Hogde Indices

Sometimes, the determination of the effect of one substringular phenomenon upon another is not the multiplicitly Minkowski or Hilbert volume itself, yet the number of indices or the number of commutators associated with the construction or framework of the discussed phenomenon upon another. When what determines the direction of gauge-metric in terms of not just directoralization and the ability of motion, yet also helping to determine the velocity, acceleration, and jerking of two or more substringular phenomena over a Fourier Series integration that involves a sequence of iteration within a set region or locus, then the condition of relative distribution of first-ordered point particles is often what helps to determine the prior stated Fourier operations that help indicate the kinematic hermitian or perturbative phenomena translation of a set of gauge-actions and/or superstrings through a certain locus or region over a set of iterations that are defined by a given group metric. When such a scenario involves the addition of the first-ordered point particles as compared in two different phenomena regions, then a first-ordered point particle would be one Hodge Index basis, and the Hodge Index of the two respective phenomena would be the total sum of how many first-ordered point particles could fit in each of the two respective phenomena individually that are interacting within a locus or region. This correlation of relative Hodge Index will define an attribute of relative substringular or gauge-action sway, pulse, or motion via the Hamiltonian basis that describes the general momentum of the phenomena of a region or locus. When the Hodge Index basis is defined by the relative amount of second-ordered point particles that could fit in two respective phenomena that will interact with a momentum in a given direction, the dual Hodge Indices that thus correspond will help define the relative sway, pulse, motion, and directoralization of the interaction of these given phenomena through a described locus or region. A Hodge Index as one point particle fill or a basis is a volume determined operator. Yet, the integration of Hodge Indices though a locus or region that helps to define the relative thrust of a subspace or of a phenomenon is a Laplacian operation. This is Laplacin here because it does not happen in time, it is a timeless occurrence, or, in other words, it is description of a phenomena that already is in one set iteration of time. If the Hodge Index basis involves a counting of third-ordered point particles from within a phenomena that exists in a locus or region, then the respective Hodge Index Laplacian operation will be based on the number of third-ordered point particles that could fit in that given locus or region of phenomena if these were theoretically all flushly integrated together in that region of space. In either case, a Hodge Index basis never includes the kernels in-between where the fit-in point particles would set within a stratum. It (the Hodge Index as a Laplacian operation) only describes the number of theoretical points that could fit in a given stratum if these points were to roll into it as spheres with a separation of their basic actual field impedance. This, by helping to determine relative substringlar thrust in a direction, helps to determine the unfolding of activities in the substringular.