Proton factorial cumulants K4, K5 and K6 in 0-40$\%$ and 50-60$\%$ Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Proton factorial cumulants K4, K5 and K6 in 0-40$\%$ and 50-60$\%$ Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Proton factorial cumulants K4, K5 and K6 in 0-40$\%$ and 50-60$\%$ Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Proton factorial cumulants K4, K5 and K6 from UrQMD model (0-40$\%$ and 50-60$\%$ centrality) for Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. UrQMD calculation for 3 GeVis with rapidity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5). In addition, two-component model (0-40$\%$) calculations for facorial cumulants are also given.

Proton factorial cumulants K4, K5 and K6 from UrQMD model (0-40$\%$ and 50-60$\%$ centrality) for Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. UrQMD calculation for 3 GeVis with rapidity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5). In addition, two-component model (0-40$\%$) calculations for facorial cumulants are also given.

Proton factorial cumulants K4, K5 and K6 from UrQMD model (0-40$\%$ and 50-60$\%$ centrality) for Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. UrQMD calculation for 3 GeVis with rapidity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5). In addition, two-component model (0-40$\%$) calculations for facorial cumulants are also given.

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 - 200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, measurement is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) from UrQMD model in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 -200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, UrQMD calculation is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) from UrQMD model in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 -200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, UrQMD calculation is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Net-proton cumulant ratios C4/C2, C5/C1, C6/C2 (0-40$\%$ and 50-60$\%$ centrality) and C3/C1 (0-40$\%$ centrality) from UrQMD model in Au+Au collisions from $\sqrt{s_{NN}}$ = 3 -200 GeV. At $\sqrt{s_{NN}}$ = 3 GeV, UrQMD calculation is done for protons instead of net-protons, and with halfrapdity coverage (-0.5 $<$ y $<$ 0) while for rest of energies the rapidity coverage is (-0.5 $<$ y $<$ -0.5).

Fifth-to-first (KS5/KS1) and sixth-to-second (KS6/KS2) order K-statistic ratios of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0-40$\%$ and 50-60$\%$ centrality.

Fifth-to-first (KS5/KS1) and sixth-to-second (KS6/KS2) order K-statistic ratios of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0-40$\%$ and 50-60$\%$ centrality.

Fifth-to-first (KS5/KS1) and sixth-to-second (KS6/KS2) order K-statistic ratios of net-proton distributions in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV for 0-40$\%$ and 50-60$\%$ centrality.

Net-proton cumulant ratio C6/C2 and corresponding K-statistic ratio (0-40$\%$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of sample size. Uncertainties are only statistical.

Net-proton cumulant ratio C6/C2 and corresponding K-statistic ratio (0-40$\%$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of sample size. Uncertainties are only statistical.

Net-proton cumulant ratio C6/C2 and corresponding K-statistic ratio (0-40$\%$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7 GeV as a function of sample size. Uncertainties are only statistical.

Cumulant ratios C4/C2, C5/C1 and C6/C2 of net-proton distributions measured with half rapdity coverage (-0.5 $<$ y $<$ 0) in 0-40$\%$ central Au+Au collisions for collider energies from $\sqrt{s_{NN}}$ = 7.7 - 54.4 GeV.

Cumulant ratios C4/C2, C5/C1, C6/C2 and C3/C1 of net-proton distributions measured with half rapdity coverage (-0.5 $<$ y $<$ 0) in 0-40$\%$ central Au+Au collisions for collider energies from $\sqrt{s_{NN}}$ = 7.7 - 54.4 GeV.

Cumulant ratios C4/C2, C5/C1, C6/C2 and C3/C1 of net-proton distributions measured with half rapdity coverage (-0.5 $<$ y $<$ 0) in 0-40$\%$ central Au+Au collisions for collider energies from $\sqrt{s_{NN}}$ = 7.7 - 54.4 GeV.

Cumulant ratios C5/C1 of net-proton distributions measured in 40-50$\%$, 60-70$\%$, and 70-80$\%$ Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV. This is supplemental data and was not part of the original paper.