Canonical representatives and interval independence in Ekedahl's equivalence

Ekedahl’s equivalence reconstructs coherent Raynaud complexes from coherent F-gauges by a completed derived functor. We study this inverse before totalization. At a fixed finite level, we construct finite projective resolutions and express the inverse as a tensor product with a complex of bimodules. Its cohomology in the resolution direction gives actual R-complex representatives of diagonal cohomology. We prove that these representatives are independent of the interval and obtain an exact fully faithful functor from the diagonal heart to Ch®, splitting localization. Finally, we compute the domino factors for three cyclic crystalline presentations of supergeneral abelian threefolds. The resulting elementary factor types are {2,3,4}, {2,3,7}, and {2,3,6}.