kinexys by j.p. morgan
i'm building pono, an engine that measures mev on solana. flagging atomic arbitrages, sandwich attacks, and soon other mev transactions, pono produces relevant cryptoeconomic data on this class of transactions. currently, this project is in the measurement phase; i'm optimizing for performance and robustness when it comes to flagging relevant transactions.
kalshi and polymarket have now processed millions of dollars in trades; i'm mapping vol surfaces to study how prices for contracts traded on these platforms evolve over time, comparing against traditional derivatives.
the core problems are calibration and consistency. for events with liquid traditional derivatives, do prediction market prices agree with options-implied probabilities, and which is better calibrated ex-post? separately, do overlapping contracts on the same event satisfy static no-arbitrage conditions like calendar spread monotonicity, or do thin books produce systematic violations?
the more interesting structural question is how implied vol decays as a contract approaches resolution. equity options have a well-understood term structure, but the binary payoff changes the terminal condition entirely; it's not clear whether $\sqrt{T}$ diffusion applies or whether something more irregular governs the surface near expiry. related to this is the identification problem: on thin order books, separating genuine probability curvature from bid-ask spread artifacts requires either a microstructure model or enough data to back out the two effects independently.
the deepest question is whether there exists a stochastic process that is simultaneously risk-neutral, consistent with the binary payoff structure, and fits the observed surface shape. the natural candidate is a jump-diffusion hitting 0 or 1 at expiry, but parameterizing and estimating it from sparse data is non-trivial.
chainweb is kadena's proof-of-work consensus protocol which extends bitcoin's nakamoto consensus by braiding together multiple parallel chains. i'm currently investigating incentive compatibility and other economic properties of the network as well as formally verifying key functions and features.
chaos-based cryptography has not been successfully constructed; any ventures to do so have been broken. however, multidimensional or hyperchaotic systems could offer better security properties allowing for computationally efficient and platform-agnostic cryptographic primitives.
the core difficulty is that informal hardness — sensitivity to initial conditions, ergodicity, high kolmogorov-sinai (ks) entropy — does not imply computational hardness in the sense required for a post-quantum security proof. i'm working through a set of problems that try to bridge this gap by grounding chaos-based constructions in lattice hardness assumptions, specifically ring learning with errors (rlwe) and module short integer solution (msis).
the most immediate question is whether the map $\varphi(a) = a^2 + e$ over the ring $R_q = \mathbb{Z}_q[x]/(x^n + 1)$ — with $e$ drawn from the rlwe error distribution — is ergodic, and whether its ks entropy $h_{\mathrm{KS}}(\varphi)$ can be maximized at parameters where rlwe remains hard. if so, the deeper question is whether distinguishing the orbit $\mathcal{O}(a_0) = \{a_0, \varphi(a_0), \varphi^2(a_0), \ldots\}$ from uniform reduces to solving rlwe — which would give the construction an actual post-quantum security proof.
on the p-adic side, anashin's theorem characterizes 1-lipschitz ergodic maps on $\mathbb{Z}_p^n$, but it says nothing about computational hardness of inversion. i'm looking at whether polynomial maps like $x \mapsto x^2 + c$ over $\mathbb{Z}_p^n$ are lwe-hard to invert, and more generally what structural conditions force ergodicity and hardness to coexist. a related question involves hyperbolic toral automorphisms $T_M(x) = Mx \bmod q$: if $M$ is drawn from an ntru-like distribution, does inverting $T_M^t$ reduce to msis or ntru? the spectral gap of $M$ controls mixing rate, and it's not clear whether fast mixing and hard key recovery are compatible at the same parameters.
the most pragmatic angle is nonlinear lwe (nlwe($\varphi$)): replacing the linear map in an lwe instance with a chaotic $\varphi: \mathbb{Z}_q \to \mathbb{Z}_q$. even if this adds no formal hardness, it may raise concrete security by destroying the gaussian structure that lattice reduction and blum-kalai-wasserman (bkw) attacks rely on. underlying all of this is a discretization problem; naive projection of a continuous chaotic map onto $\mathbb{Z}_q$ collapses orbits to length $O(\sqrt{q})$ via a birthday argument, which is cryptographically useless. finding maps whose discretized orbits grow as $\Omega(q)$ while remaining hard to invert is the prerequisite for any of the above to work.