This is a continuation paper to the authors’ previous work demonstrating an integrative surgery formula for framed instanton homology. First, we introduce a large-scale operative formula enhancement, a reasonable operative formula for null homology knots on arbitrary 3-manifolds, and a formula that encodes most of $I^\sharp(S^3_0(K))$ present. Second, we use the integral surgery formula to study the assembled instanton homology of many of his 3-manifolds. Seiffert fiber spaces with non-zero orbifold order, especially non-trivial circular bundles on arbitrary orientable surfaces, the family of alternating knot surgeries, and all twisted Whitehead doubles, splicing with twisted knots. Finally, using previous techniques and computations, we find that there is approximately a knot ${\it ie}$, $\dim I^\sharp(S_n^3(K) in L-space $n\in\mathbb{N} _+$ versus )=n+2$ . Approximately L-space knots of genus at least $2 are fibrized and strongly orthonormal, and genus-1 approximately L-space knots are either figure-of-eight or mirrors of Rolfsen’s $5_2 knots. Indicates that you must knot table.
