Mathematical expression of the logic structure projection theorem under the influence of nonlinear perturbation variable field and Derivation of a Conjecture on the Biological Co-evolutionary Equilibrium from a Formalization Framework --Logical reasoning based on interdisciplinary biomathematics

Abstract I have devised new formulas and created novel mathematical concepts and symbols solely through logic and insight. I have updated the concept of “Evolution” in biology, updated the Mathematical Logic with in Virus Transmission Models in Biology, I discussed the concepts of “speed” and “time” in biology. Based on this discussion, I proposed a systematic evolutionary logic conjecture, and a certain branch of this conjecture, namely Conjecture on the Evolutionary Theory of Selection-Determined Orientation , I proposed a Conjecture on Co-evolutionary Pathways, by considering the relationship between local perturbations and systemic change, this groundwork paves the way for the theory I will subsequently propose. I have written three sets of formulae. The first is a Mathematical expression of the logic structure projection theorem under the influence of nonlinear perturbation variable field—a novel mathematical concept of my own creation. For this formula, I introduced three new notations: projection, tend to, and Path-Feedback-Expression. The second set is aMathematical Expression of Multidimensional Infection Pathways Projection. The third set comprises the derivation of the formula for the Biological Co-evolutionary EquilibriumFormalization system . Key words : conservation;biological co-evolutionary;Evolution; Biomathematics ; Math ------ This record permanently preserves the original Chinese manuscript of this research and its accompanying English translation. It is created to:1. Establish the intellectual provenance of the work, acknowledging that its core ideas were conceived and articulated in Chinese.2. Provide direct access to the source text for scholars interested in precise terminology, theoretical nuance, or translation studies. Relationship to Other PreprintsAn English version of this work has been submitted to SSRN for broader academic exposure ,and is currently under review. For general international citation and discussion, please refer to the final version on SSRN once available.This Zenodo archive remains the authoritative source for the original Chinese text.Once the review process is complete and the paper is publicly available on SSRN, this record will be updated with its permanent link. Citation SuggestionWhen analyzing conceptual origins, linguistic details, or translation fidelity, cite this Zenodo record (specifying the Chinese PDF as needed). ----- Important Note on Translation & Terminology (Updated: 2026-02-11) A preliminary full calibration of the English terminology and expressions was completed on February 12. Further revisions will follow as needed.