Sequential vs Spatial Observables in Prime Fluctuations: A Methodological Case Study Related to the Riemann Hypothesis

This methodological preprint applies the Anton Matrix, an internal cartographic framework, to approaches surrounding the Riemann Hypothesis. It does not claim to prove RH or introduce a new mathematical result on the zeta function. The main contribution is methodological: it distinguishes between sequential observables on prime gaps and spatial observables based on prime counting over physical intervals in ℕ. Numerical tests show that raw sequential gap observables do not stably recover the spectral ordinates γₙ of the non-trivial zeros of ζ, while spatial prime-counting observables such as π(x+h)−π(x) do exhibit the expected spectral signature, consistently with the classical explicit formula. The work also provides a structured cartography of major RH-related approaches, their shared conventions, imports, and methodological locks, with the goal of clarifying where conceptual confusions may arise.