Notes

An analog computer is one that is analogous to the problem: the wind tunnel to flight, the tide machine to the sea. When the analogy is exact the word is isomorphism, and a quantum simulator is the deepest example.

Anthropic's current flagship is Claude Fable 5.1 (released 2026-09-01), shipped as one set of weights under two safeguard configurations. The lab's training story runs from constitutional AI in 2022 to a rewritten constitution in 2026, with interpretability tools now used in pre-release audits.

World Labs announced Atlas on 2026-09-01 as a single multimodal model for camera-controlled video, 3D reconstruction, and simulation. It is in early access only; no paper, weights, or pricing have been published.

A path continuous everywhere and differentiable nowhere broke ordinary calculus. Itô's lemma repaired it with one extra term, tuned exactly to Brownian roughness.

As of September 2026, at least five Chinese labs ship open-weight models within a few months of the closed frontier. The shared pattern is sparse mixture-of-experts at trillion-parameter scale, aggressive long-context efficiency work, and permissive licenses. Cost claims need care.

Why the environment acts as an unwanted measurement, why that forces thousands of physical qubits per logical qubit, and why the physical-to-logical ratio is the number to watch.

Why entangled particles are correlated more strongly than any pre-written script allows, shown through the CHSH game, the three-polarizer experiment, and the 2√2 bound. Originally Appendix B of The Resolution of Reality.

Any physically realistic signal is a sum of sines and cosines; the transform recovers which ones and how strongly. Built to solve the heat equation, it is also the engine of Shor's algorithm.

Google DeepMind's newest release is Gemini 3.8 Flash (2026-09-02); its top reasoning model is still Gemini 3.1 Pro from February 2026, with Gemini 3.5 Pro unreleased and Gemini 4 in pretraining. Distinctive features are native multimodality, a 1M-token context as standard, and a vertically owned TPU stack.

Two measurements of roughness that are one measurement: for a self-affine path, D = 2 − H. A random walk has H = 0.5 and D = 1.5; anything else is a path of another roughness.

The three algorithm families that define what quantum computers are for, the speedup each delivers, and why the speedups differ. Originally Appendix D of The Resolution of Reality.

OpenAI's current flagship is GPT-6 Astra (released 2026-09-03), the first model it has rated Critical for cybersecurity. The o-series reasoning line has been folded into the GPT numbering, and the product emphasis has shifted to computer use and the Codex agent harness.

Feynman's 1982 proposal and Lloyd's 1996 proof: a quantum computer can efficiently simulate any local quantum system. The case where the machine and the problem share the same physics.

Superconducting circuits, trapped ions, photons, silicon spins, and topological qubits: what each is, the trade-off each makes, and who is building it. Originally Appendix C of The Resolution of Reality.

A model of a market changes the market. Soros's reflexivity, the Lucas critique, and Goodhart's law are three statements of the same limit, and it is the one way markets are permanently harder than chemistry: molecules do not read the paper.

Lyons (1998): a rough path alone does not determine the integrals along it, so enrich the path with its iterated integrals. Once you do, differential equations driven by paths of any roughness become well defined, with no probability required.

Gatheral, Jaisson, and Rosenbaum (2018) measured the Hurst exponent of realized volatility across many markets and found values near 0.1. Volatility is far rougher than a Brownian path, and the standard models are the wrong calculus for it.

How RSA turns the difficulty of factoring into a lock, why the lock has a hidden period, and a worked example with small numbers. Originally Appendix A of The Resolution of Reality.

Shor's algorithm is period finding: prepare a superposition, apply the periodic function, and read off the period with a Fourier transform. It is the bridge between the quantum primer and the mathematics essay.

A qubit before measurement holds amplitudes for both outcomes; computation is the controlled interference of those amplitudes. The double slit is the physical demonstration.

Reconstruct a smooth function from its derivatives at one point. The first tool mathematics built for prediction, and the one that assumes the world is smooth.

A map of who is shipping frontier-class models as of 2026-09-08: four US closed-weight labs, Meta re-entering with a closed model, and a group of Chinese labs shipping open weights a few months behind. Links out to one note per lab.

Quantum processors will be called by classical systems for the specific subproblems they are native to, the way a CPU offloads to a GPU. The classical side keeps control, logic, and storage.

Iterate z → z² + c and ask whether the orbit stays bounded. The boundary between staying and escaping is infinitely intricate, and it is a picture of where prediction fails.

Computational advantage depends on how much structure a problem has and where the structure comes from: isomorphic (the problem is physics), structural (hidden mathematical regularity), or generic (nothing to exploit). Derived, borrowed, or learned.

The phrase 'world model' now covers two different research programs: a learned dynamics model an agent plans inside, and a generative model of visual or 3D space. This note separates them and explains why the distinction matters.

xAI, now a SpaceX unit branded SpaceXAI, ships Grok 4.6 (released 2026-08-12) as its flagship. Its documented differences are a very large owned GPU cluster, heavy use of agentic RL and model-generated SFT data, and privileged access to Cursor, X, and SpaceX data. Several widely repeated claims are founder statements, not documentation.