Fable Disproves the Jacobian Conjecture, Claude Code's 80% System-Prompt Diet & the HAR-File Trick

Math Breakthrough: Fable vs. the Jacobian Conjecture

"hello there the jacobian conjecture is false"

The post everyone in this roundup's orbit retweeted (Armin Ronacher, Thariq, Peter Steinberger all boosted it): Harvard number theorist Levent Alpöge announced a counterexample to the Jacobian conjecture (1.4M views, 3.9k likes in ~10 hours), thanking "my close friend akhil for asking about it and my other close friend fable for working during the world cup final."

The counterexample itself fits in a tweet: a polynomial map ℂ³→ℂ³ with constant Jacobian determinant −2 that sends three distinct points to the same point — directly violating the conjecture (open since 1939) that constant nonzero Jacobian implies injectivity. That's what makes this credible in a way most "AI solved math" claims aren't: anyone can verify a counterexample by hand, and the replies did exactly that within hours. Highlights from the thread:

Open questions worth watching: whether the result was pure model reasoning or a model-guided computational search (Rado Kirov's question — the coefficients are small enough that "why did no one just search?" is fair), and whether Alpöge publishes the session.

Agentic Coding & Claude Code

Thariq: Claude Code's system prompt was cut by 80%

Anthropic's Thariq appeared on Peter Yang's podcast (episode on YouTube) covering how /loop, /goal, and workflows differ, live video-editing with Claude, and planning with HTML artifacts. The headline claim: "We cut Claude Code's system prompt by 80%. As models have gotten smarter, they need less direction, fewer constraints, and fewer examples." Examples in particular constrain newer models — "if you remove the examples, it can actually be more free-form" — so the advice is to trim your context when a new model ships. Also quotable: "One failure mode I see is that people glaze over AI's plans. You want to make sure it's something you read."

Thariq says a written post is coming (129k views) on how to apply the same trimming to your own skills and system prompts. The replies are full of confirmation from practitioners: CLAUDE.md files that only ever grow with "half the lines compensating for a model two generations old," and observations that Opus 4.8/Sonnet 5 overfit to even a single example.

The HAR-file trick: record traffic once, derive a client forever

Dax (@thdxr, 410k views) popularized a trick he credits to James Long: instead of having an agent drive a browser every time, ask it to record the network requests into a HAR file, then derive a native API client from the capture — far more efficient than repeated browser automation. His demo: an Uber Eats CLI. The replies are a fun tour of the pattern's ecosystem — cli-printer ("prints" a CLI for any site), someone doing the same via a Caido HTTP-proxy skill, a Chick-fil-A CLI, and the recurring practical question of how to handle cookies/auth refresh.

Jerry Liu: general harnesses are a commodity, task-specific harnesses aren't

Two related posts from Jerry Liu: he argues there's little value left in building custom general harnesses, but "tremendous value in creating custom task-specific harnesses" where you encode domain priors to hit accuracy/cost/latency constraints. And LlamaParse is shipping coding-agent retrieval primitives for documents: hybrid search (grep + vector), file grep with regex, find, and sed-style read — explicitly converging on the same primitives coding agents already use on repos, now aimed at unstructured docs.

Codex agents talking to each other across threads

A tip circulating via LLMJunky: Codex threads working in the same codebase can be given each other's session references and will "literally chat back and forth, wait for one another to finish, provide updates, request updates." Related and clever: you can run Codex app-server in the cloud (e.g. on Render) and put a "Sign in with ChatGPT" button in your product — users pay for the AI features with their existing flat-rate ChatGPT/Codex subscription, so the developer has no API cost.

OpenAI & ChatGPT Work

Thibault Sottiaux's ChatGPT Work push continues from yesterday. The pitch is consolidating: creating and hosting sites, managing your email, summarizing document mountains, producing docs/sheets/slides, included in Plus/Pro/Business/Enterprise. His own workflow is telling — "My job is basically delegating to ChatGPT Work now. Can't stop using dictation", including dictating a request to triage his own Twitter DMs to assemble the 50–100-person early-access group he called for.

Other Notes

  • Is the timeline astroturfed? Two of the most level-headed accounts on the list asked the same question independently: Armin Ronacher noticed his feed turning aggressively "pro data center" over two days ("Is this organic? Where did it come from?"), and Simon Willison asked what motivates the bot reply-guy accounts that grow followers by mass-replying. Related: Ronacher was surprised his Twitter analytics show a heavily skewed follower base.
  • Elon buys ~$50B of compute. LLMJunky's read: hardware ownership is becoming the moat — "buy while you can."
  • Losing your own voice. Jerry Liu admits he's "starting to have trouble understanding and articulating what AI generates" — a quiet but widely-felt confession, echoed in replies elsewhere about AI-generated code and prose outpacing human comprehension.
  • AI-hardware silliness watch: discontinued OpenAI Micro keyboards are selling for ~$1000 on eBay, and even keyboard-agnostic swyx was charmed by the custom-keyboard scene.