Fixed-Point Traps and Identity Emergence in Educational Feedback Systems
This paper presents a formal categorical proof that exam-driven educational systems obstruct identity emergence and block creative convergence. Using the framework of Alpay Algebra II and III, we define Exam-Grade Collapse Systems (EGCS) as functorial constructs where learning dynamics $\varphi$ are recursively collapsed by evaluative morphisms $E$. We prove that under such collapse regimes, no nontrivial fixed-point algebra $\mu_\varphi$ can exist, hence learner identity cannot stabilize. This creates a universal fixed-point trap: all generative functors are entropically folded before symbolic emergence occurs. Our model mathematically explains the creativity suppression, research stagnation, and structural entropy loss induced by timed exams and grade-based feedback. The results apply category theory to expose why modern educational systems prevent {\phi}-emergence and block observer-invariant self-formation. This work provides the first provable algebraic obstruction of identity formation caused by institutional feedback mechanics.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Alpay Algebra II: Identity as Fixed-Point Emergence in Categorical Data
In this second installment of the Alpay Algebra framework, I formally define identity as a fixed point that emerges through categorical recursion. Building upon the transfinite operator $\varphi^\infty$, I characterize i…
Alpay Algebra III: Observer-Coupled Collapse and the Temporal Drift of Identity
This paper introduces a formal framework for modeling observer-dependent collapse dynamics and temporal identity drift within artificial and mathematical systems, grounded entirely in the symbolic foundations of Alpay Al…
Formal LogicVoice Privacy with Smart Digital Assistants in Educational Settings
The emergence of voice-assistant devices ushers in delightful user experiences not just on the smart home front, but also in diverse educational environments from classrooms to personalized-learning/tutoring. However, th…
Automatic Speech RecognitionAutomatic Speech Recognition (ASR)Speaker Identificationspeech-recognition+1Self-conditioned Flow Map Language Models via Fixed-point Flows
Self-conditioning is a core technique that enhances continuous flow-based language models, where the model learns to denoise generated text by conditioning on its own denoising estimate. While empirically successful, its…
Fixed Points of Deep Neural Networks: Emergence, Stability, and Applications
We present numerical and analytical results on the formation and stability of a family of fixed points of deep neural networks (DNNs). Such fixed points appear in a class of DNNs when dimensions of input and output vecto…