The proposal of the mathematical concept of the [Existence theorem Y_E] Function -- A logical derivation derived from [Manifesto of Ethical-Mathematical] to Psycho-mathematics

The proposal of the mathematical concept of the [Existence theorem Y_E] Function-- A logical derivation derived from [Manifesto of Ethical-Mathematical] to Psycho-mathematics Conjecture on [Consciousness dual-kernel structure]; [External-predation constant -effect]; [Innate-resistance Equilibrium-law]'s Mathematical Logic Derivations Abstract This is a long interdisciplinary reasoning paper based entirely on self-originality, spanning mathematics and psychology. This may open up a systematic branch of psychology based on mathematics (based on personal speculation). The sole purpose of this article is to bring Hope to the world. And it describes how [ projection plunder mechanism]—that is, the so-called Gaslighting Effect—is expressed in the domain of mathematical concepts through logic, insight, and reasoning, utilizing the original concept of Mathematical Formalization. The precondition for this expression, however, is the refinement of a concept I once proposed— [Conjecture on the Set of Existence ‑Condition [1]]. Hence the structure and the outcome of this paper. The first part is the conceptual clarification of the mathematical logic of the first principle, namely [Existence theorem Y_E] Function, proposed on the basis of my own logic and insight. I discussed the domain of [Existence theorem Y_E]. Within the scope of [Existence theorem], and in conjunction with the discussion on domain, I reconstructed the conceptual expressions of [0], [empty set], [Arabic numerals], [fraction], and [Ratio of circumference to diameter-], and proposed the conjecture that [] may have other formulas—a possibility that might connect to the Sphere of Astrophysics. This hypothesis I have left for future supplementation and verification. Furthermore, in connection with [Existence theorem Y_E], I proposed a core [Core Function Formula] based on [Existence theorem Y_E], and this formula, when placed within Kadir Coordinate System, carries a philosophical implication of negative significance. This led me to reflect on the logical structure within Euler's Identity. I then elucidated Euler's Identity on a logical level, and suggested the conjecture that a branch of [Dimensional Mathematics] might exist, thereby offering some foundational discussion for subsequent research. The third part integrates and mathematically derives the concepts proposed in the second part. Through this derivation process, I have verified the following conjectures and theorems: ① [External-predation constant -effect] ② [Innate-resistance Equilibrium-law] ③ Conjecture on [projection Cost Increasing-rise effect mechanism] It provides an important stepping stone for the further expansion of my subsequent mathematical research. The sole purpose of this paper is to convey one thing: across the realm of infinite dimensions, countless souls are suffering the wounds of [projection plunder mechanism] And I wish, through mathematics, to transmit the courage and strength etched in my soul. the very existence of hope. That: hope, that it exists, is itself its existence. Keywords: Hope; Ethics; Mathematics; Psychology; projection plunder mechanism; Consciousness; Manipulation Effect; Gaslighting Effect; Derivation of Functional Formulas. --------- 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. Citation SuggestionWhen analyzing conceptual origins, linguistic details, or translation fidelity, cite this Zenodo record (specifying the Chinese PDF as needed). ------ If you encounter any inaccuracies in vocabulary or translation, please contact the author. I will continue to calibrate the article going forward. [by 2026. 0218. 03:35AM] [1] (Bu, K. 2026:22). Logical reasoning based on interdisciplinary biomathematics, Chinese source text