Structural Collapse as Information Loss: The Exponential Decay Mechanism under Accumulating Constraints

Large language models exhibit abrupt reasoning collapse when structural contradictions accumulate in their context---a phenomenon distinct from gradual degradation under factual noise. Through controlled experiments (3 models, 3 vendors), we characterize this collapse and find: (i) multiplicative interaction between context margin (μ) and structural contradiction (δ)---two individually non-lethal stressors become lethal in combination, ruling out additive degradation models; (ii) a dimensional structure in δ where, in models with sufficient baseline accuracy, a single structural contradiction causes more damage than 10 factual contradictions; and (iii) a cushion mechanism where RLHF alignment absorbs contradictions until overwhelmed, producing a system-specific critical threshold δ_c. These patterns are explained by the first moment method from combinatorics. Defining cumulative information loss δ = Σ I(constraint_i) in nats, we show that the multiplicative survival potential S = N_eff · (μ/μ_c) · e^(−δ) captures both the LLM collapse patterns and, in Boolean satisfiability (SAT) where δ is exactly computable, yields parameter-free predictions: the decay rate ratio α_XOR/α_random = ln 2 / |ln(7/8)| = 5.19× is an upper bound confirmed experimentally (observed: 5.04 ± 0.25, CV = 5%). The exponential penalty e^(−δ) is not an approximation but a mathematical identity with the first moment of the SAT solution count. Its contribution is an operational methodology---measuring structural conflict as information loss in nats via the first moment correspondence---validated in two controlled domains.