Paper 9. The Exact Form of the Obstruction

Osman, Mohamed

Paper 9. The Exact Form of the Obstruction

An identity for the twin count with no error term, and why an ordinary sieve cannot cross it

Mohamed Osman · ORCID 0009-0004-5912-999X · independent researcher · 2026-10-16

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Abstract. Under a depth cut the twin count satisfies T = C - R + S with no error term, which turns the twin problem into a comparison of two counts and shows the comparison needs a sign, not a bound.

No progress toward the twin-prime conjecture is claimed. Priority is not claimed for any result. Every number printed is regenerated by a script in code/ of the repository. Licence: CC BY 4.0 (text), MIT (code).