FIG. 5: Electric field strength dependence of extracted proton parameters. Plots are as in Fig. 3. TABLE II: Summary of fit results for proton two-point functions using the time window: 6 ≤ t/a$_{t}$ ≤ 28. Tabulated entries are as in Table I, with the exception that we have denoted the magnetic couplings as anomalous using tildes. P n a$_{t}$E ( n ) ˜ µ $^{latt}$( n ) χ $^{2}$/d 1 − P 0 0 . 2052(24) – 0 . 61 0 . 93 1 0 . 2072(17) 53(6) 0 . 65 0 . 97 2 0 . 2118(22) 48(3) 0 . 81 0 . 80 3 0 . 2198(26) 46(2) 0 . 86 0 . 74 4 0 . 2293(29) 41(1) 1 . 5 0 . 02 P a$_{t}$M α latt E χ $^{2}$/d 1 − P ˜ µ latt χ $^{2}$/d 1 − P I 0 . 205(2) 32(13)(1) 0 . 14 0 . 98 52(3)(1) 1 . 3 0 . 3 II 0 . 205(2) 31(25)(4) 0 . 16 0 . 96 52(4)(1) 1 . 7 0 . 2 GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.200 0.205 0.210 0.215 0.220 0.225 0.230 0.235 0.240 a$_{t}$ a$_{s}$ e GLYPH<ScriptCapE> a t E GLYPH<LParen1> GLYPH<ScriptCapE> GLYPH<RParen1> P: I GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.200 0.205 0.210 0.215 0.220 0.225 0.230 0.235 0.240 a$_{t}$ a$_{s}$ e GLYPH<ScriptCapE> a t E GLYPH<LParen1> GLYPH<ScriptCapE> GLYPH<RParen1> P: II GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> 0.000 0.005 0.010 0.015 0.020 0.025 0.030 35 40 45 50 55 60 65 a$_{t}$ a$_{s}$ e GLYPH<ScriptCapE> Μ latt GLYPH<LParen1> GLYPH<ScriptCapE> GLYPH<RParen1> P: I GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> GLYPH<SolidCircle> 0.000 0.005 0.010 0.015 0.020 0.025 0.030 35 40 45 50 55 60 65 a$_{t}$ a$_{s}$ e GLYPH<ScriptCapE> Μ latt GLYPH<LParen1> GLYPH<ScriptCapE> GLYPH<RParen1> P: II We perform fits to proton correlations functions on the entire bootstrap ensemble. This enables us to form an ensemble of extracted parameters for each value of the field strength, In particular, we consider the ensemble of extracted ground state rest energies, { E$_{i}$ ( n ) } , and ground state anomalous magnetic moments, { ˜ µ$_{i}$ ( n ) } . Collectively we denote these ensembles by O$_{i}$ ( n ), with the ensemble average denoted by O ( n ). Electric field correlated fits are performed using the fit functions in Eqs. (21) and (22). For the latter it is the electric field dependence of the anomalous couplings that is being fit. Furthermore, we extract the anomalous magnetic moment using the constraint µ latt EEE = 0, which results in better fits. For both observables, we perform the fit using all the data (fit I), and excluding results for the largest field strength (fit II). Results of the fits are collected in Table II. The electric field strength dependence of the extracted rest energies and anomalous magnetic couplings are shown in Fig. 5. Also depicted are the field-correlated fits to these quantities. The values 15