Research

Open code, versioned computational artifacts, and explanatory notes written for technically trained readers entering a neighboring field.

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Releases and notes

Each entry pairs a public research package with an account of the mathematical or computational problem around it.

Literature Note 002

Prediction markets
Statistical mechanics

External literature · peer-reviewed foundations and labeled preprints

When does a prediction market become a thermodynamic system?Partition functions, information work, susceptibility, and phase structure in markets for belief

An exact statistical-mechanical account of logarithmic market makers, extended to correlated events, information work, and carefully qualified phase structure.

Mean-field belief landscapeβJ = 1.18
two collective statesm = tanh(βJm)
Literature Note 001

Quantum foundations
Mathematical physics

External literature · published and preprint sources distinguished

Where did the imaginary unit go?Real quantum mechanics and the cost of composition

A guide to the 2026 real-quantum-mechanics debate, and to the precise distinction between removing complex notation and removing complex structure.

Complex structure · real coordinatesα = 42°
naïve local flags4mn
physical composite2mn
the scalar disappears; its geometry does notd → ℝ2d
Research Note 001

Open quantum systems
Numerical analysis

Released · code and certified data available

Runge–Kutta methods at the complete-positivity boundary

How a familiar time integrator can converge to the correct qubit damping channel while approaching it from the nonphysical side at every finite refinement.

Fixed-horizon refinementN = 8 steps
step sizex = X/8
convergence|error| ↓
Choi signλmin < 0
convergent does not mean completely positiveλmin → 0

Repository index

Stable paths to released code, data, and reproduction instructions.

01rk-choi-complete-positivity

Exact symbolic calculations, Sturm-certified boundaries, sign charts, and figure-generation code.

v1.0.0Repository ↗

Research Notes

New work, with enough context to use it

Occasional email when we publish a reproducibility package or a substantial technical explainer. No general organizational announcements and no fixed sending schedule.

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