Theoretical analysis demonstrates proofs for structural reductions in twin-prime propagation, indicating refined mathematical conjectures shaped by covering lemmas.
I introduced the Twin-Prime Propagation Conjecture and the Twin-Gap Existence Conjecture in two earlier notes [2, 3], and gave a structural reduction of both in [4]. This note records the proofs of every local statement used in that reduction, and restates the two conjectures in the form that the covering lemmas force.
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Dacomb Bierton (2026) studied this question.
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