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Essays

  • 4 min read

Huawei's τ Scaling Law: Reframing Semiconductor Competition from Geometry to Time

Source: Global Semi Research (Substack)
Date: May 25, 2026

TL;DR

Huawei's announcement of Tau (τ) Scaling Law is analysed as a strategic move to reframe semiconductor competition from geometric scaling to time-domain optimisation — a battlefield that plays to Huawei's strengths given restricted access to cutting-edge EUV lithography. The τ framework spans 12 orders of magnitude (transistor ps → system s). Its first major engineering implementation is LogicFolding in the Kirin 2026 chip, achieving +55% transistor density and +41% energy efficiency at a fixed process node — no new lithography needed.

  • 4 min read

Leadership Lessons from 2,000 Years of the Catholic Church

Source: IE Insights
Author: Professor Javier Fernández Aguado
Book: 2000 Años Liderando Equipos (Kolima, 2020)

TL;DR

The Catholic Church is presented as the world's most durable organisation — a uniquely illuminating case study in management, leadership, and resilience. Professor Aguado argues that the Church pioneered concepts like interim management, employer branding, and VUCA thinking centuries before they had modern names. Its recipe for 2,000-year survival: holding fast to a core mission (servant leadership) while continuously reinventing structures through councils, schisms, and adaptation. Monasteries were the "Silicon Valley" of the Middle Ages. The Church's resilience outlasts any individual leader — including its worst failures.

  • 2 min read

LLM Hallucinations in the Wild: Large-Scale Evidence from Non-Existent Citations

Source: arXiv:2605.07723
Authors: (CC BY 4.0 licensed)
Subjects: Digital Libraries (cs.DL); Artificial Intelligence (cs.AI); Computers and Society (cs.CY); Physics and Society (physics.soc-ph)

TL;DR

This paper systematically studies LLM citation hallucinations — instances where language models fabricate references to academic papers that do not exist. By examining large-scale real-world outputs, the authors document the prevalence, patterns, and distribution of non-existent citations across domains. The work bridges AI reliability research, bibliometrics, and computational social science.

  • 4 min read

SkillOpt: Executive Strategy for Self-Evolving Agent Skills

Source: SkillOpt: Self-Evolving Agent Skills via Controllable Text-Space Optimization
Date Published: 2026-05
Authors: Yifan Yang et al. (Microsoft, SJTU, Tongji, Fudan)
Code: aka.ms/SkillOpt

TL;DR

SkillOpt treats an agent's skill document as trainable external state — analogous to weight-space optimization — using a separate optimizer model that applies bounded add/delete/replace edits accepted only when they strictly improve a held-out validation score. The result: best or tied-best across all 52 evaluated benchmark cells, with average lifts of +19–25 pts across GPT-5.5, Codex, and Claude Code harnesses.

  • 3 min read

Ukraine's Intermediate-Range Strike Campaign and a New Phase of the War

Source: Institute for the Study of War
Authors: George Barros, Kateryna Stepanenko
Date: May 25, 2026

TL;DR

The war is transitioning from a positional stalemate (dominant since 2023) into a new phase of tactical manoeuvre. Ukraine is systematically degrading the Russian "Tactical Reconnaissance-Strike Complex" (TSRC) through a combination of matured operational art, intensified intermediate-range strike campaigns, tactical drone supremacy, and the limited reintroduction of mechanised manoeuvre. Russia's theory of victory — slow attrition — is being invalidated. In April 2026, Russian forces suffered a net loss of 116 km² of territory — the first such monthly loss since Summer 2023.

  • 4 min read

11 Types of Cross-Industry Innovation

Source: SatPost by Trung Phan
Author: Trung Phan
Date Published: April 29, 2023

TL;DR

Trung Phan's SatPost distills Matt Ridley's How Innovation Works framework into a simple insight: innovation is recombination — "ideas having sex" across industries. He catalogs 11 concrete examples where borrowing from an unrelated field produced breakthrough innovations, from the printing press (grape press) to the Dyson vacuum (sawmill cyclone). The post also covers AI spam on Amazon, Disney's missed BuzzFeed acquisition, Dr. Dre meeting Eminem, and other current events.

  • 4 min read

Two Erdős Problems on Points in the Plane and AI

Source: Computational Complexity Blog \ Author: Lance Fortnow and Bill Gasarch \ Date Published: May 24, 2026

TL;DR

Bill Gasarch (writing on the Computational Complexity blog he co-authors with Lance Fortnow) contrasts two classic Erdős problems from 1946 that took very different paths to resolution — one solved by decades of steady human effort, the other cracked by an OpenAI model this month. He uses the comparison to reflect on the nature of mathematical progress, the role of AI, and what mathematicians should learn from the moment.

  • 2 min read

Tokenisation via Convex Relaxations (ConvexTok)

Source: arXiv:2605.22821
Authors: Jan Tempus, Philip Whittington, Craig W. Schmidt, Dennis Komm, Tiago Pimentel (ETH Zürich, Kensho)
Date: May 2026

TL;DR

Current tokenisers (BPE, Unigram) are greedy and produce sub-optimal compression — but finding the globally optimal tokeniser is NP-hard. ConvexTok reformulates tokeniser construction as an Integer Program, relaxes it to a Linear Program, solves it on an NVIDIA GH200, and rounds the result. The solution is provably within 1% of optimal at common vocabulary sizes, and on downstream tasks (CORE benchmark, multilingual Flores+) it matches or outperforms BPE — especially at larger vocabulary sizes.

The Problem with Greedy Tokenisers

BPE makes locally optimal merge decisions that compound into globally sub-optimal vocabularies. Example from the paper: on dataset D = {abc, abd, abe, bc, bd, be} with budget 3 tokens:

  • BPE: Merges a+b→ab (saves 3), then arbitrary (saves 1 each) → total savings 5
  • Optimal: Merges bc, bd, be → total savings 6

How ConvexTok Works

  1. Graph Formulation: Tokenisation recast as a shortest-path DAG problem
  2. Integer Program (IP): Minimizes compressed sequence length subject to vocabulary budget — NP-hard
  3. LP Relaxation: Variables relaxed to continuous [0,1], solved with NVIDIA CuOPT (~4 hours on 1 GH200, ~99M constraints)
  4. Rounding: Several schemes convert fractional LP solutions back to discrete vocabularies

Key Results

Vocabulary Tokeniser Gap to Optimal
32k BPE 101.29%
32k ConvexTok 100.07%
128k BPE 100.39%
128k ConvexTok 100.23%
256k ConvexTok 99.99%

Downstream: ConvexTok matches or beats BPE on CORE benchmark and generalizes better out-of-distribution (Flores+). Takeaway: Existing tokenisers are already close to optimal on compression — significant gains must come from other architectural changes.

  • 2 min read

Remarks on the Disproof of the Unit Distance Conjecture

Source: arXiv:2605.20695
Authors: Noga Alon, Thomas F. Bloom, W. T. Gowers, Daniel Litt, Will Sawin, Arul Shankar, Jacob Tsimerman, Victor Wang, Melanie Matchett Wood
Date: May 2026

TL;DR

An OpenAI general-purpose reasoning model autonomously disproved the Erdős Unit Distance Conjecture (1946) — that the maximum number of unit distances among n points in the plane is roughly n — by constructing point sets achieving a provably larger exponent. Nine leading mathematicians verified the proof and published an expository paper. Thomas Bloom called it "a $500 Erdős problem solved." Jacob Tsimerman said he would "accept it for any journal without hesitation."

Historical Context

  • The Problem (Erdős 1946): What is the maximum number of unit distances among n points in the plane?
  • Previous Bounds: Erdős gave n^(1+c/log log n) using √n × √n grids. The best upper bound was O(n^(4/3)). The consensus belief was that the true answer was n^(1+o(1)) — that is, nearly linear.
  • The Conjecture: That n^(1+o(1)) is the correct order of growth.

The AI's Breakthrough

The key insight came when the AI shifted perspective: rather than varying the point structure within a fixed number field (as everyone had tried), it fixed the primes and varied the number field — a paradigm shift no human mathematician had considered.

The construction uses:

  1. CM fields — algebraic number fields where having absolute value 1 in one embedding implies the same in all embeddings
  2. Golod-Shafarevich infinite class field towers — to build fields of increasing degree with bounded root discriminant
  3. A geometry-of-numbers lemma — projecting lattice points from high dimensions onto a single coordinate

The resulting exponent is roughly 1 + 6.24 × 10⁻³⁸ — tiny but definitively > 0, disproving the conjecture.

Why It Matters

  • First AI-disproved prominent open conjecture in mathematics (not just AI-assisted, but AI-originated)
  • Kolmogorov complexity modulo experts (Gowers' phrase): the proof has low complexity but required a non-obvious paradigm shift — precisely where AI excels
  • Methodological lesson: The AI wasn't substituting for human reasoning — it was exploring combinatorially larger search spaces for the right conceptual framing
  • 2 min read

Illegal Factories Undermine China's Solar Overcapacity Crackdown

Source: South China Morning Post
Date: May 22, 2026

TL;DR

China's two-year campaign to eliminate severe solar overcapacity is being undermined by illegal factories that flout the Ministry of Industry and Information Technology's strict "capacity quotas." Industry insiders estimate that China's actual solar glass production is 5-10% higher than permitted capacity, as some factories break ground without quotas or secretly expand production lines — often with local government complicity.

The Overcapacity Problem

China's solar industry has been plagued by severe overcapacity that sparked vicious price wars, undermined domestic manufacturers' bottom lines, and fueled protectionist policies overseas. In response, Beijing introduced tough policies with the Ministry of Industry and Information Technology enforcing strict capacity quotas.

The Underground Response

Permitted capacity for solar glass has dropped from ~130,000 tonnes/day (2024 peak) to just over 80,000 tonnes/day. However:

  • Some factories ignore the rules entirely — breaking ground without obtaining quotas
  • Others build production lines exceeding their approved capacity
  • Estimated 5-10% excess production beyond official figures

Local Government Complicity

The key enabler: local governments often give tacit consent to these violations because they want to "attract hi-tech companies to boost the local economy and tax revenues." This creates a classic central-local tension in Chinese industrial policy.

Historical Context

During 2020-2021, China's solar glass industry experienced a "gold rush" with prices soaring to ~40 yuan/m² (against ~13 yuan/m² costs). This led a wave of firms to enter the market — including companies with no background in glass manufacturing — setting up the capacity that now needs to be unwound.