Maths

A month of deliberate demolition produces a proof of Conway’s refinement conjecture

Dan Abramov spent a month pointing frontier models at a 50-year-old problem about omnific integers — the integer part of the surreals — and came out with a Lean proof that mechanically verifies. The interesting part is not the result but the method: separate agents for exploration, red-teaming, Lean formalisation and project management, with the Lean checker as the only thing allowed to say something was true.

The failure modes are the story. One-shot attempts produced confident nonsense. A tower of thirty “papers” collapsed when a single foundational lemma turned out to be circular. What eventually worked was burning it all down and keeping only the parts that had survived verification — the errors made visible, then deliberately re-sought.

Overreacted — How I vibed a proof of Conway’s conjecture

Maths

The graph sandwich closes after 22 years

Kim and Vu conjectured in 2004 that a random regular graph can be squeezed between two random binomial graphs — contained in the lower one, containing the upper one. Richard Montgomery, Natalie Behague and Daniel Iľkovič have now finished the proof, building on a 2019 partial result from Pu Gao’s group.

The payoff is leverage: binomial graphs are the best-understood random objects in combinatorics, and the sandwich lets any property proved there transfer straight across to regular graphs. Behague’s own description of the correspondence is that it “seems almost too good to be true”.

Quanta Magazine

Embedded

Photons show where the lock is; a laser flips it

Ledger’s Donjon lab broke secure debug on the RP2350 (A4 silicon) in two stages. Photon-emission microscopy watched infrared light leak out of switching transistors to physically locate the DEBUGEN register on the die; a 980 nm pulsed laser then faulted two specific bits through the back side of the chip, re-enabling debug despite a permanent disable. Combined with the rescue-reset path, they pulled a 128-bit secret out of OTP.

The conclusion is the useful bit for anyone writing firmware: every protection — OTP redundancy, lock bits, runtime locks — did exactly what its datasheet said. The hole was in the interaction between them. Roughly $250k of kit and destructive decapsulation required, so this is a threat-model question, not a panic.

Ledger Donjon

AI & Software

A 121M-parameter model that fits on a microcontroller

Cactus released Needle 3: a single 8–29 MB binary aimed at phones, wearables, robots and MCUs, doing tool calling, typed extraction from messy text, and embeddings. It ships as an “intelligence ladder” — you pick 2 to 20 layers depending on what the target can afford.

Claimed numbers: beats models ten times its size on mobile tool calls, matches 2–3× bigger ones on extraction, and runs 400–4k tokens/s decode on a Raspberry Pi 5. Worth a sceptical benchmark, but the shape of it — structured extraction as a local library call rather than a network round trip — is the interesting direction.

Cactus Compute — Needle 3

Software

Cloudflare talks itself out of 90% of its hash ring

The Pingora backend router was holding millions of ketama consistent-hash points across dozens of rings, up to 6 GB per instance. Two changes fixed it. First, packing the index down from 32 to 16 bits using byte arrays instead of structs, dodging alignment padding — 25% straight off.

Second, and better: the coefficient of variation for ketama balance goes as √((N−1)/(Nk+1)), so the last 90,000 hashes per ring were buying a 0.7% reduction in imbalance. They cut points per server by 90% and reclaimed 100 TB of RAM globally, running old and new rings side by side during rollout to keep cache hits.

Cloudflare Blog

Chess

Aronian escapes from a lost position as the USA sweeps both sections

Olympiad round four in Samarkand: the United States took Ukraine 3½–½ in the open and Spain 3½–½ in the women’s. Levon Aronian took game of the day by turning a losing position against 18-year-old European champion Roman Dehtiarov into a win.

Favourites held everywhere this round — only Azerbaijan–Czechia and France–Romania drew on the top ten boards — and 21 teams are still unbeaten. IM Alice Lee is 4/4 and already in individual-medal territory.

Chess.com — Olympiad round 4

Chess

The Freestyle league documentary gets a two-night cinema run

Grandmasters, a three-part documentary from Liza Mandelup (Jawline) and Boardwalk Pictures (Welcome to Wrexham, Cheer), follows German entrepreneur Jan Henric Buettner’s attempt to stand up a rival chess league — with Magnus Carlsen recruited as the thing that makes it credible. Wesley So, Hans Niemann, Arkady Dvorkovich, Danny Rensch and Levy Rozman all appear.

Tickets are on sale now for a supercut of all three episodes, 90+ AMC screens in the US on 11 and 14 October only. No Australian dates announced, so the streaming release is probably the realistic route here.

Chess.com

Astronomy

BepiColombo caught a solar storm hitting Mercury from 165 km up

During the September 2024 flyby, the spacecraft’s SIXS instrument happened to be at closest approach exactly when a large solar particle eruption arrived. It measured high-energy charged particles punching through Mercury’s magnetic field and landing on the surface — a coincidence of timing the team describe as unique.

Mercury’s magnetosphere is much weaker than Earth’s, which makes it a useful worst-case laboratory: the data constrains how deep particle radiation would get into Earth’s near-space environment during the most powerful storms, which is the number that matters for satellites and grids.

Universe Today

Musicals

SIX returns to the Theatre Royal from 9 October

The six wives of Henry VIII as an 80-minute pop concert, back in Sydney at the Theatre Royal from 9 October. It is short, loud, and about as far from a three-hour book musical as the form gets — which makes it an easy one to take a fifteen-year-old to on a school night.

Still in town alongside it: My Fair Lady at the Opera House to 31 October, A Beautiful Noise at the Princess to 31 October, and How to Succeed in Business Without Really Trying at the Hayes to 27 September.

Theatre Royal Sydney · BroadwayWorld Sydney

Film Music

Natalie Holt scores Aardman’s Shaun the Sheep feature

Natalie Holt — the Loki and Obi-Wan Kenobi composer, and a violinist by training — wrote the score for Shaun the Sheep: The Beast of Mossy Bottom, out now on Sony Masterworks. A wordless film puts an unusual load on the music: with no dialogue the score has to carry the comic timing frame by frame, which is closer to silent-era scoring than to a normal animated feature.

Also assigned this week: Clint Mansell takes over MobLand season two for Paramount+, and Volker Bertelmann is on the psychological thriller Verity.

Film Music Reporter — weekly roundup · Mansell on MobLand