NeoArk Lab.

Current Research Focus

• Deterministic Prime Readout via Admissibility.
  Develop a deterministic, oracle-free readout operator that recovers the next prime within a fixed window by eliminating non-admissible candidates. The approach treats primes as survivors of a structural admissibility law, not as outputs of a generative process.
• Structural Admissibility and Regime Closure.
  Formalize admissibility as a scale-stable structural constraint, identifying distinct operational regimes and the minimal certification mechanism required to close survivor intrusions without expanding the base sieve.
• Branch-Selective Log–Phase Dynamics.
  Model prime progression as a relation-driven update on logarithmic phase observables (u, θ, σ), where evolution proceeds via branch selection among finite admissible laws, rather than probabilistic generation.
• Invariant Persistence under Scaling.
  Test whether observed symmetry and doublet invariants persist under scale extension, supporting their interpretation as structural constraints rather than finite-size or grid artifacts.
• Structural Closure Track: RH to Readout.
  Maintain a consistent same-observable pipeline connecting explicit-formula resonance constraints to unconditional mean-square control, framing the Riemann Hypothesis as a structural closure condition rather than a standalone spectral conjecture.

Research Principles

• No guesswork. Only mechanisms that survive systematic ablations (reference on/off, filter on/off, regime stress tests) are considered structurally meaningful.
• Hard falsifiability. If a readout operator fails to generalize across scales or windows, the hypothesis is rejected without revision.
• Minimal assumptions, maximal structure. Known sources of artificial coherence (perfect powers, small-period alignments, grid artifacts) are removed before any structural claim is made.
• Implementation-first. A theoretical construct earns legitimacy only when it compiles into a working, verifiable readout engine.

Research Program Structure

Structural overview of the admissibility research program: a layered closure framework progressing from analytic constraints to deterministic readout.