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 δc. These patterns are explained by the first moment method from combinatorics. Defining cumulative information loss δ = Σ I (constraintᵢ) in nats, we show that the multiplicative survival potential S = Nₑff · (μ/μc) · 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 αXOR/αᵣandom = 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.