear and involve editing a specific file and submitting a pull request.

AI Summary: The Odd Noncototient Conjecture proposes that all noncototients (numbers not expressible as m - phi(m)) are even. This is equivalent to stating that every odd integer greater than 5 can be represented in the form m - phi(m). The conjecture is closely linked to the Goldbach conjecture, as proving it would imply that every odd number > 5 is a sum of two primes minus one.

AI Summary: This issue proposes formalizing the conjecture that no Lychrel numbers exist in base 10. A Lychrel number is defined as a number that never becomes a palindrome when repeatedly added to its digit reversal. The primary challenge lies in defining digit reversal and palindrome checking for base-10 numbers within a formal system.

AI Summary: This issue proposes formalizing the Giuga Numbers Conjecture, which states that there are infinitely many composite integers 'n' where for every prime divisor 'p' of 'n', 'p' also divides 'n/p - 1'. The formalization is considered straightforward as the necessary number theory building blocks are already present in Mathlib, requiring only the definition of the Giuga number predicate.

AI Summary: This issue proposes formalizing the conjecture that there are infinitely many betrothed number pairs. Betrothed numbers are pairs of integers (m, n) where the sum of proper divisors of m equals n+1, and the sum of proper divisors of n equals m+1. The necessary divisor functions are available in Mathlib, but a specific predicate for betrothed pairs and infrastructure for expressing infinitude are missing.

AI Summary: This issue proposes formalizing the conjecture that there are infinitely many amicable number pairs. Amicable numbers are pairs of distinct positive integers where the sum of the proper divisors of each number equals the other. The necessary mathematical building blocks for this formalization are largely available, with only a predicate definition and infinity quantification needing to be added.

AI Summary: This issue asks whether there exist amicable numbers that are relatively prime. Amicable numbers are pairs of distinct positive integers where each number is the sum of the proper divisors of the other. The question is whether such a pair (a, b) can exist where their greatest common divisor is 1.

AI Summary: This issue asks whether pairs of betrothed numbers (also known as quasi-amicable numbers) can both be even or both be odd. Currently, all known betrothed pairs consist of one even and one odd number, and it remains an open problem to determine if same-parity pairs exist.

AI Summary: This issue requests an upgrade of the project's Java version from 8 to 17, along with updates to Gradle and Spring Boot versions. The fix also requires modifying CI workflows to accommodate the new versions and ensuring the application functions correctly when run via `java -jar` and within a Docker container.

AI Summary: This issue proposes formalizing the Idoneal Numbers Completeness Conjecture, which states that a specific list of 65 numbers are the only idoneal numbers. An idoneal number D is defined by a property related to the unique representation of integers in the form x^2 + Dy^2 with certain conditions. The formalization requires defining idoneal numbers and proving the completeness of the given list, potentially involving advanced number theory concepts.

AI Summary: This issue asks to prove or disprove the conjecture that there are no pairs of amicable numbers where one number is even and the other is odd. Amicable numbers are defined by the sum of their proper divisors. While the basic number-theoretic concepts are available in Mathlib, a formal definition of amicable pairs and specific lemmas about parity and divisor sums might need to be developed.

AI Summary: This issue proposes formalizing the conjecture that there are no "almost perfect numbers" that are not powers of 2. An almost perfect number 'n' is defined by the property that the sum of its divisors, sigma(n), equals 2n - 1. The conjecture states that all such numbers must be of the form 2^k for some integer k.

AI Summary: This GitHub issue proposes formalizing the conjecture about the existence of quasiperfect numbers. A quasiperfect number is defined as a positive integer 'n' where the sum of its proper divisors equals 'n + 1', or equivalently, the sum of all its divisors is '2n + 1'. The core question is whether such numbers exist.

AI Summary: This issue proposes the removal of a stale documentation file, `docs/spec.md`, which is no longer maintained. The content has been superseded by an auto-generated API reference at `docs/book/src/reference/api-spec.md`, ensuring accuracy. The goal is to eliminate confusion by deleting the outdated file.

AI Summary: This issue proposes adding a new provider for Ollama, a local LLM runner, to the system. The goal is to enable access to locally hosted models in a similar fashion to how Gemini and OpenAI providers are currently integrated. This enhancement aims to expand the system's LLM capabilities by supporting local deployments.

AI Summary: This issue proposes formalizing the conjecture about the infinitude of perfect numbers within a Lean proof assistant. It involves defining what a perfect number is and then expressing the idea of there being infinitely many such numbers, potentially linking it to the infinitude of Mersenne primes.

AI Summary: This issue proposes the removal of an unused `globalDryRun` feature from the `RuleReadinessController` in the Kubernetes node-readiness-controller project. The feature was never implemented or utilized, and the task is to clean up this dead code from the controllers.

AI Summary: This issue is a "good first issue" that asks a contributor to add a new Japanese grammar point, "〜に向けて" (meaning "toward / in preparation for"), to a JSON file. The task involves locating the specific file, appending the new grammar string to an array, and submitting a pull request.

AI Summary: This issue proposes an agent to automate the repurposing of blog posts and other content into Twitter/X threads by ingesting RSS feeds. The agent will fetch content, generate a summarized thread using AI, and either post it directly or save it as a draft, demonstrating a complete real-world workflow for content teams.

AI Summary: This issue requests a visual adjustment for dark mode in the application. Specifically, the color of the graph axis on the statistics page needs to be changed from light blue to white to improve visibility, matching the color of the title.

AI Summary: This issue is a "good first issue" that asks contributors to add a new trivia question about a Japanese city known for its snow festival to a JSON file. The instructions clearly outline the file to edit, the exact JSON object to add, and the steps for submitting a pull request.

AI Summary: This issue is a "good first issue" that asks contributors to add a new cultural fact about Japan to a JSON file. The fact is about the 'shichi-go-san' festival. The instructions clearly outline the steps for adding the fact and submitting a pull request.

AI Summary: This issue is a "good first issue" that asks contributors to add a new Japanese grammar point, "〜に加えて" (meaning "in addition to..."), to a JSON file. The task involves opening a specific file, appending the new grammar string with proper JSON formatting, and submitting a pull request.

AI Summary: This issue is a "good first issue" that asks contributors to add a new trivia question about the Peace Memorial Park to a JSON file. The instructions are very clear, detailing the exact file to modify, the format of the new entry, and the steps for submitting a pull request.

AI Summary: A CI test in Shard 3, specifically `test/graphql/types/Mutation/updateVenue.test.ts`, is consistently failing with a "minio failure" error. This failure is blocking PR #5147, even though the PR's changes are unrelated to the failing test, indicating a recurring or unresolved issue with the MinIO service in that specific CI shard.

AI Summary: Shard 3 of the test suite is failing in PR #5147 due to suspected MinIO connection errors, potentially caused by test races, state pollution, or unawaited async operations. The issue is blocking the merge of the PR, and several action items are proposed to investigate and fix the MinIO instability and test cleanup.

AI Summary: This issue is a "good first issue" requesting a simple addition of a cultural fact about Japan to a JSON file. The task involves opening a specific file, appending a new fact about 'mono no aware', and submitting a pull request with a predefined title and issue closing.

AI Summary: This issue is a "good first issue" that asks contributors to add a famous anime quote from Mob Psycho 100 to a JSON file. The task involves locating the correct file, appending a new JSON object with the quote details, and submitting a pull request following specific instructions.

AI Summary: This issue consolidates several minor code review findings from a pull request. It includes a mix of typos, incorrect type annotations, dead code, docstring inaccuracies, and a logical bug in validation. Most of these are straightforward fixes.

AI Summary: This issue is a "good first issue" that asks contributors to add a new Japanese grammar point, "〜によると" (meaning "according to..."), to a JSON file. The task involves locating the file, appending the new grammar string with proper JSON formatting, and submitting a pull request.