ZeroResistWe hypothesize the intersection of information theory, dynamical systems, aperiodic order, number theory, and control holds the secrets of the universe—and, more immediately, the unlock to bio-mimicked superintelligence. We're following our curiosity, not a market. But we do aspire to beat Bragg for the youngest Nobel Prize ever awarded. The holographic principle keeps us up at night.
Twist a system harder and harder, and its stable orbits break one by one. A computer-certified proof that the circle rotating at the golden mean is the most robust of its class — the last to break.
Certified stability margins for systems that must not drift: particle accelerators, magnetically confined plasmas, long-horizon orbital design.
A map of every average direction a torus system can drift. Tune the parameter and that map jumps at every rational value yet glides smoothly through every irrational one — order and chaos interleaved on the number line.
Mode-locking and synchronization: coupled oscillators, phase-locked loops, and digital control systems that quantize their inputs.
Delete one direction from a noisy dataset and watch the entropy respond. Below the detection threshold a planted signal never appears as an outlier — instead it tilts the entire spectrum, leaving a footprint combed across every eigenvalue.
Recovering signals conventional PCA declares invisible — weak-factor detection in finance, genomics, and sensor arrays.
At the exact moment a signal grows strong enough to escape the noise bulk, the spectrum kinks — yet every smooth statistic stays perfectly analytic. The emerging outlier steals exactly the residue the bulk loses; the books balance to all orders.
A no-go result for detection: smooth spectral statistics cannot flag the birth of a signal — sharper tests must read the edge, not the bulk.
Spectra usually end with a square-root profile and Tracy–Widom fluctuations. Here is an ensemble whose edge vanishes as a cube root instead, its new local process resolved through a twelve-ray Riemann–Hilbert problem with exact threefold symmetry.
A candidate universality class for extreme values beyond Tracy–Widom — correlated growth processes, the stiffest modes of constrained systems.
Forbid eigenvalues from a window beside that fractional edge and the spectrum splits in two, displaced mass reappearing across the gap. The pressure this exclusion exerts is exact: free energy grows as the 8/3 power of the gap.
Exact rare-event costs for spectral exclusion zones — outage probabilities in MIMO communication, constrained ensembles in statistical physics.
Compress a dataset down to its covariance eigenvalues and almost everything about the raw entries is erased. What survives, exactly, is one number — the fourth cumulant, the spectrum’s only remaining memory of non-Gaussianity.
Knowing precisely what spectrum-only pipelines can and cannot see — privacy-aware sketching, Gaussianity tests in cosmology and risk modeling.
Approximate Bayesian evidence ranks neural models well — until two models sit near a decision boundary, where curvature-approximation error can silently flip the verdict. A fragility score flags exactly which comparisons not to trust.
Audit rules for automated model selection — Bayesian deep learning, AutoML pipelines, safety cases built on evidence comparisons.
How much better is one information source than another when the state labels are hidden? The answer meets a hard barrier: no number of independent samples can substitute for the cross-state relations you never observed.
Fundamental limits for comparing sensors, datasets, and models without shared labels — data valuation, privacy-preserving benchmarking.
An averaging operator built from reflections turns out to be a random walk: activate the edges of a random tree one by one and shuffle accordingly. Its complete spectrum, its mixing cutoff, and the ordered-tree character behind both — all exact.
Exact mixing-time guarantees for shuffling-type Markov chains — MCMC design, distributed consensus, randomized linear algebra.
The theorist. Seyed Ali generates the unbounded conjectures — high-dimensional, non-convex, often with no proven bounds — then sprints to the next frontier the moment one stops surprising him.
The empiricist. Surya observes where those conjectures lead. He constraints them against real physics - boundary conditions, conservation laws, measure able observables - and carries them to working theory.
The realist. A nuclear engineering PhD and semiconductor physics expert, Dr. Sai has spent three decades pushing silicon to its physical limits — advanced Logic/FinFET, 3D NAND, and DRAM at Applied Materials, Director of Engineering at Veeco, now Director of Technology at Intel. He advises on how our theoretical work applies to industry.