This paper makes for a very interesting read because of the Evidence of 
direct CP-violation at such a high level!
In General the paper is well-written, but is clearly a vast cut down 
of a large and complicated study. 
As such some of the important technical details are lost.

1) What does the measured number mean?
The charge asymmetries (including background) vary strongly 
over the Dalitz plot phase space. 
Do we correct over of the full Dalitz plot the effects of the
kinematical cuts corresponding to the LHCb acceptance and
reconstruction? Is there some (MC) extrapolation involved?

2) In the Babar paper [4] the physics motivation is better given
to investigate the contribution of possible resonances in
the Dalitz plot.
Please add some, any, discussion on the theory in these decay modes. 
Without that it is not possible for the reader to see if this could 
be new physics.

3) It is really a pity that you show asymmetries based on 
signal and background together in the Dalitz plot bins
and not those of background subtracted events.

4) We don't understand why you call your measurement an inclusive
asymmetry. It is exclusive since it is only one decay mode, 
and it is exclusive since you remove D0 resonances. 
We think you mean "total" asymmetry, "integrated over the 
remaining Dalitz plot", or simply "asymmetry" with no qualifier.

5) If possible, can you please give a plot or description of 
efficiencies and detector asymmetries in the same bins 
as are used in Fig. 4? 

6) There is a mistake on line 133. Although the pion detector 
asymmetries were used in the Ds+/- study, they are calculated 
from comparing partially-reconstructed and completely reconstructed 
D*-decays, not from the Ds-decays as is suggested.

Comments by line
================

Abstract:
- Remove "inclusive" from "inclusive charge asymmetry"
In what sense "inclusive"? This is not clear here. 
The decay mode is "exclusive"; we do not "miss" particles.
If we would have selected a resonance we would have indicated
that in the decay mode. 
In fact we do remove D0-decays into two hadrons.

- Change for instance to
"and the third is the uncertainty on the B+- production asymmetry,
given by ACP(B+->J/psiK)."
It is unclear that the third uncertainty is effectively 
the production asymmetry.
No need to quote the PDG here.

- Change to
"Charge asymmetries are measured at the level of 4.4 standard deviations ..."
Significance is not a well defined statistical object. And never used
in plural "significances". 

- Change last sentence to
"For both decay modes this is the first evidence of direct CP violation."

- Add the finding of very large charge asymmetries in certain parts
of the Dalitz plots.
This is very important additional information to the measured 
charge asymmetries.

Introduction:
Line 6:
Remove "inclusive" in "evidence of an inclusive CP asymmetry"
The only place where it is not called "inclusive charge asymmetry"

Line 11:
Both decays proceed through a ... penguin and a ... tree transition. ->
Both decays can proceed through a ... penguin and a ... tree transition.

Line 13:
What is "integrated CP asymmetry"?

Line 15:
Change for instance to "but did not include a measurement of its asymmetry [3]."
A publication cannot "measure an asymmetry".

Line 18:
Change "... data ... makes these modes a promising place to search ..." to
"... data ... allow (data is plural) for more statistical accuracy ...".

Line 21:
Replace "A^RAW_CP" to "A^RAW".
It is a raw charge asymmetry in the experiment and not a
raw CP asymmetry.
Also at other places.

Line 25:
Change "The physical inclusive charge asymmetry ..." to
"The resulting charge asymmetry is the CP asymmetry ...".
"Physical" has nothing to do with "physics".
It is wrong to call A_CP a charge asymmetry.
Also in line 130.

Data sample ...:

Line 40:
Change to
"an impact resolution down to 20 um, for tracks with the highest 
transverse momentum used in this analysis."
For LHCb, the Pt distribution is much lower than the central 
detectors, whereas it is much higher than previous experiments. 
Readers outside of LHCb will have difficulties to understand.

Line 62:
Add "an" to "and impact parameter"

Line 65:
Replace "greater" by "larger" (also in 63).

Replace ", and the sum ... large." by
". We also select daughter tracks that come from a primary vertex. 
The chi2 of the track-vertex consistency summed across the daughter
tracks must be larger than (a give value)."
The chi2 is not defined, nor how large "large" is.

Line 70: 
Change "selected" to "required" or equivalent.

Line 71:
Give the cut value on sin \theta, which is used in the 
following expression.

Line 75:
Remove "relative to its flight direction".
This addition makes it less clear than its definition.

Line 80:
Replace by
"We combine the information of different subdetectors, 
forming a global combined likelihood of different particle
identification (PID) hypotheses."
Also an LHCb reference would be nice here.

Lines 83-87:
This information is missing in section 6, where Fig. 3 is discussed.
Move it to that section.

3 Signal yield determination

Lines 104-105: 
Replace by "modified Gaussian PDF, with an added exponential tail."

Replace "of" by "for".

Line 108,112 
Add "for the combined sample" after "29 \% of the signal yield".
It will be different for the other fits if it is left free.
Can you give the mass range for which this background ratio is given?
Why do we need to know this number?

Line 113
Replace "equally" by "proportional".
Why not for fitted for each sample?
Could this help to assign a systematic uncertainty to A_CP
due to this background?

Line 115
Remove "with two free parameters for the slope and the normalisation".
This is superfluous information.
An exponential does not have a slope and cannot be normalized in the
same sense as a gaussian.

Line 123:
Describe how this "modified Gaussian" is modified,
if it is not same as the one mention above.

Table 1:
Remove the third row.
The "Combined sample" is superfluous and not mentioned in line 127.

4 A_CP measurement

Line 131:
Replace "have an even number or zero kaons" to
"have two or zero kaons",

or replace "Since B->pi pi pi and B->K K pi have an even number 
or zero kaons ... term, A_D, refers to pions." to
"Since B->K K pi has an even number of kaons ... term, A_D, in Eq.(2) 
 depends on pion detection efficiencies."

Replace "kaon detection asymmetry momentum dependence is weak" by
"kaon detection asymmetry is small and its momentum dependence can
be ignored in the analysis".
It did not say that A_D is small for kaons. 
Later you do give -0.010(2). 

Eq.(3): 
- Put A_P on the left side by interchanging A_P and A^RAW
and changing + to - in the right side of the equation.
- As in Eq.(2) remove CP below RAW.
- Remove "B->" and keep "J/psi K+-" between the brackets
as in line 140 and in the results below line 149.

Line 140:
Replace "... was obtained to be A^RAW_CP=...42 from" by
"... , A^RAW =...42, was obtained from".

Line 146-148:
Remove this sentence.
It is not clear what selections are made and why is there cancellation?

Line 148:
Replace by 
"The measured CP asymmetries follow from Eqs (2) and (3),
The trigger subsamples are removed above.
You do not measure from an equation.

Line 150:
Remove the first "statistical".

Line 151:
Replace "for the signal channel" by "for B+- ->pi+_ pi+ pi- or
B+- ->K+ K- pi+-".
Otherwise confusion with "signal" in relation to "background".

Table 2:
There is a typo that the totals for the pipipi and KKpi are reversed.

5 Systematic ...

Line 153-155:
What is "the signal model"?
Should in not be "the model to describe signal and background"?
Shortly indicate it as "fit function model".
The procedure the get its uncertainty is not clear to me.

Lines 160 - 166.
We like this cross check.
Is there also a magnet-up vs magnet-down cross check done? 

6 CP asymmetries in phase space

Fig. 3:
- Please mention the white bands are from the D0-exclusion, 
otherwise the tendancy is to suspect a binning effect.
- What is the horizontal band in the right figure around (m_Kpi)^2 = 10 GeV2 ?

Fig. 4:
Can you give a list of bin edges, or plot the bin edges more clearly?
The figure is meaningless in black/white.

Fig. 5:
- Replace the second "<" by ">" in the caption.
- Indicate the separation line at 15 GeV2/c4 in Fig. 5 (top).
- Remove all CP's.

Line 189: 
Replace "m_0" by "m_B+".
m_0 is not defined.

Line 192: 
Remove typo in "togheter".

Line 221: 
Please, motivate (m_high)^2 > 15, as you do for (m_low)^2 < 0.4.

Fig. 6: 
- Add a legend for the empty/full triangles in the figure.
This will also clean up the caption.
- Indicate the B+ and B- events with the same triangles
in the bottom plots in the mass range m_B+-40 MeV/c2.

Line 241:
Replace "This unknown structure" by
"This enhancement of the B+- event yield".

Line 268:
Remove "seemingly"

Line 272, 282, 284: 
Replace "collaboration" by "Collaboration".

Line 272:
Remove one "," in ",,". 

Line 282:
Replace "Physics Letters" by "Phys. Lett".