Additive combinatorics

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L274_signed_sidon_moment_extension/: For N at least 55, genuine fixed-cardinality moments through degree two have signed degree-four extensions satisfying every Sidon zero and cardinality identity; for N at least 58 the parity square can also be preserved. No matrix positivity is asserted.

L31_finite_sidon_prefix_extension/: Delete finitely many conflicting differences from a Singer set and separate the three types of pair sums to preserve an arbitrary fixed prefix.

L38_restricted_difference_basis_convergence/: A Singer lift and an explicit endpoint patch prove convergence of the restricted difference-basis ratio and an infimum formula with an additive two.

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These claims concern finite additive configurations and their extensions. Each source-dependent argument records the theorem it uses and the extent to which that source has been inspected.