Phase Transition Mechanism and Emergent Picture in Self-Construction Theory: From Fully Excited Chaotic Superposition State to Layer-by-Layer Differentiated Structural Relational Network

Abstract: This paper systematically expounds the complete mechanism and picture of the spacetime complex field K in the Self-Construction Theory (SCT) evolving from a fully excited chaotic superposition state, through constructive renormalization and layer-by-layer freezing, to gradually differentiate into a trivial configuration (spacetime substrate) and non-trivial configurations (matter carriers). The core contributions are as follows:

(1) The “homologous synchronization” mechanism of the trivial and the non-trivial: the information compression operation of constructive renormalization simultaneously establishes two complementary relational configurations in the same step—the simplest connections that are successfully flattened (the trivial configuration, i.e., continuous spacetime) and the complex weavings that cannot be flattened due to topological obstruction (the non-trivial configuration, i.e., carriers). The two are not two successive stages but two complementary outcomes of the same selection process. The synergy of π (the flattenable proportion) and ζ₃ (the non-flattenable proportion) in the constant spectrum ensures that these two outputs are completed simultaneously in the same screening.

(2) The chiral distinction and annihilation mechanism of matter-antimatter carriers: the distinction between matter and antimatter carriers is determined by the chirality of time-string weaving, independent of quantum numbers—a right-handed knot is a matter carrier, a left-handed knot is an antimatter carrier. Annihilation occurs after time-point freezing and before time-string freezing (L2 layer), is a pure chiral pairing process, and does not require dimensional probes to first assign quantum numbers to carriers. Annihilation is an incremental transformation from non-trivial configurations to trivial ones—the mutual deconstruction of matter-antimatter carrier pairs makes continuous spacetime “flatter”.

(3) The energy-information unified framework: energy is a measure of the information gap between spacetime configurations, not a conserved quantity. Matter is the residual of information gap that has not been flattened, dark energy is an intrinsic property of the information substrate, and spacetime resonance excitations are the propagation of information gaps as wave motions in spacetime.

This paper uses SCT’s own language—without borrowing the conceptual framework of field theory—to systematically answer the fundamental questions of phase transition emergence. This paper belongs to the spacetime genesis series of SCT, and together with previously published papers on matter genesis, forms a complete physical narrative from “pure form” to “content”.

Keywords: Self-Construction Theory; spacetime complex field; constructive renormalization; homologous synchronization; chirality; layer-by-layer freezing; information gap; origin of energy