Table A.2

Stellar and planetary parameters from the photodynamical modelling of the 2:1 resonance solution on Kepler long- and short-cadence data, the 6:2:1 resonance solution on Kepler data, the 3:2:1 resonance solution on Kepler data, the 3:2:1 resonance solution on Kepler data and the three KOINet transit light curves, and some corrections from investigating stellar evolution models in Sect. 5.4.

Parameter	Kepler data	Kepler data	Kepler data	Kepler &	MESA
				KOINet data
	2:1	6:2:1	3:2:1	3:2:1	3:2:1
Kepler-82b
mb∕mS
	207 ± 10
ab,corr		0.999927 ± 0.000011
	0.1684 ± 0.0021	0.1683 ± 0.0020	0.1683 ± 0.0020	0.1683 ± 0.0020
	26.44 ± 0.48	26.44 ± 0.48	26.44 ± 0.48	26.44 ± 0.48
eb
	0 (fixed)
	254.6 ± 1.3
	0.079 ± 0.018
	354.6 ± 1.3
Rb∕RS
Kepler-82c
mc∕mb	0.156 ± 0.012	1.06 ± 0.14
	32.2 ± 2.2				14.3 ± 1.3
ac,corr
	0.2637 ± 0.0032	0.2626 ± 0.0032	0.2626 ± 0.0032	0.2626 ± 0.0032
	51.84 ± 0.95	51.53 ± 0.94	51.53 ± 0.94	51.54 ± 0.94
ec
config. I		89.96 ± 0.18
config. II		–
config. I				1.6 ± 2.1
config. II	0.29 ± 0.10	–	–	–
				− 0.507 ± 0.020
Rc ∕RS
Kepler-82f
mf ∕mc	–
	–	415 ± 23	20.9 ± 1.0	20.9 ± 1.0
Pf ∕Pc	–
(d)	–			75.732 ± 0.012
	–	0.5616 ± 0.0068	0.3395 ± 0.0041	0.3395 ± 0.0041
ef	–
config. I	–			86.30 ± 0.56
config. II	–	–
	–		1.9 ± 2.2
	–
	–
Kepler-82
mS (M⊙)	0.91 ±0.03 (fixed, Johnson et al. 2017)
RS (R⊙)
c1,Kepler
c2,Kepler