Ioannis Tsiokos

To Flatten a Stone with Six Birds: Critical Pairs, Holonomy, and Confluence in Rewriting Systems

Confluence says that the order in which rewrite steps are applied does not matter in the end; flatness says that, locally, transport does not depend on the route taken. This paper makes the analogy precise at the local level and tests it computationally. The natural carrier is no...

To Spend a Stone with Six Birds: Currency-Constraint Duality and Shadow Prices Across Closure Layers

Physics has temperatures, economics has prices, statistics has regularization strengths, and models of attention have precision weights. Each is a single number that prices a limited resource. This paper asks why such numbers appear whenever a stable descriptive layer forms, and...

Riemann Hypothesis via Self-Dual Trace Confinement: A Conditional Closure

For any positive integer weights mρ, the Riemann hypothesis is equivalent to the vanishing of AZ = Σρ mρ(Re ρ − ½)2 over the nontrivial zeros. A companion paper proves a duality-confinement theorem: for a strongly measurable observable with values in a real Hilbert space that int...

Audited Operational Realisability: Canonical Inference Closure and Evidence-Preserving Composition

Conditional mathematical arguments need careful bookkeeping: which obligations were incurred, which have been addressed, and which were addressed in a way that actually proves the target. Audited Operational Realisability (AOR) is a mathematical theory of this bookkeeping. An aud...

Adequacy Residuals and Blind-Spot Currency

Suppose a vector is observed through two families of linear measurements: a native family that we already control and a target family that we would like to control. How much of the target response is left unexplained by the native measurements? We answer this question on finite-d...

Audited Operational Realisability: Canonical Inference Closure and Evidence-Preserving Composition

Conditional mathematical arguments need careful bookkeeping: which obligations were incurred, which have been addressed, and which were addressed in a way that actually proves the target. Audited Operational Realisability (AOR) is a mathematical theory of this bookkeeping. An aud...

Emergence IS the Needle Killer

A needle is a persistent obstruction: a direction in which a declared budget is violated, typically because the available measurements cannot see or explain the response in that direction. We give a linear-algebraic account of when a richer family of measurements removes such an...

Emergence IS the Needle Killer

A needle is a persistent obstruction: a direction in which a declared budget is violated, typically because the available measurements cannot see or explain the response in that direction. We give a linear-algebraic account of when a richer family of measurements removes such an...

A Conditional Physical-Closure Theorem for Three-Dimensional Navier-Stokes

We prove a conditional global regularity theorem for the three-dimensional incompressible Navier–Stokes equations with positive viscosity and real divergence-free initial data in Hγ0(ℝ3), γ0 > 5/2. The hypothesis, which we call a physical window closure, asks that on every time i...