Monday, 20 July 2026

An AI model reportedly produces a counterexample to the 85-year-old Jacobian Conjecture; a study finds AI advice makes people three times less accurate but twice as confident; and a leaked 2022 email shows Sam Altman pitched open-sourcing a weak model specifically to starve competitors of funding

Today's Lead

Engineering

X (via xcancel.com)

AI Model Claude Fable Reportedly Produces Counterexample to 85-Year-Old Jacobian Conjecture

Anthropic's Claude Fable has reportedly generated a counterexample to the Jacobian Conjecture, an open problem in algebraic geometry unsolved for over 85 years: a polynomial map in three variables with a constant Jacobian determinant of -2 that nonetheless maps distinct points to the same output. Unlike many AI-math claims, this one appears to hold up — multiple independent researchers verified the construction using Sage, Wolfram Alpha, and Lean formal verification, and a Princeton mathematician quoted in the discussion said 'there is no way this counterexample is wrong.' The live debate on Hacker News (361 points, 210 comments) isn't about correctness but attribution — whether the model exhibited genuine mathematical insight or recombined known patterns from the literature — which is itself a preview of the harder evaluation problem AI-assisted math is about to create.

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Engineering

Hacker News

Show HN: I Replaced a $120k Bowling Center System With $1,600 in ESP32s

An SRE who bought an abandoned 8-lane bowling center found that a 1:1 replacement of its 2008-era scoring system — camera-based pin detection, ball-speed tracking, fouling, pinsetter control — runs $80-120k from vendors, with $4,000 replacement parts for equipment whose actual job is triggering a single relay on a 70-year-old mechanical pinsetter. He built OpenLaneLink instead: ESP32 microcontrollers in an ESPNow mesh (with RS485 as a wired fallback), reporting sensor events to a Raspberry Pi running Redis and a React front end, for about $200-400 per lane-pair. The post (2,221 points, 236 comments on HN) is a vivid case study in how much of a 'six-figure, decades-old proprietary system' is actually just vendor lock-in wrapped around commodity sensors and a relay — and how cheaply that wrapper can be replaced once someone's willing to write the firmware.

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dependablec.org

Dependable C

Dependable C is a documented subset of the C language aimed at safety-critical and long-lived systems, built on a C89 foundation and deliberately avoiding newer standard features that lack universal, battle-tested compiler support across decades of platforms. The pitch inverts the usual 'use the latest standard' advice: for code that has to keep compiling and behaving identically across architectures and toolchains for 20+ years, specification purity matters less than a track record of every implementation actually agreeing on what the code does. It's a useful reminder that 'modern' and 'reliable' are frequently in tension, and that the right subset of a language depends entirely on how long the code needs to survive.

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Hashcloak

Introduction to Formal Verification with Lean (Part 1)

This tutorial walks cryptographic engineers new to formal verification through Lean, a theorem prover and functional language, by proving the correctness of the One-Time Pad cipher from first principles — XOR properties, the Shannon cipher definition, and the proof tactics needed to connect them. Rather than treating formal methods as an academic detour, it frames machine-checked proof as a direct extension of the rigor cryptographic engineers already claim to want, just enforced by a proof checker instead of a code reviewer's attention span.

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Xiaomi

Xiaomi Robotics-1: A Foundation Model for Real-World Robot Manipulation

Xiaomi introduced Robotics-1, a 10B-parameter foundation model trained on 100,000+ hours of real-world manipulation trajectories across 1,700+ scenarios, applying LLM-style pre-training (embodiment-free pre-training followed by hardware-aligned post-training) to robot control. It reports 75% success on novel tasks from minimal demonstrations and scaling behavior that transfers from simulation to physical hardware. Reception on Hacker News (174 points, 112 comments) split along familiar lines: enthusiasm for the scaled-training methodology and comparatively small model size, against skepticism about the robot's visibly slow, imprecise movements and how well any of this generalizes across different hardware platforms.

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Humanities

Simon Willison

Sam Altman's 2022 Email Reveals the Strategic Logic Behind an Open Model Release

Simon Willison surfaces a 2022 email from Sam Altman to OpenAI's board, exposed during the 2026 Musk v. Altman litigation, proposing a GPT-3-capability model that could run locally on consumer hardware. The stated rationale wasn't community benefit: Altman wrote the release should happen 'before Stability or someone else does,' because 'this helps discourage others from releasing similarly-powerful models, and makes it harder for new efforts to get funded.' It's a clean, documented case of open-sourcing used not as a gift but as a competitive weapon — flooding a market with a 'good enough' free option specifically to deny oxygen to rivals and their fundraising — which complicates any story about open-weights releases as straightforwardly altruistic or community-driven.

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