Constructibility Boundaries in Neural Learning Systems under Synthetic Corruption: A Phenomenological Framework

We study the relationship between a corruption intensity proxy H, a model capacity proxy C, and dataset scale n in neural learning systems. We propose a Constructibility Framework in which learning success is governed by an effective capacity constraint L(S) = Cβ·nγ/Hα. Through controlled corruption injection and systematic scaling of transformer architectures (DistilBERT, BERT-base, RoBERTa-large) on two benchmarks (IMDb, SST-2), we observe sharp, reproducible collapse boundaries in test accuracy. Key advances: Proposition 1 provides operator-wise analytical justification for Assumption A3; Lemma 1 (Risk Bridge) closes the formal gap in Theorem 3; Theorems 4 and 5 characterise the information–capacity tradeoff and monotone boundary; Proposition 2 provides a mechanistic interpretation of collapse sharpness. The collapse coefficient λ = γ/α = 0.331 is derived analytically from the fitted scaling exponents — it is not independently optimised. An empirical scaling law E(S) ~ H1.42/(C0.31 ·n 0.47) is fit with R² = 0.91 across both benchmarks.