A Hodge-based index is generally conceived of as bearing a Real-based integer eigenbase of scalar amplitude. Yet, often a Hodge-based index may be conceived of as bearing an irrational scalar amplitude of eigenbase, and, often a Hodge-based index may be conceived of as bearing an Imaginary scalar amplitude of eigenbase, and, often a Hodge-based index may be conceived of as bearing a scalar amplitude that is both Imaginary and irrational in eigenbase. In so long as one is able to tally-up the sum of any given arbitrary Hodge-Index eigenbasis -- based upon the additive correlation of discrete units of scalar amplitude -- that is respectively consistent upon whatever the directly corresponding eigenbase of Hodge-based index is appertaining to, in any respective given arbitrary case, uniquely and individually per each case scenario that this would then here be attributive to -- then, the so-eluded-to eigenbases of the respective given arbitrary Hodge-Indices may be viewed of as being specifically rigorous -- depending upon each given arbitrary respective case. So, a Hodge-Index is an additive consistent numerical eigenbasis that is discrete, in the process of adding-up the attribution of Hamiltonian-based eigenstates -- that is utilized in the process of working to determine the affectual interaction of one covariant eigenbase of physically present codeterminable codifferentiable holonomic substrate with another covariant eigenbase of physically present codeterminable codifferentiable holonomic substrate -- as such eigenbases are kinematically integrable in each appertaining respective given arbitrary case scenario, over time.
To Be Continued!!! I will continue with the suspense later! Sincerely, Sam Roach.
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