Wangyue

On Observational Results and Actual Change

This article distinguishes change at an actual structural scale from the result obtained under finite observational resolution. Through examples of small positional steps and differently ordered paths, it shows how actual change may leave a reading unchanged, how a sequence of sm...

On Discreteness and Continuity

This article develops a view of discreteness and continuity as states determined by observational conditions, resolution, structural scale, and rules of change. A process may be described as continuous at a specified scale when its allowed neighboring relations produce no identif...

On Observational Results and Actual Change

This article distinguishes change at an actual structural scale from the result obtained under finite observational resolution. Through examples of small positional steps and differently ordered paths, it shows how actual change may leave a reading unchanged, how a sequence of sm...

On the Separation of Number and Operation: A Minimal Arithmetic Machine

This paper proposes a minimal foundation for arithmetic by separating numerical generation from independently specified arithmetic operations. Four primitive generative acts—progression, reflection, refinement, and turning—are proposed as the foundations of the natural, integer,...

On Observation and Scale

This article investigates observation and scale as internal conditions of mathematical description rather than external limits imposed after calculation. At a current resolution h > 0, a newly generated term may be below, at, or above the threshold of independent recognition. The...

On Real Numbers

Ordinary real numbers permit subdivision to arbitrary depth. This paper investigates a real-number syntax with finite resolution depth, while retaining ordinary real numbers as a language of theoretically infinite depth. Rather than truncating real numbers or replacing them with...

A Finite Algebraic Machine at the Birch–Swinnerton-Dyer Interface: Magnus Histories, Deformation Channels, Fox Determinants, and Hecke–Frobenius Readouts

We isolate a finite algebraic mechanism that may underlie the apparent duality between the analytic and arithmetic sides of the Birch–Swinnerton-Dyer conjecture. The starting point is not an \(L\)-function and not a Selmer group, but a finitely controlled presentation consisting...

Cyclotomic Arithmetic Dynamics of Catalan's Constant: Gauss's Period Calculus, Prime Transitions, and a Quadratic-Cone Representation

This preprint develops a cyclotomic-arithmetic reading of Catalan's constant. It realizes the alternating signs as a second-order readout of a four-step unit-circle orbit, introduces symmetric and antisymmetric fourth-order period states, and derives their finite sum-and-differen...

Navier-Zakharov Five-Paper Package: A Formal-Numerical Research Package

This archive contains five narrow working papers, English TeX/PDF reading copies, public-source evidence tables, one exact 21-row finite-truncation companion experiment, and a standalone finite-dimensional Lean project. It is a bounded formal-numerical research package. It does n...

Navier-Zakharov Five-Paper Package: A Formal-Numerical Research Package

This archive contains five narrow working papers, English TeX/PDF reading copies, public-source evidence tables, one exact 21-row finite-truncation companion experiment, and a standalone finite-dimensional Lean project. It is a bounded formal-numerical research package. It does n...