Katsuya Tagawa

Observer-Relative History, Spatial Escape, and Directional Ghost Ideals in Local Quantum Systems

We formulate a static notion of observer-relative History for asymptotic families of finite local quantum systems. Starting from a norm-storage quotient and observer seminorms with independently bounded algebraic word depth and spatial radius, we define a fixed-complexity silent...

Generative Response Geometry and First-Residue Accessibility

We develop a finite operational response theory for controlled quantum systems in which observer closure, hidden microscopic structure, and higher-order response are treated within a single algebraic framework. The central distinction is between generic higher-order observability...

Covariant Finite Reclosure and the Emergence of a Local Lorentzian Response Envelope

We establish a local structural route from finite quadratic reclosure to a Lorentzian response envelope. First, a faithful and lossless alternating reclosure map Q: Λ²W → V with dim W = dim V = n > 0 selects n = 3 by the dimension identity dim Λ²W = n(n − 1)/2. We then realize th...

Finite Reclosure and Temporal Fisher Transport: A Local Lorentzian Response-Curvature Construction

We construct an explicit local Lorentzian response geometry with nonzero curvature from two previously separated ingredients: the Fisher–Rao geometry obtained as a hidden-flow quotient of a finite closure–residue system, and a continuous-time population flow induced by a finite-d...

Closure–Residue Filtration and Non-Markovian Shadows: A Finite Generative Principle for Non-Exhaustive Observational Closure

We introduce a finite-dimensional closure–residue filtration for quantum dynamics relative to a chosen observational algebra. Let A_N = M_N(C), let D_N be the diagonal algebra, and let Δ_D and Q = I − Δ_D denote the diagonal and off-diagonal projections. For a finite dynamics Φ:...

Higher-Order Return and Persistent Silence: Fisher–Rao Geometry as a Weighted Hidden-Flow Quotient

We study finite-dimensional observational return beyond the quadratic residue level. Starting from a hidden-defect filtration relative to a diagonal observational algebra, we introduce higher cyclic return operators and distinguish temporary quadratic silence from persistent alge...

Exact Second-Order Survivors in Decohering Quantum Matrix Algebras

We present a finite-dimensional exact model of second-order survival under decoherence. Working in the matrix algebra M_N(C), we consider a pure dephasing semigroup whose fixed-point algebra is the commutative diagonal algebra. The associated stable memory projection erases first...

Closure–Residue Filtration and Non-Markovian Shadows: A Finite Generative Principle for Non-Exhaustive Observational Closure

We introduce a finite-dimensional closure–residue filtration for quantum dynamics relative to a chosen observational algebra. Let A_N = M_N(C), let D_N be the diagonal algebra, and let Δ_D and Q = I − Δ_D denote the diagonal and off-diagonal projections. For a finite dynamics Φ:...

Continuous-Time Quantum Dynamics from the Local Geometry of Discrete CPTP Maps

We derive continuous-time quantum dynamical semigroups from the local geometric structure of discrete completely positive trace-preserving (CPTP) maps on finite-dimensional Hilbert spaces. Rather than assuming a continuous time parameter and differentiability from the outset, we...

Continuous-Time Quantum Dynamics from the Local Geometry of Discrete CPTP Maps

We derive continuous-time quantum dynamical semigroups from the local geometric structure of discrete completely positive trace-preserving (CPTP) maps on finite-dimensional Hilbert spaces. Rather than assuming a continuous time parameter and differentiability from the outset, we...

Exact Second-Order Survivors in Decohering Quantum Matrix Algebras

We present a finite-dimensional exact model of second-order survival under decoherence. Working in the matrix algebra M_N(C), we consider a pure dephasing semigroup whose fixed-point algebra is the commutative diagonal algebra. The associated stable memory projection erases first...

Higher-Order Return and Persistent Silence: Fisher–Rao Geometry as a Weighted Hidden-Flow Quotient

We study finite-dimensional observational return beyond the quadratic residue level. Starting from a hidden-defect filtration relative to a diagonal observational algebra, we introduce higher cyclic return operators and distinguish temporary quadratic silence from persistent alge...