Sidon extension and density interfaces

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constants_and_polynomial_images: Leading constants, multiplicative conventions, root normalization and compatible infinite extensions remain separate from order estimates.

difference_endpoints: Processing the least missing difference bounds its eventual endpoints; a counting-function estimate alone does not control that processing order.

finite_extremality: Separate global size estimates from local threshold gaps, fixed-prefix completion, ambient scaling and arbitrary-set compression.

greedy_saturation: The existing cubic blocker count bounds every greedy prefix, while sparse maximal constructions and dissociation require different interfaces.

infinite_density: Bounded sum multiplicity, bounded difference multiplicity, all-cutoff density and zero-liminf conclusions require different hypotheses.

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These notes retain explicit deductions, source specializations and useful obstructions. Each note states the exact remaining hypothesis or test. All original arguments are author-recorded by Plasma AI; source premises keep their stated reading and acceptance limits.