<table><caption>**Table B.1. Continued from the previous page.**</caption><thead><tr><th>Date (UT)</th><th>Facility</th><th>Planet(s)</th><th>Epoch(s)</th><th>N<sub>points</sub></th><th>T<sub>exp</sub> (s)</th><th>Baseline model</th><th>Residual RMS (%)</th><th>β<sub>w</sub></th><th>β<sub>r</sub></th></tr></thead><tbody><tr><td>2020-09-01</td><td>TESS</td><td>c</td><td>52</td><td>240</td><td>120</td><td>o</td><td>0.115</td><td>0.91</td><td>1.00</td></tr><tr><td>2020-09-02</td><td>TESS</td><td>d</td><td>51</td><td>236</td><td>120</td><td>o</td><td>0.131</td><td>1.04</td><td>1.08</td></tr><tr><td>2020-09-03</td><td>TESS</td><td>b</td><td>86</td><td>208</td><td>120</td><td>o</td><td>0.110</td><td>0.87</td><td>1.07</td></tr><tr><td>2020-09-03</td><td>TESS</td><td>f</td><td>13</td><td>288</td><td>120</td><td>o</td><td>0.112</td><td>0.88</td><td>1.32</td></tr><tr><td>2020-09-04</td><td>TESS</td><td>b, c</td><td>87, 53</td><td>361</td><td>120</td><td>o</td><td>0.120</td><td>0.93</td><td>1.50</td></tr><tr><td>2020-09-07</td><td>CHEOPS</td><td>e, g</td><td>34, 10</td><td>555</td><td>60</td><td>sp(r) + p(t)</td><td>0.060</td><td>1.06</td><td>1.71</td></tr><tr><td>2020-09-10</td><td>TESS</td><td>b</td><td>90</td><td>207</td><td>120</td><td>o</td><td>0.131</td><td>1.03</td><td>1.48</td></tr><tr><td>2020-09-11</td><td>TESS</td><td>c</td><td>55</td><td>238</td><td>120</td><td>o</td><td>0.124</td><td>0.98</td><td>1.56</td></tr><tr><td>2020-09-12</td><td>TESS</td><td>b</td><td>91</td><td>207</td><td>120</td><td>o</td><td>0.115</td><td>0.91</td><td>1.25</td></tr><tr><td>2020-09-14</td><td>TESS</td><td>b</td><td>92</td><td>195</td><td>120</td><td>o</td><td>0.120</td><td>0.95</td><td>1.34</td></tr><tr><td>2020-09-14</td><td>TESS</td><td>c</td><td>56</td><td>216</td><td>120</td><td>o</td><td>0.126</td><td>0.99</td><td>1.26</td></tr><tr><td>2020-09-15</td><td>TESS</td><td>d</td><td>53</td><td>287</td><td>120</td><td>o</td><td>0.138</td><td>1.09</td><td>1.24</td></tr><tr><td>2020-09-16</td><td>TESS</td><td>b</td><td>93</td><td>207</td><td>120</td><td>o</td><td>0.135</td><td>1.07</td><td>1.33</td></tr><tr><td>2020-09-17</td><td>TESS</td><td>e</td><td>35</td><td>308</td><td>120</td><td>o</td><td>0.129</td><td>1.02</td><td>1.03</td></tr><tr><td>2020-09-18</td><td>TESS</td><td>c</td><td>57</td><td>240</td><td>120</td><td>o</td><td>0.122</td><td>0.96</td><td>1.00</td></tr><tr><td>2020-09-18</td><td>TESS</td><td>b</td><td>94</td><td>207</td><td>120</td><td>o</td><td>0.116</td><td>0.91</td><td>1.48</td></tr><tr><td>2020-09-18</td><td>TESS</td><td>f</td><td>14</td><td>267</td><td>120</td><td>o</td><td>0.125</td><td>0.98</td><td>1.37</td></tr><tr><td>2020-09-28</td><td>CHEOPS</td><td>b, d, g</td><td>99, 55, 11</td><td>434</td><td>60</td><td>sp(r) + p(b)</td><td>0.061</td><td>1.05</td><td>1.16</td></tr><tr><td>2020-10-03</td><td>CHEOPS</td><td>b, f</td><td>102, 15</td><td>426</td><td>60</td><td>sp(r) + p(y)</td><td>0.057</td><td>1.02</td><td>1.25</td></tr><tr><td>2020-10-04</td><td>CHEOPS</td><td>d</td><td>56</td><td>483</td><td>60</td><td>sp(r) + p(b)</td><td>0.059</td><td>1.05</td><td>2.19</td></tr><tr><td>2020-10-05</td><td>CHEOPS</td><td>b</td><td>103</td><td>365</td><td>60</td><td>sp(r) + p(b)</td><td>0.057</td><td>1.01</td><td>1.31</td></tr><tr><td>2020-10-07</td><td>CHEOPS</td><td>c, e</td><td>63, 37</td><td>486</td><td>60</td><td>sp(r) + p(y)</td><td>0.059</td><td>1.05</td><td>1.27</td></tr><tr><td>2020-10-07</td><td>CHEOPS</td><td>b</td><td>104</td><td>374</td><td>60</td><td>sp(r) + o</td><td>0.056</td><td>1.00</td><td>1.58</td></tr><tr><td>2020-10-09</td><td>CHEOPS</td><td>b</td><td>105</td><td>394</td><td>60</td><td>sp(r) + o</td><td>0.058</td><td>1.04</td><td>1.03</td></tr><tr><td>2020-10-19</td><td>CHEOPS</td><td>b, f</td><td>110, 16</td><td>329</td><td>60</td><td>sp(r) + p(t)</td><td>0.057</td><td>1.02</td><td>1.27</td></tr><tr><td>2020-10-23</td><td>CHEOPS</td><td>c</td><td>68</td><td>258</td><td>60</td><td>sp(r) + p(t)</td><td>0.061</td><td>1.08</td><td>1.16</td></tr><tr><td>2020-10-28</td><td>CHEOPS</td><td>b</td><td>115</td><td>205</td><td>60</td><td>sp(r) + o</td><td>0.062</td><td>1.11</td><td>1.36</td></tr><tr><td>2020-10-30</td><td>CHEOPS</td><td>c</td><td>70</td><td>282</td><td>60</td><td>sp(r) + p(ttt)</td><td>0.060</td><td>1.07</td><td>1.68</td></tr><tr><td>2020-11-02</td><td>CHEOPS</td><td>c</td><td>71</td><td>268</td><td>60</td><td>sp(r) + p(t)</td><td>0.061</td><td>1.09</td><td>1.75</td></tr><tr><td>2020-11-03</td><td>CHEOPS</td><td>b, f</td><td>118, 17</td><td>233</td><td>60</td><td>sp(r) + p(ttt)</td><td>0.057</td><td>1.00</td><td>1.49</td></tr><tr><td>2020-11-06</td><td>CHEOPS</td><td>e</td><td>40</td><td>297</td><td>60</td><td>sp(r) + o</td><td>0.056</td><td>1.00</td><td>1.84</td></tr><tr><td>2020-11-06</td><td>CHEOPS</td><td>d</td><td>61</td><td>247</td><td>60</td><td>sp(r) + o</td><td>0.059</td><td>1.06</td><td>1.90</td></tr><tr><td>2020-11-07</td><td>CHEOPS</td><td>b</td><td>120</td><td>229</td><td>60</td><td>sp(r) + o</td><td>0.060</td><td>1.08</td><td>1.41</td></tr><tr><td>2020-11-08</td><td>CHEOPS</td><td>g</td><td>13</td><td>223</td><td>60</td><td>sp(r) + o</td><td>0.056</td><td>1.00</td><td>2.56</td></tr><tr><td>2021-08-04</td><td>CHEOPS</td><td>b, f, c</td><td>261, 35, 156</td><td>293</td><td>60</td><td>sp(r) + o</td><td>0.063</td><td>1.12</td><td>2.10</td></tr><tr><td>2021-08-04</td><td>CHEOPS</td><td>c, g</td><td>156, 26</td><td>343</td><td>60</td><td>sp(r) + p(y)</td><td>0.066</td><td>1.18</td><td>1.48</td></tr><tr><td>2021-10-08</td><td>CHEOPS</td><td>b, c</td><td>295, 176</td><td>365</td><td>60</td><td>sp(r) + o</td><td>0.057</td><td>1.01</td><td>2.66</td></tr><tr><td>2021-10-15</td><td>CHEOPS</td><td>b</td><td>299</td><td>327</td><td>60</td><td>sp(r) + o</td><td>0.058</td><td>1.01</td><td>1.47</td></tr><tr><td>2021-10-17</td><td>CHEOPS</td><td>b</td><td>300</td><td>296</td><td>60</td><td>sp(r) + o</td><td>0.067</td><td>1.15</td><td>1.43</td></tr></tbody></table>

**Table B.1.** Photometric baseline models, residual RMS, and error scaling factors $\beta_w$ and $\beta_r$ for each transit light curve used in our global transit analysis (see Sect. 4.1). For the baseline function, $o$ is a simple constant (to account for any out-of-transit flux offset), $sp(r)$ is a cubic spline against the spacecraft roll angle $r$, and $p(\alpha)$ denotes a first-order polynomial function of the parameter $\alpha$, with $\alpha$ that can be $t$ = time, $b$ = background, $a$ = airmass, $x$ and $y$ = x- and y- position of the target on the detector, or $ttt$ = telescope tube temperature. Epochs are relative to the updated mean transit ephemerides given in Tables 3 (planets b, c, and d) and 4 (planets e, f, and g).
## Appendix B.2: Prior distributions

<table><caption>**Table B.2.** Prior probability distribution functions assumed in our global transit analysis (see Sect. 4.1). N(μ, σ²) represents a normal distribution of mean μ and variance σ².</caption><thead><tr><th>Parameter (unit)</th><th>Prior</th></tr></thead><tbody><tr><td>Mass, M<sub>★</sub> (M<sub>☉</sub>)</td><td>N(0.647, 0.030<sup>2</sup>)</td></tr><tr><td>Radius, R<sub>★</sub> (R<sub>☉</sub>)</td><td>N(0.662, 0.010<sup>2</sup>)</td></tr><tr><td>Effective temperature, T<sub>eff</sub> (K)</td><td>N(4316, 70<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>1</sub>, CHEOPS</td><td>N(0.538, 0.023<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>2</sub>, CHEOPS</td><td>N(0.157, 0.033<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>1</sub>, TESS</td><td>N(0.487, 0.019<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>2</sub>, TESS</td><td>N(0.193, 0.047<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>1</sub>, NGTS</td><td>N(0.529, 0.030<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>2</sub>, NGTS</td><td>N(0.171, 0.045<sup>2</sup>)</td></tr></tbody></table>

## Appendix C: Results: Individual transit timings

<table><thead><tr><th>Epoch</th><th>Transit timing<br>(BJD<sub>TDB</sub> − 2 450 000)</th><th>TTV<br>(min)</th><th>Source</th></tr></thead><tbody><tr><td colspan="4" style="text-align: center; font-weight: bold;">TOI-178 c</td></tr><tr><td>-176</td><td>8356.0989<sup>+0.0080</sup><sub>-0.0138</sub></td><td>−2.89<sup>+11.53</sup><sub>-19.87</sub></td><td>TESS</td></tr><tr><td>-175</td><td>8359.3408<sup>+0.0061</sup><sub>-0.0050</sub></td><td>2.09<sup>+8.76</sup><sub>-7.21</sub></td><td>TESS</td></tr><tr><td>-174</td><td>8362.5850<sup>+0.0086</sup><sub>-0.0095</sub></td><td>10.29<sup>+12.43</sup><sub>-13.75</sub></td><td>TESS</td></tr><tr><td>-173</td><td>8365.8208<sup>+0.0096</sup><sub>-0.0078</sub></td><td>6.56<sup>+13.82</sup><sub>-11.29</sub></td><td>TESS</td></tr><tr><td>-172</td><td>8369.052<sup>+0.016</sup><sub>-0.013</sub></td><td>−3.38<sup>+23.47</sup><sub>-19.30</sub></td><td>TESS</td></tr><tr><td>-171</td><td>8372.308<sup>+0.011</sup><sub>-0.015</sub></td><td>21.06<sup>+16.42</sup><sub>-22.18</sub></td><td>TESS</td></tr><tr><td>-170</td><td>8375.5181<sup>+0.0077</sup><sub>-0.0052</sub></td><td>−19.55<sup>+11.10</sup><sub>-7.53</sub></td><td>TESS</td></tr><tr><td>-169</td><td>8378.7718<sup>+0.0075</sup><sub>-0.0077</sub></td><td>2.43<sup>+10.77</sup><sub>-11.16</sub></td><td>TESS</td></tr><tr><td>44</td><td>9068.5625<sup>+0.0104</sup><sub>-0.0086</sub></td><td>4.00<sup>+14.98</sup><sub>-12.40</sub></td><td>CHEOPS</td></tr><tr><td>45</td><td>9071.797<sup>+0.014</sup><sub>-0.012</sub></td><td>−1.78<sup>+20.74</sup><sub>-17.28</sub></td><td>CHEOPS</td></tr><tr><td>46</td><td>9075.034<sup>+0.008</sup><sub>-0.010</sub></td><td>−3.44<sup>+11.49</sup><sub>-14.98</sub></td><td>CHEOPS</td></tr><tr><td>51</td><td>9091.2349<sup>+0.0047</sup><sub>-0.0055</sub></td><td>8.67<sup>+6.78</sup><sub>-7.99</sub></td><td>TESS</td></tr><tr><td>52</td><td>9094.4701<sup>+0.0026</sup><sub>-0.0038</sub></td><td>3.99<sup>+3.74</sup><sub>-5.47</sub></td><td>TESS</td></tr><tr><td>53</td><td>9097.7094<sup>+0.0082</sup><sub>-0.0094</sub></td><td>5.20<sup>+11.88</sup><sub>-13.55</sub></td><td>TESS</td></tr><tr><td>55</td><td>9104.1840<sup>+0.0086</sup><sub>-0.0076</sub></td><td>1.86<sup>+12.36</sup><sub>-11.00</sub></td><td>TESS</td></tr><tr><td>56</td><td>9107.4252<sup>+0.0073</sup><sub>-0.0077</sub></td><td>5.81<sup>+10.56</sup><sub>-11.10</sub></td><td>TESS</td></tr><tr><td>57</td><td>9110.6629<sup>+0.0075</sup><sub>-0.0050</sub></td><td>4.74<sup>+10.81</sup><sub>-7.16</sub></td><td>TESS</td></tr><tr><td>63</td><td>9130.0860<sup>+0.0031</sup><sub>-0.0018</sub></td><td>−6.21<sup>+4.46</sup><sub>-2.62</sub></td><td>CHEOPS</td></tr><tr><td>68</td><td>9146.2850<sup>+0.0033</sup><sub>-0.0029</sub></td><td>3.59<sup>+4.77</sup><sub>-4.18</sub></td><td>CHEOPS</td></tr><tr><td>70</td><td>9152.7557<sup>+0.0053</sup><sub>-0.0049</sub></td><td>−5.30<sup>+7.70</sup><sub>-7.07</sub></td><td>CHEOPS</td></tr><tr><td>71</td><td>9155.9917<sup>+0.0089</sup><sub>-0.0097</sub></td><td>−8.88<sup>+12.76</sup><sub>-14.00</sub></td><td>CHEOPS</td></tr><tr><td>156</td><td>9431.2758<sup>+0.0098</sup><sub>-0.0069</sub></td><td>14.06<sup>+14.05</sup><sub>-9.92</sub></td><td>CHEOPS</td></tr><tr><td>176</td><td>9496.0299<sup>+0.0065</sup><sub>-0.0056</sub></td><td>−7.38<sup>+9.30</sup><sub>-8.02</sub></td><td>CHEOPS</td></tr></tbody></table>

*Continued on the next page.*
## Appendix B.2: Prior distributions

<table><caption>**Table B.2.** Prior probability distribution functions assumed in our global transit analysis (see Sect. 4.1). $N(μ, σ^2)$ represents a normal distribution of mean $μ$ and variance $σ^2$.</caption><thead><tr><th>Parameter (unit)</th><th>Prior</th></tr></thead><tbody><tr><td>Mass, M<sub>★</sub> (M<sub>☉</sub>)</td><td>N(0.647, 0.030<sup>2</sup>)</td></tr><tr><td>Radius, R<sub>★</sub> (R<sub>☉</sub>)</td><td>N(0.662, 0.010<sup>2</sup>)</td></tr><tr><td>Effective temperature, T<sub>eff</sub> (K)</td><td>N(4316, 70<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>1</sub>, CHEOPS</td><td>N(0.538, 0.023<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>2</sub>, CHEOPS</td><td>N(0.157, 0.033<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>1</sub>, TESS</td><td>N(0.487, 0.019<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>2</sub>, TESS</td><td>N(0.193, 0.047<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>1</sub>, NGTS</td><td>N(0.529, 0.030<sup>2</sup>)</td></tr><tr><td>Quadratic limb-darkening coefficient u<sub>2</sub>, NGTS</td><td>N(0.171, 0.045<sup>2</sup>)</td></tr></tbody></table>

## Appendix C: Results: Individual transit timings

<table><thead><tr><th>Epoch</th><th>Transit timing<br>(BJD<sub>TDB</sub> - 2 450 000)</th><th>TTV<br>(min)</th><th>Source</th></tr></thead><tbody><tr><td colspan="4" style="text-align: center;">TOI-178 c</td></tr><tr><td>-176</td><td>8356.0989<sup>+0.0080</sup><sub>-0.0138</sub></td><td>-2.89<sup>+11.53</sup><sub>-19.87</sub></td><td>TESS</td></tr><tr><td>-175</td><td>8359.3408<sup>+0.0061</sup><sub>-0.0050</sub></td><td>2.09<sup>+8.76</sup><sub>-7.21</sub></td><td>TESS</td></tr><tr><td>-174</td><td>8362.5850<sup>+0.0086</sup><sub>-0.0095</sub></td><td>10.29<sup>+12.43</sup><sub>-13.75</sub></td><td>TESS</td></tr><tr><td>-173</td><td>8365.8208<sup>+0.0096</sup><sub>-0.0078</sub></td><td>6.56<sup>+13.82</sup><sub>-11.29</sub></td><td>TESS</td></tr><tr><td>-172</td><td>8369.052<sup>+0.016</sup><sub>-0.013</sub></td><td>-3.38<sup>+23.47</sup><sub>-19.30</sub></td><td>TESS</td></tr><tr><td>-171</td><td>8372.308<sup>+0.011</sup><sub>-0.015</sub></td><td>21.06<sup>+16.42</sup><sub>-22.18</sub></td><td>TESS</td></tr><tr><td>-170</td><td>8375.5181<sup>+0.0077</sup><sub>-0.0052</sub></td><td>-19.55<sup>+11.10</sup><sub>-7.53</sub></td><td>TESS</td></tr><tr><td>-169</td><td>8378.7718<sup>+0.0075</sup><sub>-0.0077</sub></td><td>2.43<sup>+10.77</sup><sub>-11.16</sub></td><td>TESS</td></tr><tr><td>44</td><td>9068.5625<sup>+0.0104</sup><sub>-0.0086</sub></td><td>4.00<sup>+14.98</sup><sub>-12.40</sub></td><td>CHEOPS</td></tr><tr><td>45</td><td>9071.797<sup>+0.014</sup><sub>-0.012</sub></td><td>-1.78<sup>+20.74</sup><sub>-17.28</sub></td><td>CHEOPS</td></tr><tr><td>46</td><td>9075.034<sup>+0.008</sup><sub>-0.010</sub></td><td>-3.44<sup>+11.49</sup><sub>-14.98</sub></td><td>CHEOPS</td></tr><tr><td>51</td><td>9091.2349<sup>+0.0047</sup><sub>-0.0055</sub></td><td>8.67<sup>+6.78</sup><sub>-7.99</sub></td><td>TESS</td></tr><tr><td>52</td><td>9094.4701<sup>+0.0026</sup><sub>-0.0038</sub></td><td>3.99<sup>+3.74</sup><sub>-5.47</sub></td><td>TESS</td></tr><tr><td>53</td><td>9097.7094<sup>+0.0082</sup><sub>-0.0094</sub></td><td>5.20<sup>+11.88</sup><sub>-13.55</sub></td><td>TESS</td></tr><tr><td>55</td><td>9104.1840<sup>+0.0086</sup><sub>-0.0076</sub></td><td>1.86<sup>+12.36</sup><sub>-11.00</sub></td><td>TESS</td></tr><tr><td>56</td><td>9107.4252<sup>+0.0073</sup><sub>-0.0077</sub></td><td>5.81<sup>+10.56</sup><sub>-11.10</sub></td><td>TESS</td></tr><tr><td>57</td><td>9110.6629<sup>+0.0075</sup><sub>-0.0050</sub></td><td>4.74<sup>+10.81</sup><sub>-7.16</sub></td><td>TESS</td></tr><tr><td>63</td><td>9130.0860<sup>+0.0031</sup><sub>-0.0018</sub></td><td>-6.21<sup>+4.46</sup><sub>-2.62</sub></td><td>CHEOPS</td></tr><tr><td>68</td><td>9146.2850<sup>+0.0033</sup><sub>-0.0029</sub></td><td>3.59<sup>+4.77</sup><sub>-4.18</sub></td><td>CHEOPS</td></tr><tr><td>70</td><td>9152.7557<sup>+0.0053</sup><sub>-0.0049</sub></td><td>-5.30<sup>+7.70</sup><sub>-7.07</sub></td><td>CHEOPS</td></tr><tr><td>71</td><td>9155.9917<sup>+0.0089</sup><sub>-0.0097</sub></td><td>-8.88<sup>+12.76</sup><sub>-14.00</sub></td><td>CHEOPS</td></tr><tr><td>156</td><td>9431.2758<sup>+0.0098</sup><sub>-0.0069</sub></td><td>14.06<sup>+14.05</sup><sub>-9.92</sub></td><td>CHEOPS</td></tr><tr><td>176</td><td>9496.0299<sup>+0.0065</sup><sub>-0.0056</sub></td><td>-7.38<sup>+9.30</sup><sub>-8.02</sub></td><td>CHEOPS</td></tr></tbody></table>

*Continued on the next page.*
<table><caption>Table C.1– Continued from the previous page.</caption><thead><tr><th>Epoch</th><th>Transit timing<br>(BJD<sub>TDB</sub> − 2 450 000)</th><th>TTV<br>(min)</th><th>Source</th></tr></thead><tbody><tr><td colspan="4"><em>TOI-178 d</em></td></tr><tr><td>-61</td><td>8360.2385<sup>+0.0033</sup><sub>-0.0026</sub></td><td>−6.00<sup>+4.82</sup><sub>−3.72</sub></td><td>TESS</td></tr><tr><td>-60</td><td>8366.8025<sup>+0.0020</sup><sub>-0.0021</sub></td><td>2.97<sup>+2.84</sup><sub>−3.02</sub></td><td>TESS</td></tr><tr><td>-59</td><td>8373.3593<sup>+0.0040</sup><sub>-0.0082</sub></td><td>1.58<sup>+5.82</sup><sub>−11.88</sub></td><td>TESS</td></tr><tr><td>-58</td><td>8379.9157<sup>+0.0033</sup><sub>-0.0028</sub></td><td>−0.27<sup>+4.72</sup><sub>−4.02</sub></td><td>TESS</td></tr><tr><td>47</td><td>9068.4744<sup>+0.0039</sup><sub>-0.0029</sub></td><td>−3.27<sup>+5.63</sup><sub>−4.16</sub></td><td>CHEOPS</td></tr><tr><td>48</td><td>9075.0314<sup>+0.0039</sup><sub>-0.0055</sub></td><td>−4.22<sup>+5.56</sup><sub>−7.92</sub></td><td>CHEOPS</td></tr><tr><td>51</td><td>9094.7023<sup>+0.0036</sup><sub>-0.0055</sub></td><td>−7.51<sup>+5.13</sup><sub>−7.92</sub></td><td>TESS</td></tr><tr><td>53</td><td>9107.8186<sup>+0.0040</sup><sub>-0.0043</sub></td><td>−6.24<sup>+5.75</sup><sub>−6.25</sub></td><td>TESS</td></tr><tr><td>55</td><td>9120.9395<sup>+0.0012</sup><sub>-0.0013</sub></td><td>1.58<sup>+1.73</sup><sub>−1.83</sub></td><td>CHEOPS</td></tr><tr><td>56</td><td>9127.4973<sup>+0.0022</sup><sub>-0.0022</sub></td><td>1.74 ± 3.17</td><td>CHEOPS</td></tr><tr><td>61</td><td>9160.2843<sup>+0.0016</sup><sub>-0.0018</sub></td><td>−0.70<sup>+2.30</sup><sub>−2.64</sub></td><td>CHEOPS</td></tr><tr><td colspan="4"><em>TOI-178 e</em></td></tr><tr><td>-40</td><td>8362.9541<sup>+0.0058</sup><sub>-0.0031</sub></td><td>0.07<sup>+8.29</sup><sub>−4.51</sub></td><td>TESS</td></tr><tr><td>-39</td><td>8372.9091<sup>+0.0085</sup><sub>-0.0091</sub></td><td>−9.80<sup>+12.25</sup><sub>−13.05</sub></td><td>TESS</td></tr><tr><td>31</td><td>9070.2469<sup>+0.0041</sup><sub>-0.0039</sub></td><td>5.65<sup>+5.88</sup><sub>−5.66</sub></td><td>CHEOPS</td></tr><tr><td>33</td><td>9090.1771<sup>+0.0077</sup><sub>-0.0087</sub></td><td>15.11<sup>+11.16</sup><sub>−12.60</sub></td><td>TESS</td></tr><tr><td>34</td><td>9100.1317<sup>+0.0016</sup><sub>-0.0014</sub></td><td>4.77<sup>+2.28</sup><sub>−1.96</sub></td><td>CHEOPS</td></tr><tr><td>35</td><td>9110.1036<sup>+0.0087</sup><sub>-0.0112</sub></td><td>19.29<sup>+12.54</sup><sub>−16.13</sub></td><td>TESS</td></tr><tr><td>37</td><td>9130.0109<sup>+0.0012</sup><sub>-0.0012</sub></td><td>−4.29<sup>+1.71</sup><sub>−1.70</sub></td><td>CHEOPS</td></tr><tr><td>40</td><td>9159.9040<sup>+0.0061</sup><sub>-0.0054</sub></td><td>6.72<sup>+8.80</sup><sub>−7.78</sub></td><td>CHEOPS</td></tr><tr><td colspan="4"><em>TOI-178 f</em></td></tr><tr><td>-35</td><td>8364.9143<sup>+0.0039</sup><sub>-0.0041</sub></td><td>−3.41<sup>+5.57</sup><sub>−5.92</sub></td><td>TESS</td></tr><tr><td>-34</td><td>8380.1582<sup>+0.0090</sup><sub>-0.0101</sub></td><td>13.87<sup>+12.99</sup><sub>−14.54</sub></td><td>TESS</td></tr><tr><td>13</td><td>9096.0564<sup>+0.0056</sup><sub>-0.0051</sub></td><td>8.78<sup>+8.02</sup><sub>−7.39</sub></td><td>TESS</td></tr><tr><td>14</td><td>9111.2650<sup>+0.0092</sup><sub>-0.0056</sub></td><td>−24.86<sup>+13.31</sup><sub>−7.99</sub></td><td>TESS</td></tr><tr><td>15</td><td>9126.5155<sup>+0.0015</sup><sub>-0.0012</sub></td><td>1.90<sup>+2.22</sup><sub>−1.70</sub></td><td>CHEOPS</td></tr><tr><td>16</td><td>9141.7445<sup>+0.0033</sup><sub>-0.0029</sub></td><td>−2.36<sup>+4.74</sup><sub>−4.12</sub></td><td>CHEOPS</td></tr><tr><td>17</td><td>9156.9773<sup>+0.0016</sup><sub>-0.0015</sub></td><td>−1.13<sup>+2.25</sup><sub>−2.20</sub></td><td>CHEOPS</td></tr><tr><td>35</td><td>9431.1468<sup>+0.0093</sup><sub>-0.0103</sub></td><td>−9.23<sup>+13.35</sup><sub>−14.83</sub></td><td>CHEOPS</td></tr><tr><td colspan="4"><em>TOI-178 g</em></td></tr><tr><td>-26</td><td>8354.5502<sup>+0.0038</sup><sub>-0.0041</sub></td><td>8.97<sup>+5.46</sup><sub>−5.89</sub></td><td>TESS</td></tr><tr><td>-25</td><td>8375.2603<sup>+0.0045</sup><sub>-0.0046</sub></td><td>9.30<sup>+6.51</sup><sub>−6.64</sub></td><td>TESS</td></tr><tr><td>-6</td><td>8768.7409<sup>+0.0029</sup><sub>-0.0031</sub></td><td>−1.81<sup>+4.18</sup><sub>−4.49</sub></td><td>NGTS</td></tr><tr><td>10</td><td>9100.0936<sup>+0.0041</sup><sub>-0.0025</sub></td><td>−10.13<sup>+5.93</sup><sub>−3.60</sub></td><td>CHEOPS</td></tr><tr><td>11</td><td>9120.8067<sup>+0.0018</sup><sub>-0.0014</sub></td><td>−5.61<sup>+2.64</sup><sub>−2.07</sub></td><td>CHEOPS</td></tr><tr><td>13</td><td>9162.2292<sup>+0.0131</sup><sub>-0.0118</sub></td><td>−1.65<sup>+18.86</sup><sub>−16.99</sub></td><td>CHEOPS</td></tr><tr><td>26</td><td>9431.4659<sup>+0.0020</sup><sub>-0.0022</sub></td><td>9.74<sup>+2.87</sup><sub>−3.18</sub></td><td>CHEOPS</td></tr></tbody></table>

**Table C.1.** Individual transit timings returned by our global transit analysis (see Sect. 4.1) for the five outer TOI-178 planets. The epochs and corresponding TTVs given here are relative to the updated mean transit ephemerides given in Tables 3 (planets b, c, and d) and 4 (planets e, f, and g).
<table><caption>Table C.1– Continued from the previous page.</caption><thead><tr><th>Epoch</th><th>Transit timing<br>(BJD<sub>TDB</sub> − 2 450 000)</th><th>TTV<br>(min)</th><th>Source</th></tr></thead><tbody><tr><td colspan="4"><em>TOI-178 d</em></td></tr><tr><td>-61</td><td>8360.2385<sup>+0.0033</sup><sub>−0.0026</sub></td><td>−6.00<sup>+4.82</sup><sub>−3.72</sub></td><td>TESS</td></tr><tr><td>-60</td><td>8366.8025<sup>+0.0020</sup><sub>−0.0021</sub></td><td>2.97<sup>+2.84</sup><sub>−3.02</sub></td><td>TESS</td></tr><tr><td>-59</td><td>8373.3593<sup>+0.0040</sup><sub>−0.0082</sub></td><td>1.58<sup>+5.82</sup><sub>−11.88</sub></td><td>TESS</td></tr><tr><td>-58</td><td>8379.9157<sup>+0.0033</sup><sub>−0.0028</sub></td><td>−0.27<sup>+4.72</sup><sub>−4.02</sub></td><td>TESS</td></tr><tr><td>47</td><td>9068.4744<sup>+0.0039</sup><sub>−0.0029</sub></td><td>−3.27<sup>+5.63</sup><sub>−4.16</sub></td><td>CHEOPS</td></tr><tr><td>48</td><td>9075.0314<sup>+0.0039</sup><sub>−0.0055</sub></td><td>−4.22<sup>+5.56</sup><sub>−7.92</sub></td><td>CHEOPS</td></tr><tr><td>51</td><td>9094.7023<sup>+0.0036</sup><sub>−0.0055</sub></td><td>−7.51<sup>+5.13</sup><sub>−7.92</sub></td><td>TESS</td></tr><tr><td>53</td><td>9107.8186<sup>+0.0040</sup><sub>−0.0043</sub></td><td>−6.24<sup>+5.75</sup><sub>−6.25</sub></td><td>TESS</td></tr><tr><td>55</td><td>9120.9395<sup>+0.0012</sup><sub>−0.0013</sub></td><td>1.58<sup>+1.73</sup><sub>−1.83</sub></td><td>CHEOPS</td></tr><tr><td>56</td><td>9127.4973<sup>+0.0022</sup><sub>−0.0022</sub></td><td>1.74 ± 3.17</td><td>CHEOPS</td></tr><tr><td>61</td><td>9160.2843<sup>+0.0016</sup><sub>−0.0018</sub></td><td>−0.70<sup>+2.30</sup><sub>−2.64</sub></td><td>CHEOPS</td></tr><tr><td colspan="4"><em>TOI-178 e</em></td></tr><tr><td>-40</td><td>8362.9541<sup>+0.0058</sup><sub>−0.0031</sub></td><td>0.07<sup>+8.29</sup><sub>−4.51</sub></td><td>TESS</td></tr><tr><td>-39</td><td>8372.9091<sup>+0.0085</sup><sub>−0.0091</sub></td><td>−9.80<sup>+12.25</sup><sub>−13.05</sub></td><td>TESS</td></tr><tr><td>31</td><td>9070.2469<sup>+0.0041</sup><sub>−0.0039</sub></td><td>5.65<sup>+5.88</sup><sub>−5.66</sub></td><td>CHEOPS</td></tr><tr><td>33</td><td>9090.1771<sup>+0.0077</sup><sub>−0.0087</sub></td><td>15.11<sup>+11.16</sup><sub>−12.60</sub></td><td>TESS</td></tr><tr><td>34</td><td>9100.1317<sup>+0.0016</sup><sub>−0.0014</sub></td><td>4.77<sup>+2.28</sup><sub>−1.96</sub></td><td>CHEOPS</td></tr><tr><td>35</td><td>9110.1036<sup>+0.0087</sup><sub>−0.0112</sub></td><td>19.29<sup>+12.54</sup><sub>−16.13</sub></td><td>TESS</td></tr><tr><td>37</td><td>9130.0109<sup>+0.0012</sup><sub>−0.0012</sub></td><td>−4.29<sup>+1.71</sup><sub>−1.70</sub></td><td>CHEOPS</td></tr><tr><td>40</td><td>9159.9040<sup>+0.0061</sup><sub>−0.0054</sub></td><td>6.72<sup>+8.80</sup><sub>−7.78</sub></td><td>CHEOPS</td></tr><tr><td colspan="4"><em>TOI-178 f</em></td></tr><tr><td>-35</td><td>8364.9143<sup>+0.0039</sup><sub>−0.0041</sub></td><td>−3.41<sup>+5.57</sup><sub>−5.92</sub></td><td>TESS</td></tr><tr><td>-34</td><td>8380.1582<sup>+0.0090</sup><sub>−0.0101</sub></td><td>13.87<sup>+12.99</sup><sub>−14.54</sub></td><td>TESS</td></tr><tr><td>13</td><td>9096.0564<sup>+0.0056</sup><sub>−0.0051</sub></td><td>8.78<sup>+8.02</sup><sub>−7.39</sub></td><td>TESS</td></tr><tr><td>14</td><td>9111.2650<sup>+0.0092</sup><sub>−0.0056</sub></td><td>−24.86<sup>+13.31</sup><sub>−7.99</sub></td><td>TESS</td></tr><tr><td>15</td><td>9126.5155<sup>+0.0015</sup><sub>−0.0012</sub></td><td>1.90<sup>+2.22</sup><sub>−1.70</sub></td><td>CHEOPS</td></tr><tr><td>16</td><td>9141.7445<sup>+0.0033</sup><sub>−0.0029</sub></td><td>−2.36<sup>+4.74</sup><sub>−4.12</sub></td><td>CHEOPS</td></tr><tr><td>17</td><td>9156.9773<sup>+0.0016</sup><sub>−0.0015</sub></td><td>−1.13<sup>+2.25</sup><sub>−2.20</sub></td><td>CHEOPS</td></tr><tr><td>35</td><td>9431.1468<sup>+0.0093</sup><sub>−0.0103</sub></td><td>−9.23<sup>+13.35</sup><sub>−14.83</sub></td><td>CHEOPS</td></tr><tr><td colspan="4"><em>TOI-178 g</em></td></tr><tr><td>-26</td><td>8354.5502<sup>+0.0038</sup><sub>−0.0041</sub></td><td>8.97<sup>+5.46</sup><sub>−5.89</sub></td><td>TESS</td></tr><tr><td>-25</td><td>8375.2603<sup>+0.0045</sup><sub>−0.0046</sub></td><td>9.30<sup>+6.51</sup><sub>−6.64</sub></td><td>TESS</td></tr><tr><td>-6</td><td>8768.7409<sup>+0.0029</sup><sub>−0.0031</sub></td><td>−1.81<sup>+4.18</sup><sub>−4.49</sub></td><td>NGTS</td></tr><tr><td>10</td><td>9100.0936<sup>+0.0041</sup><sub>−0.0025</sub></td><td>−10.13<sup>+5.93</sup><sub>−3.60</sub></td><td>CHEOPS</td></tr><tr><td>11</td><td>9120.8067<sup>+0.0018</sup><sub>−0.0014</sub></td><td>−5.61<sup>+2.64</sup><sub>−2.07</sub></td><td>CHEOPS</td></tr><tr><td>13</td><td>9162.2292<sup>+0.0131</sup><sub>−0.0118</sub></td><td>−1.65<sup>+18.86</sup><sub>−16.99</sub></td><td>CHEOPS</td></tr><tr><td>26</td><td>9431.4659<sup>+0.0020</sup><sub>−0.0022</sub></td><td>9.74<sup>+2.87</sup><sub>−3.18</sub></td><td>CHEOPS</td></tr></tbody></table>

**Table C.1.** Individual transit timings returned by our global transit analysis (see Sect. 4.1) for the five outer TOI-178 planets. The epochs and corresponding TTVs given here are relative to the updated mean transit ephemerides given in Tables 3 (planets b, c, and d) and 4 (planets e, f, and g).
## Appendix D: Dynamical analysis: TTV mass and eccentricity posteriors for different mass priors

<table><caption>**Table D.1.** TTV mass and eccentricity posteriors for the five outer planets of the TOI-178 system.</caption><thead><tr><th></th><th>Source</th><th>Prior</th><th>TOI-178 c</th><th>TOI-178 d</th><th>TOI-178 e</th><th>TOI-178 f</th><th>TOI-178 g</th></tr></thead><tbody><tr><td>M<sub>p</sub> [M<sub>⊕</sub>]</td><td>RVs (Leleu et al. 2021a)</td><td>–</td><td>4.77 ± 0.68</td><td>3.01 ± 1.03</td><td>3.86 ± 1.25</td><td>7.72 ± 1.67</td><td>3.94 ± 1.62</td></tr><tr><td>M<sub>p</sub> [M<sub>⊕</sub>]</td><td>TTVs</td><td>RV</td><td>4.70<sup>+0.63</sup><sub>-0.63</sub></td><td>3.35<sup>+0.81</sup><sub>-0.79</sub></td><td>3.11<sup>+0.96</sup><sub>-0.87</sub></td><td>7.50<sup>+1.27</sup><sub>-1.18</sub></td><td>3.12<sup>+1.10</sup><sub>-1.11</sub></td></tr><tr><td>M<sub>p</sub> [M<sub>⊕</sub>]</td><td>TTVs</td><td>default</td><td>0.22<sup>+0.78</sup><sub>-0.17</sub></td><td>7.73<sup>+2.09</sup><sub>-1.71</sub></td><td>3.61<sup>+1.31</sup><sub>-1.13</sub></td><td>0.78<sup>+0.99</sup><sub>-0.59</sub></td><td>0.17<sup>+0.51</sup><sub>-0.12</sub></td></tr><tr><td>M<sub>p</sub> [M<sub>⊕</sub>]</td><td>TTVs</td><td>high-mass</td><td>8.08<sup>+7.98</sup><sub>-5.26</sub></td><td>8.33<sup>+2.33</sup><sub>-2.23</sub></td><td>3.12<sup>+1.64</sup><sub>-1.45</sub></td><td>6.76<sup>+2.62</sup><sub>-2.51</sub></td><td>1.88<sup>+1.47</sup><sub>-1.19</sub></td></tr><tr><td>Δ<sub>M</sub></td><td>Robustness criterion</td><td>–</td><td>10.08</td><td>0.29</td><td>0.37</td><td>6.06</td><td>3.34</td></tr><tr><td>e<sub>p</sub></td><td>TTVs</td><td>RV</td><td>0.0073<sup>+0.0083</sup><sub>-0.0051</sub></td><td>0.010<sup>+0.011</sup><sub>-0.007</sub></td><td>0.0080<sup>+0.0100</sup><sub>-0.0057</sub></td><td>0.0105<sup>+0.0071</sup><sub>-0.0061</sub></td><td>0.0056<sup>+0.0058</sup><sub>-0.0039</sub></td></tr><tr><td>e<sub>p</sub></td><td>TTVs</td><td>default</td><td>0.0071<sup>+0.0081</sup><sub>-0.0050</sub></td><td>0.0051<sup>+0.0067</sup><sub>-0.0036</sub></td><td>0.0041<sup>+0.0054</sup><sub>-0.0029</sub></td><td>0.012<sup>+0.016</sup><sub>-0.008</sub></td><td>0.022<sup>+0.027</sup><sub>-0.016</sub></td></tr><tr><td>e<sub>p</sub></td><td>TTVs</td><td>high-mass</td><td>0.0033<sup>+0.0038</sup><sub>-0.0023</sub></td><td>0.0049<sup>+0.0055</sup><sub>-0.0034</sub></td><td>0.0050<sup>+0.0057</sup><sub>-0.0035</sub></td><td>0.0068<sup>+0.0065</sup><sub>-0.0045</sub></td><td>0.0039<sup>+0.0045</sup><sub>-0.0028</sub></td></tr></tbody></table>
Appendix D: Dynamical analysis: TTV mass and eccentricity posteriors for different mass priors

<table><caption>Table D.1. TTV mass and eccentricity posteriors for the five outer planets of the TOI-178 system.</caption><thead><tr><th></th><th>Source</th><th>Prior</th><th>TOI-178 c</th><th>TOI-178 d</th><th>TOI-178 e</th><th>TOI-178 f</th><th>TOI-178 g</th></tr></thead><tbody><tr><td>M<sub>p</sub> [M<sub>⊕</sub>]</td><td>RVs (Leleu et al. 2021a)</td><td>–</td><td>4.77 ± 0.68</td><td>3.01 ± 1.03</td><td>3.86 ± 1.25</td><td>7.72 ± 1.67</td><td>3.94 ± 1.62</td></tr><tr><td>M<sub>p</sub> [M<sub>⊕</sub>]</td><td>TTVs</td><td>RV</td><td>4.70<sup>+0.63</sup><sub>-0.63</sub></td><td>3.35<sup>+0.81</sup><sub>-0.79</sub></td><td>3.11<sup>+0.96</sup><sub>-0.87</sub></td><td>7.50<sup>+1.27</sup><sub>-1.18</sub></td><td>3.12<sup>+1.10</sup><sub>-1.11</sub></td></tr><tr><td>M<sub>p</sub> [M<sub>⊕</sub>]</td><td>TTVs</td><td>default</td><td>0.22<sup>+0.78</sup><sub>-0.17</sub></td><td>7.73<sup>+2.09</sup><sub>-1.71</sub></td><td>3.61<sup>+1.31</sup><sub>-1.13</sub></td><td>0.78<sup>+0.99</sup><sub>-0.59</sub></td><td>0.17<sup>+0.51</sup><sub>-0.12</sub></td></tr><tr><td>M<sub>p</sub> [M<sub>⊕</sub>]</td><td>TTVs</td><td>high-mass</td><td>8.08<sup>+7.98</sup><sub>-5.26</sub></td><td>8.33<sup>+2.33</sup><sub>-2.23</sub></td><td>3.12<sup>+1.64</sup><sub>-1.45</sub></td><td>6.76<sup>+2.62</sup><sub>-2.51</sub></td><td>1.88<sup>+1.47</sup><sub>-1.19</sub></td></tr><tr><td>Δ<sub>M</sub></td><td>Robustness criterion</td><td>–</td><td>10.08</td><td>0.29</td><td>0.37</td><td>6.06</td><td>3.34</td></tr><tr><td>e<sub>p</sub></td><td>TTVs</td><td>RV</td><td>0.0073<sup>+0.0083</sup><sub>-0.0051</sub></td><td>0.010<sup>+0.011</sup><sub>-0.007</sub></td><td>0.0080<sup>+0.0100</sup><sub>-0.0057</sub></td><td>0.0105<sup>+0.0071</sup><sub>-0.0061</sub></td><td>0.0056<sup>+0.0058</sup><sub>-0.0039</sub></td></tr><tr><td>e<sub>p</sub></td><td>TTVs</td><td>default</td><td>0.0071<sup>+0.0081</sup><sub>-0.0050</sub></td><td>0.0051<sup>+0.0067</sup><sub>-0.0036</sub></td><td>0.0041<sup>+0.0054</sup><sub>-0.0029</sub></td><td>0.012<sup>+0.016</sup><sub>-0.008</sub></td><td>0.022<sup>+0.027</sup><sub>-0.016</sub></td></tr><tr><td>e<sub>p</sub></td><td>TTVs</td><td>high-mass</td><td>0.0033<sup>+0.0038</sup><sub>-0.0023</sub></td><td>0.0049<sup>+0.0055</sup><sub>-0.0034</sub></td><td>0.0050<sup>+0.0057</sup><sub>-0.0035</sub></td><td>0.0068<sup>+0.0065</sup><sub>-0.0045</sub></td><td>0.0039<sup>+0.0045</sup><sub>-0.0028</sub></td></tr></tbody></table>