Associated Preprints: CEC (Convergent-Explosive Communication) Theory, DOI: 10.5281/zenodo.18721306 Associated Working Papers: Practical Guide to the Core Formula of CEC Theory DOI: 10.5281/zenodo.19021233 Reverse Regulation of the Core Formula of CEC Theory, DOI:10.5281/zenodo.19022668 Abstract Aiming at the core problem of chaotic coupling and difficulty in quantitative modeling and precise regulation of complex social communication systems, this paper, based on the core of Convergent-Explosive Communication (CEC) Theory, systematically sorts out high-level classic achievements and cutting-edge progresses in the fields of applied mathematics complex system modeling, complex network communication dynamics, and social communication quantitative analysis. It anchors the academic positioning of this paper in the field of interdisciplinary quantitative modeling by targeting the theoretical shortcomings and methodological limitations of existing research. Starting from the underlying laws of real communication, it completes the original variable definition and dimension reduction from scratch, constructs a dual-core formula system for CEC, and realizes the logical closed-loop of probability prediction and intensity regulation. The paper strictly defines the parameter connotation and calibration specifications, integrates calculus, asymptotic analysis and stability theory for formal mathematical derivation, deeply demonstrates the existence, uniqueness, monotonicity, convergence and robustness of the formula, calculates the convergence rate, defines the error bound and completes the optimality judgment, consolidating the mathematical hardcore depth; meanwhile, it demonstrates the rationality of natural logarithm ln(N) selection and the rigid constraint of variable quantity, analyzes the adaptation relationship between the formula and the whole cycle of communication, carries out special case and boundary expansion analysis, connects the mechanism of forward prediction and reverse regulation, and realizes theoretical promotion and universal extension. Focusing on theoretical construction and mathematical rigor demonstration, this paper puts forward a supporting theoretical verifiable framework and standardized empirical methodology, supplemented by preliminary numerical examples to verify the theoretical rationality, providing a complete path for the academic community to carry out empirical test and model expansion in the subsequent period. It refines the applicable boundary, error sources and sensitivity analysis of the model, making up for the shortcomings of traditional communication research, such as mainly qualitative research, insufficient mathematical rigor, weak theoretical verifiability and lack of expansibility. This achievement has both theoretical rigor and practical applicability, providing a new paradigm for the quantitative research of complex social communication systems, and is a basic theoretical research achievement with originality and leading nature in the interdisciplinary field of applied mathematics. Update 1 | Core Significance of This Paper: Mathematical Implementation of CEC Theory and 0-1 Breakthrough in Communication Science (Beijing Time 02:02, 2026-03-16) This paper, Dual-Core Formula and Mathematical System Construction of Convergent-Explosive Communication, serves as the core mathematical cornerstone of CEC Theory and represents a 0-1 breakthrough at the intersection of communication science and applied mathematics. It distills the abstract laws of "base accumulation—fission detonation—exponential explosion" from CEC Theory into a dual-core formula system that is computable, verifiable, and regulable, transforming an ideological framework into a usable mathematical tool. It also introduces advanced mathematical tools such as asymptotic analysis and Lyapunov stability into the field of communication for the first time, opening a new paradigm for quantitative research on complex social communication systems. It can stand alone as an original contribution to applied mathematics, or form a complete closed loop of "ideation—mathematics—implementation—regulation" together with the main preprint and two supporting working papers. You see, when you open this paper, plug in the formulas, and verify the data, you are not just reading a paper—you are personally strengthening the hetero-confirmation and self-confirmation structure of CEC Theory. This theory has evolved from "ideological innovation" to "theoretical maturity" not only through my derivations, but also through every read, share, and verification from all of you. Is this not marvelous? Together, we are creating an "evergreen" theoretical system in which authors and readers participate and strengthen it hand in hand.
Relike Zhou (Sun,) studied this question.