  In the quest for mathematical foundations of M-theory, the "Hypothesis H"
that fluxes are quantized in Cohomotopy theory, implies, on flat but possibly
singular spacetimes, that M-brane charges locally organize into equivariant
homotopy groups of spheres. Here we show how this leads to a correspondence
between phenomena conjectured in M-theory and fundamental mathematical
concepts/results in stable homotopy, generalized cohomology and Cobordism
theory Mf:
  Stems of homotopy groups correspond to charges of probe p-branes near black
b-branes; stabilization within a stem is the boundary-bulk transition; the
Adams d-invariant measures G4-flux; trivialization of the d-invariant
corresponds to H3-flux; refined Toda brackets measure H3-flux; the refined
Adams e-invariant sees the H3-charge lattice; vanishing Adams e-invariant
implies consistent global C3-fields; Conner-Floyd's e-invariant is H3-flux seen
in the Green-Schwarz mechanism; the Hopf invariant is the M2-brane Page charge
(G7-flux); the Pontrjagin-Thom theorem associates the polarized brane
worldvolumes sourcing all these charges. Cobordism in the third stable stem
witnesses spontaneous KK-compactification on K3-surfaces; the order of the
third stable stem implies 24 NS5/D7-branes in M/F-theory on K3. Quaternionic
orientations correspond to unit H3-fluxes near M2-branes; complex orientations
lift these unit H3-fluxes to heterotic M-theory with heterotic line bundles. In
fact, we find quaternionic/complex Ravenel-orientations bounded in dimension;
and we find the bound to be 10, as befits spacetime dimension 10+1.
