Ritsuki Kawada

Trace Balance, Reachability, and Support Localization

The note studies what retained-trace observations determine in a finite trace-balanced process. It proves an exact finite-horizon trace ledger, identifies complementary maps on reachable cones and their complex spans, and develops weighted order-domination bounds. A zero weighted...

Finite Balance Identities and Weighted Error Bounds

Telescoping and the triangle inequality determine how much local information survives in a finite total. The note proves exact finite balance identities, characterizes endpoint equality and strictness under nonnegative losses, and derives weighted local-to-global error bounds. Fo...

Trace Balance, Reachability, and Support Localization

The note studies what retained-trace observations determine in a finite trace-balanced process. It proves an exact finite-horizon trace ledger, identifies complementary maps on reachable cones and their complex spans, and develops weighted order-domination bounds. A zero weighted...

Quadratic Remainder Bounds and Local Isolation

A quadratic leading term with a remainder controlled relatively to its magnitude satisfies a sharp two-sided absolute-value bound. Below the exact cancellation threshold, a nonzero coefficient isolates the zero without a sign restriction on the coefficient. The note proves the th...