Theta Toy Model: From First Distinction to Relational Inscription in Dynamic Present Theory

This note introduces Theta, a minimal relational toy model within Dynamic Present Theory(DPΦ). Theta studies how Continuous Present Actualization (CPA) can generate candidaterelations, carry constraint forward, and produce closure, inscription, densification, and burn-downin a finite formal system.The motivating symbolic transition is written (0 → 1). The notation carries no arithmeticcontent and no claim of emergence from literal nothingness. Here (0) denotes undifferentiatedadmissibility: a state without a carried distinction, no stabilized relation, and no inheritedconstraint. The transition to (1) denotes the first held distinction: an actualized differenceby which relation becomes possible. Genesis in this formal sense names the origin of writablerelational difference from unpartitioned admissibility.A bare symbol (0 → 1) creates nothing by itself. Structure appears when first distinction isfollowed by lawful relational closure: subsequent CPA steps generate a structured candidate space.In the tested regimes, this minimal setup produced a working vocabulary for first distinction,candidate bloom, relational inscription, lock-in, pressure densification, and non-regenerativeclosure. Its value is foundational: a relational map for how CPA may be modeled before physicalinterpretation is added. The surprising result is that lawful relation, once minimally actualized, is not inert. It opens, narrows, densifies, and exhausts its own candidate space.