OBJECTIVES: THE SOLAR MAGNETIC FIELD IS THE ENERGY SOURCE FOR VIOLENT SOLAR ACTIVITY IN THE FORM OF FLARES CORONAL MASS EJECTIONS (CMES) AND PROMINENCE ERUPTIONS. THE ENERGY IS BELIEVED TO BE STORED AS FREE MAGNETIC ENERGY (ENERGY ABOVE THE POTENTIAL FIELD STATE) PRIOR TO ERUPTION. ONE OF THE OUTSTANDING PROBLEMS IN SOLAR PHYSICS IS TO UNDERSTAND THE MECHANISM(S) OF THIS ENERGY RELEASE TO THE POINT OF OBTAINING A PREDICTIVE CAPABILITY. AN INTRIGUING RESULT FROM RECENT SIMULATIONS (E.G. AMARI ET AL. NATURE 514 2014) IS THAT THE ENERGY OF A PARTICULAR FIELD THE PARTIALLY OPEN FIELD APPEARS TO BOUND THE ENERGY STORAGE OF AN ERUPTING REGION I.E. WHEN THE FREE ENERGY OF A REGION APPROACHES THIS BOUND THE CONFIGURATION ERUPTS. IF THIS PROVES TO BE TRUE IN GENERAL IT WOULD PROVIDE A POWERFUL WAY TO ESTIMATE THE POSSIBLE ENERGY RELEASE PRIOR TO ERUPTION. THE PRIMARY OBJECTIVE OF THIS PROPOSAL IS TO DIRECTLY TEST THIS THEORETICAL IDEA USING SOLAR DYNAMICS OBSERVATORY (SDO) HELIOSEISMIC AND MAGNETIC IMAGER (HMI) AND ATMOSPHERIC IMAGING ASSEMBLY (AIA) DATA. DATA: OUR INVESTIGATION WILL PRIMARILY USE SDO HMI LINE-OF-SIGHT AND VECTOR MAGNETOGRAMS AND SDO AIA EUV IMAGES. METHODOLOGY: THE ALY-STURROCK THEOREM (ALY APJ 375 1991; STURROCK APJ 380 1991) STATES THAT A FORCE-FREE MAGNETIC FIELD CANNOT HAVE AN ENERGY THAT EXCEEDS THAT OF THE OPEN FIELD OF A MAGNETIC FLUX DISTRIBUTION; IF THE THEOREM HOLDS THE MAXIMUM FREE ENERGY THAT CAN BE STORED IN A REGION CORRESPONDS TO THE DIFFERENCE BETWEEN THE ENERGIES OF THE OPEN AND POTENTIAL FIELDS. HOWEVER IT IS DIFFICULT TO APPLY THIS THEOREM TO REAL FLARES/CMES WHICH OPEN ONLY A PORTION OF THE FIELD SO THAT THE ALY-STURROCK THEOREM CAN GREATLY OVERESTIMATE THE POSSIBLE STORED ENERGY. SIMULATION STUDIES HAVE FOUND THAT THE ENERGY OF A CLOSELY-RELATED FIELD THE PARTIALLY OPEN FIELD MAY PROVIDE A MORE PRACTICAL BOUND FOR THE ENERGY THAT CAN BE STORED IN AN ERUPTING REGION. THIS FIELD IS DEFINED TO BE OPEN EVERYWHERE IN A SUBDOMAIN S_O ON THE SOLAR SURFACE AND CLOSED EVERYWHERE ELSE. S_O IS THE REGION WHERE THE FIELD OPENS AND/OR RECONNECTS. A RECENTLY DEVELOPED FLARE-RIBBON DATABASE (KAZACHENKO ET AL. APJ 845 2017) CAN PROVIDE A CRITICAL TEST OF THIS THEORY. THIS DATABASE INCLUDES OVER 3000 FLARES FROM 2010 TO EARLY 2016. THE FLARE RIBBON MASKS (THE AREA SWEPT OUT BY THE RIBBONS DURING THE FLARE) ARE MEASURED USING AIA 1600A IMAGES AND PROVIDE A USEFUL ESTIMATE FOR S_O IN THE THEORY. WE WILL USE THESE MASKS TO DEFINE S_O AND COMPUTE PARTIALLY OPEN FIELDS USING HMI MAGNETIC FIELDS AS BOUNDARY CONDITIONS. WE WILL PERFORM THESE CALCULATIONS FOR A WIDE RANGE OF ERUPTIVE FLARES AND COMPARE THE FREE ENERGY LIMIT CALCULATED FOR THE PARTIALLY OPEN FIELDS TO NOAA GOES X-RAY DATA. OUR STUDIES WILL COMPREHENSIVELY TEST THIS THEORY AS WE EXPECT THERE SHOULD BE A SIGNIFICANT CORRELATION BETWEEN THE PARTIALLY OPEN FIELD ENERGIES AND GOES X-RAY FLUENCES. THE CALCULATION OF PARTIALLY OPEN FIELDS INVOLVES SOLUTIONS OF LAPLACE'S EQUATION AND FIELD LINE TRACING. WE HAVE DEVELOPED FAST SOLVERS AND TOOLS FOR THESE TASKS MAKING IT FEASIBLE TO COMPUTE HUNDREDS OF CASES. RELEVANCE: OUR PROPOSED WORK ADDRESSES KEY GOALS OF THE SDO MISSION (WHAT MAGNETIC FIELD CONFIGURATIONS LEAD TO THE CMES FILAMENT ERUPTIONS AND FLARES THAT PRODUCE ENERGETIC PARTICLES AND RADIATION?) AND THE HELIOPHYSICS DECADAL SURVEY (DETERMINE THE ORIGINS OF THE SUN'S ACTIVITY AND PREDICT THE VARIATIONS IN THE SPACE ENVIRONMENT).