Fixed-Point Traps and Identity Emergence in Educational Feedback Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918037134770176 |
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| author | Alpay, Faruk |
| author_facet | Alpay, Faruk |
| contents | 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 $φ$ are recursively collapsed by evaluative morphisms $E$. We prove that under such collapse regimes, no nontrivial fixed-point algebra $μ_φ$ 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 ϕ-emergence and block observer-invariant self-formation. This work provides the first provable algebraic obstruction of identity formation caused by institutional feedback mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21038 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed-Point Traps and Identity Emergence in Educational Feedback Systems Alpay, Faruk General Mathematics 18A15, 18C15, 91D30, 97C70, 03B70, 68T01 F.4.1; I.2.0; K.3.2 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 $φ$ are recursively collapsed by evaluative morphisms $E$. We prove that under such collapse regimes, no nontrivial fixed-point algebra $μ_φ$ 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 ϕ-emergence and block observer-invariant self-formation. This work provides the first provable algebraic obstruction of identity formation caused by institutional feedback mechanics. |
| title | Fixed-Point Traps and Identity Emergence in Educational Feedback Systems |
| topic | General Mathematics 18A15, 18C15, 91D30, 97C70, 03B70, 68T01 F.4.1; I.2.0; K.3.2 |
| url | https://arxiv.org/abs/2505.21038 |