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 a long reasoning length spatium[1] article as self-originality for real , as interdisciplinary for spanning mathematics and psychology. This may open a branch as systematic of based on psycho-mathematics (based on speculation of mine). This article with the only aim , for, carry the hope to this world. And also describes [ projection plunder mechanism], i.e., the called as Gaslighting Effect, how shown through as logic, insight and reasoning , and then , by originality Mathematical Formalization expression, on the mathematical concepts Sphere. The precondition for this expression, however, need refinement of a concept I once proposed: [Conjecture on the Set of Existence ‑Condition[2]]. Therefore , then bring forth this paper on this logic with .At the same time, this paper supplements and clarifies the part evidence of the two previous mathematical studies---[ Nonlinear Logic Structure Projection(on biomathematics) ] and [ On power ]. The article is broadly divided into three sections: The first part is clarification as conceptual on mathematical logic relation , as for the first principle that [Existence theorem Y_E]. I discussed the domain of [Existence theorem Y_E]. As with discussion on domain, within the scope of [Existence theorem Y_E], I reconstructed the conceptual expressions of [0], [Empty set], [Arabic numerals], [Fraction], and [Ratio of circumference -], and proposed the conjecture that [] may have other formulas, this may possibility connect to the Sphere of Astrophysics, This hypothesis I left here , and for future, evidence and verification. And in combination with[Existence theorem Y_E], I proposed a core Function 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 logical layer, and suggested the conjecture that a branch of [Dimensional Mathematics] may exist, thereby offering some foundational discussion for subsequent research. The second part is, proposes [Manifesto of Ethical-Mathematical Principles] of [Existence theorem Y_E]. Based on this manifesto principle, and with the concept of [ Nonlinear Logic Structure Projection] I once proposed, given the concept of [External-Logic structure projection plunder mechanism] within the Sphere of Consciousness. Proposes two important branches of [the Conditions for Determine-decide Consciousness], and proposed the [ Consciousness dual-kernel structure] Conjecture. With the above concepts, discussed [The connection between consciousness and social connectedness] as literature review form. Through the interpretation of the film content of [Gaslighting], it summarizes and proposes 10 core concepts of [Gaslighting process mechanism], and evidence after through literature. It also proposes a coping mechanism strategy for Gaslighting, and combined with Mathematical Logic Structure for go clear . These 10 core concepts are: 1【Reducing the Distance in the Information Sphere at the Dimensional Layer】 2【Increase the frequency of Informational Interaction】 3【Cut Off Channel from Environmental Connection】 4【To Define and Thereby Deprive of Judgmental Expression as on it】 5【To Definition [One’s] as a Pathologizing Condition】 6【Strategicness Pseudo‑Guidance Mechanism】 7【Cut the in-subjectness Off from Environmental Connection】 8【Pseudo‑Definitional Mechanism】 9【The Ignoretation of Emotional Expression】 10【Deprivation of in-subjectness】as for 【The in-subjectness arrived the condition that could not be revise or discerned by core self- consciousness】 The third part was integrateing and Mathematic Derivation the concepts proposed from second part. I evidenced the theorems through this derivation process, as following : ① [External-predation constant-effect] ; ② [Innate-resistance Equilibrium-law]; ③ Conjecture on [projection Cost Increasing-rise effect mechanism] Provides important stepping stone for the further expansion , on my subsequent mathematical systems. For this paper as to convey for: across the infinite worlds on dimensions, more and more souls suffering the wounds of [projection plunder mechanism] , And I, want , use through mathematics, to convey the courage , the power , from mine deepth soul , to convey , the hope , as Exist being of . For, That: hope, the exists of it that for , as, its existenced[3]. Keywords: Hope; Ethics; Mathematics; Psychology; projection plunder mechanism; Consciousness; Manipulation Effect; Gaslighting Effect; Derivation of Functional Formulas. [1] 拉丁语单词:篇幅的意思。Latin word: meaning “length.” [2] (Bu, Kuiyuan. 2026). Logical reasoning based on interdisciplinary biomathematics, Chinese source text [3] 哲学表达处理,并不是语法错误。This is a philosophical expression, not a grammatical error. ------- Article Statement This article is mine mathematical derivations, continueing from two previous papers of mine (please refer to the references), as on entirely independent research. This article as continueing the previous extend as [The Hypothesis of Existential Condition Function Relations and Predation] and [The Mathematization of Power]. This function relation as the crucial theorem that I Derivation to : [Existence theorem Y_E]. This theorem was birth in October 2025 while I was oning the Commuter train. Subsequently, I supplemented it with numerous rules and sections as gradually, then began establishing connections with various theories that as mines. Although I completed the derivation on paper quite early, but the part as paper when end of January as 2026 for start writing. About this theorem's derivation supplementing , the important time Nodes for threes (all recorded in the manuscript dates): First, written the mathematical calculation rules as [Existence theorem Y_E], while working at a convenience store at 2025-11-30 ; Second , on the 2026-02-01 5:00 am , written the concept as [Consciousness dual-kernel] as 4 sets of formulas down on mine draft paper (this article only mentions 3 sets, and the last set will be added in subsequent research); Third, while working at a convenience store on 2026-02-03, I supplemented the basic concepts of algorithm rules and mathematical symbols. This, as a theorem, born in throes . I typed, with trembling hands, words with words. But , also because as the throes, for , so precious for Exist being on seen. This theorem is also as mine favorite, I named it [Existence theorem Y_E], the porta-point of it as Ethic , not just for the logic on mathematics. I do not engagement with traditional scientific knowledge as deeply for, therefore alls logical derivation are as independent , also external to traditional research systems. I hold no ill intent. About the mathematical formulas proposal, evince, framework construction, revision, and translation , all of thems were completed independently on mines. During the writing and derivation process as this paper, no software was used for repeated deduction or proof, and I also, refuse to use any artificial intelligence software or any programs for reasoning or content generation. This is hereby declared on mine. For academic exactitudeity, the original Chinese manuscript will be uploaded to the platform(Zenodo). Chinese version as the root on noesis , on expression of mine . As for the evidence of formulas, rules of calculation, logical systems, and concepts, I leave it for time. Hence, my purpose as not to persuade, but as expression. My original intention in writing this paper was to convey a belief : for Hope. This was originally meant to be as pure math derivation, but the self-exploration in throes as mine , let outbreak the new inspiration as mines. I realized , only merely as a mathematical expression may not enough for, so I combined Psychology and Mathematics together. Originally, I had no planned include the part on Psychology for, originally, I intended to leave the exploration of Consciousness for a much later stage. But I known, that the scientificness of presenting my theories in stages , far less than the free will mathematical manifesto . I realized, in this very moment, across realm worlds, as infinite dimensions, more and more souls are suffering the [projection plunder mechanism], as for, Gaslighting, Triangulation, Manipulation Effect, and so many more. And I ,want , through as mathematics, to convey the courage and the power , as from mine soul deepth, use mathematic , to tell alls Exists, whom , had past in , throughing now , future may face on , the mechanism as plunder : Please , believe in , the beauty and preciousness of your own existence. The hope , being here as always , My mathematical theorem , as willing to be as , the deepth hope with this Exists , even for small molecular quantity. Please stand for . Be brave for. Do not give up for. Recognize the dark for .Every act of persistence becomes as the keystone of the hope futurely. I think , perhaps, the meaning of mathematics may not for a calculation, but as a expression. And so I put this work, this insight and discourse on mathematical logic, born of mine own will, to the great edifice of human knowledge. For , a light on mines own , bring to this universe, that is it . --------- This record permanently preserves the original Chinese manuscript of this research and its accompanying English translation. It is created to