Most of the comments now addressed

A few more to go, but I'm falling asleep
at the keyboard!

Appendices.tex

@@ -1,5 +1,3 @@
-%%!TEX root = KiDS_1000_3x2pt.tex
-
 \begin{appendix} 
 \section{Galaxy properties and the \tttp covariance}
 \label{app:properties}

Section_Conclusions.tex

@@ -2,7 +2,7 @@ \section{Conclusions}
 \label{sec:conc}
 In this analysis we have presented constraints on the flat $\Lambda$CDM cosmological model by combining observations of gravitational lensing and galaxy clustering to directly probe the evolution and distribution of the large-scale structures in the Universe.    Our survey of the $z \lesssim 1$ low-redshift Universe finds a matter distribution that is less clustered, compared to predictions from the best-fitting $\Lambda$CDM model to early-Universe CMB observations \citep{planck/etal:2018}.  This tendency for low-redshift probes to favour a smoother matter distribution compared to the CMB expectation has persisted since the first large-scale weak lensing survey \citep[CFHTLenS,][]{heymans/etal:2013}, but the significance of this effect has always been tantalisingly around, or below, the $\sim 3\sigma$ level.   It is therefore unclear if these differences are merely a statistical fluctuation, unaccounted for systematic errors, or a sign of interesting new physics.
 
-Our new result does not lead to a resolution in the matter of statistical fluctuations, finding a \kpoff offset in the reported values for the structure growth parameter $S_8 = \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$, where our constraint $S_8=$\kSeightval is \kpoffperc lower than the $S_8$ CMB constraint from \citet{planck/etal:2018}.   For a series of `tension' metrics that quantify differences in terms of the full posterior distributions, we find that the KiDS-1000 and {\it Planck} results agree at the $\sim 2 \sigma$ level.   Through our series of image simulation analyses \citep{kannawadi/etal:2019}, catalogue null-tests \citep{giblin/etal:inprep}, variable depth mock galaxy survey analyses \citep{joachimi/etal:inprep}, optical-to-near-infrared photometric-spectroscopic redshift calibration, validated with mocks \citep{wright/etal:2020, vandenbusch/etal:2020,hildebrandt/etal:inprep}, internal consistency tests \citep[][Fig.~\ref{fig:cosmology-params-all} and Appendix~\ref{app:sensitivity}]{asgari/etal:inprep}, and marginalisation over a series of nuisance parameters that encompass our theoretical and calibration uncertainties (Appendix~\ref{app:priors}),  we argue that we have, however, addressed the question of systematic errors, robustly assessing and accounting for all sources of systematics that are known about in the literature.    
+Our new result does not lead to a resolution in the matter of statistical fluctuations, finding a \kpoff offset in the reported values for the structure growth parameter $S_8 = \sigma_8 \sqrt{\Omega_{\rm m}/0.3}$, where our constraint $S_8=$\kSeightval is \kpoffperc lower than the $S_8$ CMB constraint from \citet{planck/etal:2018}.   For a series of `tension' metrics that quantify differences in terms of the full posterior distributions, we find that the KiDS-1000 and {\it Planck} results agree at the $\sim 2 \sigma$ level.   Through our series of image simulation analyses \citep{kannawadi/etal:2019}, catalogue null-tests \citep{giblin/etal:inprep}, variable depth mock galaxy survey analyses \citep{joachimi/etal:inprep}, optical-to-near-infrared photometric-spectroscopic redshift calibration, validated with mocks \citep{wright/etal:2020, vandenbusch/etal:2020,hildebrandt/etal:inprep}, internal consistency tests \citep[][Fig.~\ref{fig:cosmology-params-all} and Appendix~\ref{app:sensitivity}]{asgari/etal:inprep}, and marginalisation over a series of nuisance parameters that encompass our theoretical and calibration uncertainties (Appendix~\ref{app:priors}),  we argue that we have, however, addressed the question of \tttp systematic errors, robustly assessing and accounting for all sources of systematics that are known about in the literature.    
 
 The KiDS-1000 cosmic shear constraints are highly complementary to the BOSS galaxy clustering constraints, leading to tight constraints in our joint \tttp analysis that are more than twice as constraining for the matter fluctuation amplitude parameter, $\sigma_8 = 0.760^{+0.021}_{-0.023}$, compared to previous \tttp analyses.    In the future, analysis of the clustering and galaxy-galaxy lensing of photometric samples with very accurate photometric redshifts \citep[see for example][]{vakili/etal:2019}, presents an opportunity for a future alternative KiDS-only \tttp photometric analysis, similar to the approach taken in \citet{abbott/etal:2018}.
 

Section_Results.tex

@@ -5,6 +5,7 @@ \section{Results}
 \preliminary{\eqa{
 \sigma_8 &= 0.76^{+0.021}_{-0.023} \\ \nonumber
 \Omega_{\rm m} &= 0.306^{+0.011}_{-0.014} \\ \nonumber
+h &=0.678^{+0.047}_{-0.002} \\ \nonumber
 S_8 &= 0.769^{+0.018}_{-0.015} \, .
 }}
 Our constraints can be compared to the marginalised posterior distributions from {\it Planck} (shown grey in Fig.~\ref{fig:cosmology-params}), finding consistency between the marginalised constraints on $\Omega_{\rm m}$ and $h$, but an offset in $\sigma_8$,  which we discuss in detail in Sect.~\ref{sec:planck_comp}.
@@ -45,7 +46,7 @@ \section{Results}
 
 For our primary cosmological parameter, $S_8$, our constraints are uninformed by our choice of priors.    This statement cannot be made for the other $\Lambda$CDM parameters, however, as shown in Fig.~\ref{fig:cosmology-params-all}.   The most informative prior that we have introduced to our \tttp analysis is on the spectral index, $n_{\rm s}$.  As noted by \citet{troester/etal:2020}, the BOSS galaxy clustering constraints favour a low value for $n_{\rm s}$, where they find $n_{\rm s} = 0.815 \pm 0.085$. 
 From the \citet{troester/etal:2020} sensitivity analysis to the adopted maximum clustering scale, we observe that this preference appears to be driven by the amplitude of the large scale clustering signal with $s > 100 \, h^{-1}\, {\rm Mpc}$.  We note that spurious excess power in this regime could plausibly arise from variations in the stellar density impacting the BOSS galaxy selection function \citep{ross/etal:2017}.  Our choice to impose a theoretically motivated informative prior for $n_{\rm s}$, as listed in Table~\ref{tab:priors}, helps to negate this potential systematic effect without degrading the overall goodness-of-fit to the galaxy clustering measurements.  Our prior choice is certainly no more informative than the $n_{\rm s}$ priors that are typically used in weak lensing and clustering analyses \citep[see for example][]{abbott/etal:2018,eBOSS/etal:2020}. 
-We recognise, however, that this well-motivated prior choice acts to improve the BOSS-only error on $\Omega_{\rm m}$ by roughly a third, and decrease the BOSS-only best-fitting value for $\Omega_{\rm m}$ and $h$ by $\sim 0.5\sigma$.  With $<10\%$ differences on the constraints on $S_8$ and $h$, however, and only a $\sim 0.1\sigma$ difference in the BOSS-only best-fitting value for $S_8$, which is consistent with the typical variation between different {\sc Multinest} analyses, we conclude that our prior choice does not impact on our primary $S_8$ constraints.   With the informative or uninformative $n_{\rm s}$ prior, our constraints on $h$ remain consistent with the Hubble parameter constraints from both \citet{planck/etal:2018} and \citet{riess/etal:2019}.
+We recognise, however, that this well-motivated prior choice acts to improve the BOSS-only error on $\Omega_{\rm m}$ by roughly a third, and decrease the BOSS-only best-fitting value for $\Omega_{\rm m}$ and $h$ by $\sim 0.5\sigma$ (see Fig.~\ref{fig:ns-prior}).  With $<10\%$ differences on the constraints on $S_8$ and $h$, however, and only a $\sim 0.1\sigma$ difference in the BOSS-only best-fitting value for $S_8$, which is consistent with the typical variation between different {\sc Multinest} analyses, we conclude that our prior choice does not impact on our primary $S_8$ constraints.   With the informative or uninformative $n_{\rm s}$ prior, our constraints on $h$ remain consistent with the Hubble parameter constraints from both \citet{planck/etal:2018} and \citet{riess/etal:2019}.
 
 \begin{figure*}
 	\begin{center}
@@ -60,8 +61,8 @@ \section{Results}
 we ignore the impact of baryon feedback (the `No baryon' case), fixing $A_{\rm bary}=3.13$, corresponding to the non-linear matter power spectrum for a dark-matter only cosmology; 
 we limit the analysis to a linear galaxy bias model, setting all higher-order bias terms in Eq. (\ref{eq:pgg}) to zero, as well as restricting the redshift-space distortion model to a Gaussian velocity distribution; 
 and we remove individual tomographic bins from our weak lensing observables. 
-The only outlier in this series of tests is the linear-bias model, which highlights the importance of accurate non-linear galaxy bias modelling in \tttp analyses. 
-This series of tests complements the more detailed KiDS-1000 internal consistency analysis of \citet{asgari/etal:inprep}, and is dissected in Appendix~\ref{app:sensitivity}.
+The only significant outlier in this series of tests is the linear-bias model, which highlights the importance of accurate non-linear galaxy bias modelling in \tttp analyses.     
+This series of tests is dissected further in Appendix~\ref{app:sensitivity}, and complements the detailed KiDS-1000 internal consistency analysis of \citet{asgari/etal:inprep}, which demonstrates that the small change seen with the removal of tomographic bin 4 is consistent with expected statistical fluctuations.
 
 \begin{figure}
 	\begin{center}
@@ -71,7 +72,7 @@ \section{Results}
 	\end{center}
 \end{figure}
 
-Table~\ref{tab:goodness-of-fit} records the goodness-of-fit for each component in our \tttp analysis, given the MAP cosmological parameters.  For our \tttp analysis we have implemented an optimised MAP-finder (see Sect.~\ref{sec:KCAP}), in order to estimate the minimum $\chi^2$.  For all other analyses we only report the noisy MAP estimate from {\sc Multinest}, providing an upper limit for the goodness-of-fit.  
+Table~\ref{tab:goodness-of-fit} records the goodness-of-fit for each component in our \tttp analysis, given the MAP cosmological parameters.  For our \tttp analysis we have implemented an optimised MAP-finder (see Sect.~\ref{sec:KCAP}), in order to estimate the minimum $\chi^2$.  For all other analyses we only report the noisy MAP estimate from {\sc Multinest}, providing an upper limit for the minimum $\chi^2$, and hence a lower limit for the goodness-of-fit.  
 The effective number of degrees of freedom (DoF) are calculated using the estimator described in section 6.3 of \citet{joachimi/etal:inprep}, which accounts for the impact of priors and non-linear dependencies between the parameters.  
 The goodness-of-fit is excellent for the BOSS galaxy clustering.  For all other cases, the goodness-of-fit is certainly acceptable\footnote{We define acceptable as $p \geq 0.001$, which corresponds to less than a $\sim 3\sigma$ event.   \citet{abbott/etal:2018} define acceptable as $\chi^2/{\rm DoF} < 1.4$.  We meet both these requirements.}.
 We note that the cosmic shear analysis of \citet{asgari/etal:inprep}, where a different choice in the cosmic shear two-point statistic results in an excellent goodness-of-fit, shows no significant changes in the inferred cosmological parameters.    As such, we could be subject to an unlucky noise fluctuation that particularly impacts the band power estimator in Eq. (\ref{eq:cl_cosmicshear}).  Cautiously inspecting Fig.~\ref{fig:Pkk}, as `$\chi$-by-eye' is particularly dangerous with correlated data points, we nevertheless note a handful of outlying points, for example the low $\ell$-scales in the fifth tomographic bin.   We also note that \citet{giblin/etal:inprep} document a significant but low-level PSF residual systematic in the KiDS-1000 fourth and fifth tomographic bins that was shown to reduce the overall goodness-of-fit in a cosmic shear analysis, but not bias the recovered cosmological parameters \citep[see also the discussion in][]{amara/refregier:2008}.  Future work to remove these low-level residual distortions is therefore expected to further improve the goodness-of-fit.