Laurent Exponential Gauss--Manin Systems: Exact Quantum Curves, Completion, and Hard-Edge Degeneration

For polynomial--Laurent exponential phases with independentinverse-power coefficients, we construct split twisted normal formsand flat meromorphic connections, uniformly in the formalsemiclassical parameter. The localized quotient has rank $N=d+k$;the constant amplitude is cyclic and satisfies an exact monic quantumcurve of order N, with its operator-ordering correction determinedby twisted integration by parts. Exact normal-form trace identitiesgive the full period determinantC_ΓN/2bₖ(k+1)/2e-Σ/,where the total critical action Σ separates into polynomialand inverse-power coefficient contributions. This identity includesthe determinant monodromy and a Gaussian thimble normalization.For a single pole coefficient the connection is Fuchsian, withmoment-frame residue spectrum $0$ (multiplicity d) and1/k,…,k/k. A normalized completion--Tor--monodromy theorem,transferred with its full proof from the GHEA research, identifiesthe completed comparison kernel with derived Tor layers and thelocal monodromy image. Pole removal gives exact Weyl factorizations,rank loss, and a flat but non-finitely-generated unlocalized family.A Newton-gap theorem determines the number of collapsing criticalpoints and their singular action and Hessian scales when a highestpole disappears above a lower nonzero pole. A rank-five positive-rayexample has exponential irregular growth although its determinantconnection is regular singular. We also prove endpointPuiseux--logarithmic expansions and the large-parameter splittinginto polynomial and hard-edge saddles. Full signed Stokes matricesand a simultaneous multipole Tor--monodromy theorem remain open;historical novelty of the individual formulas is not asserted.