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Victor Zhorin, "Discrete Causal Topology", December 2025 | We prove that continuous dynamics emerge from discrete causal structure through a mechanism we call localization: the extraction of where a system sits in configuration space rather than enumeration of transitions between discrete states. Three necessity theorems establish that optimal prediction from discrete event sequences with terminal boundaries requires preservation of event identity, spectral temporal encoding, and learned causal attention. Each component is individually irreducible. The architecture is not engineered but derived from information-theoretic constraints.
The central result concerns gradient flow from boundary conditions. We prove that
terminal outcomes shape the entire antecedent causal field through backpropagation, creating second-order structure where early events modify interpretation of later events. This
retroactive determination parallels the holographic principle: predictive information satisfies
an area law scaling with event count, not temporal duration.
The framework unufies phenomena across substrates because localization creates shared
coordinates that enable cross-trajectory learning: populations of event sequences reveal the
universal geometry of progression toward boundary. Any system generating discrete timestamped events with terminal boundaries instantiates the same mathematical structure, dissolving the distinction between exact and statistical sciences. We prove why transformer
architectures succeed and establish that positional encoding is categorically incorrect for
timestamped data. Empirical predictions are falsifiable: architectures satisfying the necessity theorems should extract continuous dynamics that tabular methods systematically
discard.
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Townsend R.M., Zhorin V.V., "Spatial Competition among Financial Service Providers and Optimal Contract Design." Working Paper, December 2014 | We present a contract-based model of industrial organization that allows us to consider in a unified way both different information frictions (moral hazard, adverse selection,
both) and a variety of market structures (monopoly, imperfect competition, various strategic interactions). We show how this method can be applied to the spread of the banking
industry in emerging market countries, emphasizing observed transitions, namely the geographic locations of branches. Local collusive monopoly organizations and Bertrand-like
competitive environments in location and utility space are considered alongside with frictions affecting the outcome, namely provincial spatial costs and the information structure.
Mixed environments with fully informed local incumbents and entrants facing adverse selection are analyzed. Our larger goal, beyond calibrated numerical examples, is to develop
a framework with an operational toolkit for empirical work.
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Moll B., Townsend R.M., Zhorin V.V., "Economic Development, Flow of Funds and the Equilibrium Interaction of Financial Frictions."2016 | We use a variety of different data sets from Thailand to study not only the extremes of micro and macro variables but also within-country flow of funds and labor migration.
We develop a general equilibrium model that encompasses regional variation in the type of financial friction and calibrate it to measured variation in regional aggregates.
The model predicts substantial capital and labor flows from rural to urban areas even though these differ only in the underlying financial regime. Predictions for micro variables not used directly provide a model validation. Finally we estimate the impact of a policy counterfactual, regional isolationism.
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Publications
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