A KEY PREDICTION OF COLD DARK MATTER (CDM) COSMOLOGY IS A SCALE-FREE HIERARCHY OF BOUND STRUCTURE FROM THE LARGEST GALAXY CLUSTERS DOWN TO EARTH-MASS MICROHALOS. WHEN PARTNERED WITH THE WEAKLY INTERACTING MASSIVE PARTICLE (WIMP) HIGH-ENERGY PHYSICS DESCRIPTION OF CDM THIS SIMPLE COSMOLOGICAL MODEL MAKES ACCURATE PREDICTIONS FOR THE ABUNDANCE OF DARK MATTER IN THE UNIVERSE. IT SUCCESSFULLY PREDICTS DARK MATTER CLUSTERING ON LARGE SCALES. HOWEVER WIMPS HAVE NEVER BEEN DETECTED IN THE LAB AND THERE ARE PERSISTENT HINTS THAT SMALL-SCALE STRUCTURE IS UNDERABUNDANT COMPARED TO CDM PREDICTIONS. A DIRECT OBSERVATION OF SMALL DARK MATTER HALOS WOULD EITHER LEND STRONG SUPPORT TO THE WIMP/CDM PARADIGM OR CONCLUSIVELY KILL THE DOMINANT PHENOMENOLOGICAL MODEL OF DARK MATTER. GRAVITATIONAL LENSING IS A MOST PROMISING TOOL FOR DISCOVERING SMALL (<10^9 SOLAR MASS) HALOS OUTSIDE OF THE MILKY WAY. UNTIL RECENTLY THE PRIMARY BARRIER TO PROGRESS WAS OBSERVATIONAL; FEW GRAVITATIONAL LENS SYSTEMS WERE KNOWN AND AMENABLE TO SUBSTRUCTURE LENSING STUDIES. BUT AS MANY THOUSANDS OF NEW LENSES ARE FOUND IN WIDE-FIELD SURVEYS INNOVATIVE NEW METHODS TO MAXIMALLY EXPLOIT LENSES MATURE AND WITH THE ESSENTIAL FOLLOW-UP CAPABILITY OF JWST AND WFIRST WE WILL FOR THE FIRST TIME BE OPERATING IN A DATA-RICH ENVIRONMENT FOR SUBSTRUCTURE LENSING. THE MISSING INGREDIENT TO TURN THESE DATA INTO A DEFINITIVE TEST OF CDM OR NON-CDM MODELS IS A COMPREHENSIVE THEORETICAL FRAMEWORK LINKING DARK-MATTER MICROPHYSICS TO OBSERVABLES MARGINALIZING OVER UNCERTAINTIES IN GALAXY EVOLUTION PHYSICS HOST PROPERTIES AND LINE-OF-SIGHT STRUCTURE. WHILE SEVERAL BASIC ESTIMATES EXIST IN THE LITERATURE THERE ARE NO DEDICATED SIMULATIONS THAT INCLUDE ALL THESE EFFECTS FOR LENS-MASS SYSTEMS. OUR PROPOSED THEORETICAL PROGRAM IS ESSENTIAL FOR TURNING THE INCREDIBLE POTENTIAL OF THE FORTHCOMING SUBSTRUCTURE LENSING DATA INTO AN UNPRECEDENTED CONSTRAINT ON DARK MATTER MODELS. WE PROPOSE TO FORECAST CONSTRAINTS ON DARK MATTER PHYSICS FROM SUBSTRUCTURE LENSING OBSERVATIONS WITH JWST AND WFIRST BASED ON THE THEORETICAL FRAMEWORK THAT WE CREATE AS PART OF THIS PROPOSAL. WE WILL CONSTRUCT A SET OF PROBABILISTIC MODELS AND LIKELIHOOD FUNCTIONS THAT ARE BASED ON THE SEMI-ANALYTIC MODEL WE WILL DEVELOP. SEMIANALYTIC MODELS ARE TUNED TO FAITHFULLY MATCH N-BODY SIMULATIONS BUT RUN IN A TINY FRACTION OF THE TIME. THEIR SPEED ENABLES SCANS THROUGH DARK MATTER MODEL PARAMETER SPACE; THEY CAN GENERATE ENSEMBLES OF SYSTEMS MATCHING OBSERVED HOSTS; AND CAN EXPLORE AND MARGINALIZE OVER THE UNCERTAINTIES IN GALAXY EVOLUTION FEEDBACK ON SMALL-SCALE STRUCTURE. WE WILL RUN CAREFULLY STAGED SIMULATIONS IN ORDER TO BETTER PARAMETERIZE EVOLUTIONARY EFFECTS ON DARK MATTER HALOS INCLUDING THE EFFECTS OF BARYONS ON THE OBSERVATIONS AND TO TEST OUR SEMI-ANALYTIC MODEL. THE FINAL PRODUCT OF THIS WORK WILL BE A SET OF PROPOSED JWST AND WFIRST FOLLOW-UP CAMPAIGNS THAT WILL MAXIMIZE DARK MATTER SCIENCE AS A FUNCTION OF OBSERVATION TIME WITH THE EXPECTED DARK MATTER CONSTRAINTS AND THEORETICAL UNCERTAINTIES WELL QUANTIFIED. WE WILL MAKE THE SEMI-ANALYTIC MODEL AND OUR LIKELIHOOD FUNCTIONS PUBLIC TO SERVE THE WHOLE DARK MATTER ASTROPHYSICS COMMUNITY. WITH THIS WORK WE WILL FINALLY REALIZE THE POTENTIAL OF SUBSTRUCTURE LENSING TO TEST THE MOST FUNDAMENTAL PREDICTION OF THE CDM PARADIGM.