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    <div class="moz-cite-prefix">Dear Alberto, all,</div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">    I come to this copying also to the
      dm list (ObsCoire and extensions are dm stuff). As you may
      remember this point was EXTENSIVELY discussed when we upgraded
      ObsCore  from 1.0 to 1.1.</div>
    <div class="moz-cite-prefix">    This discussion was mainly in
      2014/2015. See for example these threads starting by
      <a class="moz-txt-link-freetext" href="http://mail.ivoa.net/pipermail/dm/2015-April/005147.html">http://mail.ivoa.net/pipermail/dm/2015-April/005147.html</a> and
      <a class="moz-txt-link-freetext" href="http://mail.ivoa.net/pipermail/dm/2015-April/005168.html">http://mail.ivoa.net/pipermail/dm/2015-April/005168.html</a> as well
      as <a class="moz-txt-link-freetext" href="http://mail.ivoa.net/pipermail/dm/2015-May/005174.html">http://mail.ivoa.net/pipermail/dm/2015-May/005174.html</a></div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">      The conclusion at that time was
      that we didn't have to extend ObsCore this way eventually.</div>
    <div class="moz-cite-prefix">      For several reasons.</div>
    <div class="moz-cite-prefix">       - radial velocity or redshifts 
      derivation from spectral frequencies or wl are complex things.
      querying between vel = 10 km/s and 60 km/s may give different
      results according to the radial velocity (or dopplershift) flavor.
      And if we add the constraint em_ucd =  vrad (or vopt, or ) then
      the query become really specialised.</div>
    <div class="moz-cite-prefix">      - if the velocity cube is simply
      a transform of the frequency/wavelength axis  we still have to
      select on wavelength because velocity cubes in radio domain and
      velocity cube in optical domain are really different things</div>
    <div class="moz-cite-prefix">        -  But generally speaking the
      velocity axis is not ONLY a transform of the wavelength (or
      frequency) axis, it provides different information. It is a
      different axis (although related). As Arnold pointed at that time
      you have datasets where you provide different doppler shift
      information at different spectral coordinates. What are the radial
      velocity bounds in that case ?</div>
    <div class="moz-cite-prefix">        ---> ObsCore will become
      really complex to manage and fill in these situations<br>
    </div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">        Considering your use case
      Alberto, I think we have two distinguish two steps</div>
    <div class="moz-cite-prefix">            - data  discovery (With
      ObsTAP/ SIA) = it's probably enough to let the user know that you
      have velocity cubes by providing the appropriate values in em_ucd
      and em_unit (which are there to describe the dataset content and
      not the spectral characterization). We may think to add em_ref to
      give the wl of the reference   line. velocity limits will have to
      be transformed in wavelength to fill the mandatory em_min/max
      anyway. With this you already know that the data you discover by a
      standard ObsCore (or radio extension) query are "'velocity cubes"</div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">             - SODA cutouts : there ,
      the parameters you propose are useful. A discussion started
      already some time ago to extend SODA . For example adding pixel
      cutouts, or changing the projection or the spatial sampling of the
      cutout. In this context we could also choose to extract by forcing
      velocity constraints, when appropro$iate. <br>
    </div>
    <div class="moz-cite-prefix">               To do that we need
      additional metadata (eg : the content of WCS,  and this also for
      the spectral axis). And for that, there is the old idea to have a
      SODA mode providing full metadata, CADC already implemented
      something like that. The velocity '"axis" detailed flavor can be
      described this way if it exists. This also has to be integrated in
      the SODA-next discussion. Some more on this will come soon.</div>
    <div class="moz-cite-prefix"><br>
    </div>
    <div class="moz-cite-prefix">Cheers</div>
    <div class="moz-cite-prefix">François<br>
    </div>
    <div class="moz-cite-prefix"> <br>
    </div>
    <div class="moz-cite-prefix">    <br>
    </div>
    <div class="moz-cite-prefix"> 1Le 22/02/2023 à 11:33, alberto micol
      a écrit :<br>
    </div>
    <blockquote type="cite"
      cite="mid:2E98235A-E798-4C0D-8BFB-894D85935A8B@googlemail.com">
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      Very well, thanks both Markus and Pat.
      <div class=""><br class="">
      </div>
      <div class="">So, yes, we need a v_resolution, and it must be in
        fixed units.</div>
      <div class="">Taking the Greisen et al. default, this is [m/s].</div>
      <div class=""><br class="">
      </div>
      <div class="">We though need the fravergy UCD to be able to
        discriminate the different velocity flavours.</div>
      <div class="">Is em_ucd the correct field to use? </div>
      <div class="">(Yes, I’m hit strongly by the confusion of throwing
        untested features from a data model into a relational mapping,</div>
      <div class="">that’s why I need your confirmation on this)</div>
      <div class=""><br class="">
      </div>
      <div class="">Thanks!</div>
      <div class="">Alberto</div>
      <div class=""><br class="">
      </div>
      <div class=""><br class="">
      </div>
      <div class="">
        <div class="">
          <div>
            <blockquote type="cite" class="">
              <div class="">On 21 Feb 2023, at 21:11, Alberto Micol <<a
                  href="mailto:amicol@eso.org"
                  class="moz-txt-link-freetext" moz-do-not-send="true">amicol@eso.org</a>>
                wrote:</div>
              <br class="Apple-interchange-newline">
              <div class="">
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                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">Hi James,</span><span style="font-size:
                      11pt;" class=""><o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">Thanks for the answer. I have a
                      question/doubt regarding the v_resolution and
                      v_unit.<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">ObsCore already foresees the
                      em_resolution, so I originally thought we do not
                      need the v_resolution.<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">But now I am reconsidering this, because
                      I think (in the ObsCore standard we were not
                      super-clear regarding this) the units of
                      em_resolution are the ones provided by the em_unit
                      attribute. Different cubes could have different
                      em_units, and that means that em_resolution could
                      not be used to seamlessly query across all
                      possible cubes.<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">If the above is correct, then, yes, we
                      need to have a new field,<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">v_resolution, with units fixed to e.g.
                      m/s,<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">similarly to the case of em_min/max
                      always provided in [m], whatever the value of the
                      em_unit, to support searches.<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">In which case, we do not need a v_unit,
                      as v_min/max are fixed in [m/s] and we already
                      have em_unit for the units encoded in the cube.<o:p
                        class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">Would that make sense?<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">Regarding treating frequency cubes as
                      velocity cubes (and viceversa), <o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">it is indeed useful to provide
                      characterisations both in frequency and in
                      velocity<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">(and why not energy and wavelength),
                      distinguishing the different cases according to<o:p
                        class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">the value of the em_ucd, e.g., em.freq,
                      em.wl, em.energy (see ObsCore B.6.2), or<o:p
                        class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">spect.dopplerVeloc.radio, spect.dopplerVeloc.opt, spect.dopplerVeloc.rel
                      (*) (see ObsCore B.6.2.6). <o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">So we would have:<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">em_ucd required<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">v_resolution required, fixed in m/s<o:p
                        class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">em_unit optional, expressing the unit
                      encoded in the cube for the spectral axis<o:p
                        class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">em_resolution optional, expressing the
                      resolution in the units used by the data cube<o:p
                        class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">If we converge on this, I could put
                      together a little document with a detailed
                      proposal.<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">Would that considered useful?<o:p
                        class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">Cheers,<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">Alberto<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class=""><o:p class=""> </o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">(*) cross-standard issue: the
                      spect.dopplerVeloc.rel is mentioned in the ObsCore
                      standard, <o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">but it is not a recognised value in the
                      current UCD1+ standard.<o:p class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 10.5pt; font-family: Helvetica;"
                      class="">We will need to act on this (Mireille?).<o:p
                        class=""></o:p></span></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class=""><o:p class=""> </o:p></span></div>
                  <div style="border-style: solid none none;
                    border-top-width: 1pt; border-top-color: rgb(181,
                    196, 223); padding: 3pt 0cm 0cm;" class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><b
                        class=""><span style="font-size: 12pt;" class="">From:<span
                            class="Apple-converted-space"> </span></span></b><span
                        style="font-size: 12pt;" class="">"Dempsey,
                        James (IM&T, Black Mountain)" <<a
                          href="mailto:James.Dempsey@csiro.au"
                          style="color: purple; text-decoration:
                          underline;" class="moz-txt-link-freetext"
                          moz-do-not-send="true">James.Dempsey@csiro.au</a>><br
                          class="">
                        <b class="">Date:<span
                            class="Apple-converted-space"> </span></b>Thursday,
                        16 February 2023 at 00:21<br class="">
                        <b class="">To:<span
                            class="Apple-converted-space"> </span></b>Alberto
                        Micol <<a href="mailto:amicol@eso.org"
                          style="color: purple; text-decoration:
                          underline;" class="moz-txt-link-freetext"
                          moz-do-not-send="true">amicol@eso.org</a>>,
                        "<a href="mailto:dal@ivoa.net" style="color:
                          purple; text-decoration: underline;"
                          class="moz-txt-link-freetext"
                          moz-do-not-send="true">dal@ivoa.net</a>" <<a
                          href="mailto:dal@ivoa.net" style="color:
                          purple; text-decoration: underline;"
                          class="moz-txt-link-freetext"
                          moz-do-not-send="true">dal@ivoa.net</a>><br
                          class="">
                        <b class="">Subject:<span
                            class="Apple-converted-space"> </span></b>Re:
                        ObsCore for velocity cubes<o:p class=""></o:p></span></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""><o:p class=""> </o:p></span></div>
                  </div>
                  <table class="MsoNormalTable" style="width: 356px;"
                    width="100%" cellspacing="0" cellpadding="0"
                    border="0">
                    <tbody class="">
                      <tr class="">
                        <td style="border-width: 1pt 1pt 1pt 6pt;
                          border-style: solid; border-color: orange;
                          background-color: white; padding: 7.5pt;
                          background-position: initial initial;
                          background-repeat: initial initial;" class="">
                          <div style="margin: 0cm 0cm 0.0001pt;
                            font-size: 10pt; font-family: Calibri,
                            sans-serif;" class=""><span
                              style="font-family: Arial, sans-serif;"
                              class="">This email was sent from outside
                              of ESO from the address<strong class=""><span
                                  style="font-family: Arial,
                                  sans-serif;" class="">[<a
                                    href="mailto:prvs=40330730a=James.Dempsey@csiro.au"
                                    style="color: purple;
                                    text-decoration: underline;"
                                    class="moz-txt-link-freetext"
                                    moz-do-not-send="true">prvs=40330730a=James.Dempsey@csiro.au</a>]</span></strong><span
                                style="" class="">. If it looks
                                suspicious, please report it to<span
                                  class="Apple-converted-space"> </span><a
                                  href="mailto:phishing@eso.org"
                                  style="color: purple; text-decoration:
                                  underline;"
                                  class="moz-txt-link-freetext"
                                  moz-do-not-send="true">phishing@eso.org</a>.</span><o:p
                                class=""></o:p></span></div>
                        </td>
                      </tr>
                    </tbody>
                  </table>
                  <table class="MsoNormalTable" cellspacing="0"
                    cellpadding="0" border="0">
                    <tbody class="">
                      <tr style="height: 7.5pt;" class="">
                        <td style="width: 2.78125px; padding: 0cm;
                          height: 7.5pt;" class="" width="100%">
                          <div style="margin: 0cm 0cm 0.0001pt;
                            font-size: 10pt; font-family: Calibri,
                            sans-serif; line-height: 7.5pt;" class=""><span
                              style="font-size: 7.5pt;" class=""> <o:p
                                class=""></o:p></span></div>
                        </td>
                      </tr>
                    </tbody>
                  </table>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt; color: white;" class="">Hi
                      Alberto</span><span style="font-size: 11pt;"
                      class="">,</span><o:p class=""></o:p></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class=""> </span><o:p
                      class=""></o:p></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class="">At CASDA we
                      support cutouts of velocity spectral line cubes.</span><o:p
                      class=""></o:p></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class=""> </span><o:p
                      class=""></o:p></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class="">We currently
                      require the user to provide a BAND or CHANNEL
                      parameter to the SODA service which is translated
                      by the service to the velocity frame of the target
                      cube. This works, but requiring conversions on
                      both the client and server side isn’t ideal.
                      Likewise, in our ObsCore implementation only the
                      em_ucd indicates the cubes are in velocity but it
                      would certainly be useful to have full velocity
                      information for data discovery!</span><o:p
                      class=""></o:p></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class=""> </span><o:p
                      class=""></o:p></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class="">The extension
                      you outline looks like it would work nicely for
                      the same use case in CASDA. However I think we
                      should add the following to fully describe the
                      velocity axis (as opposed to its translation into
                      wavelength for the base obscore).</span><o:p
                      class=""></o:p></div>
                  <ul style="margin-bottom: 0cm; margin-top: 0cm;"
                    class="" type="disc">
                    <li class="MsoListParagraph" style="margin: 0cm 0cm
                      0.0001pt; font-size: 10pt; font-family: Calibri,
                      sans-serif;"><span style="font-size: 11pt;"
                        class="">v_resolution – value of CDELT3 or
                        CDELT4</span><o:p class=""></o:p></li>
                    <li class="MsoListParagraph" style="margin: 0cm 0cm
                      0.0001pt; font-size: 10pt; font-family: Calibri,
                      sans-serif;"><span style="font-size: 11pt;"
                        class="">v_unit – although this should always be
                        m/s</span><o:p class=""></o:p></li>
                  </ul>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class=""> </span><o:p
                      class=""></o:p></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class="">Another
                      consideration is that a lot of our users tend to
                      use velocity to interact with frequency cubes. So
                      even for these frequency cubes we might end up
                      filling in velocity metadata if the fields were
                      defined. Tools such as CARTA tend to automatically
                      show the spectral axis as velocity where it can,
                      such that many users would assume the cubes are in
                      velocity not frequency.</span><o:p class=""></o:p></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class=""> </span><o:p
                      class=""></o:p></div>
                  <div class="">
                    <div class="">
                      <div style="margin: 0cm 0cm 0.0001pt; font-size:
                        10pt; font-family: Calibri, sans-serif;"
                        class=""><span style="font-size: 11pt;" class="">Cheers,</span><o:p
                          class=""></o:p></div>
                      <div style="margin: 0cm 0cm 0.0001pt; font-size:
                        10pt; font-family: Calibri, sans-serif;"
                        class=""><b class=""><span style="font-size:
                            11pt; color: rgb(0, 169, 206);" class="">James
                            Dempsey</span></b><o:p class=""></o:p></div>
                      <div style="margin: 0cm 0cm 0.0001pt; font-size:
                        10pt; font-family: Calibri, sans-serif;"
                        class=""><span style="font-size: 9pt;" class="">Senior
                          Developer <span class="Apple-converted-space"> </span></span><span
                          style="font-size: 9pt; color: rgb(0, 169,
                          206);" class="">|</span><span
                          style="font-size: 9pt;" class="">  CSIRO </span><o:p
                          class=""></o:p></div>
                      <div style="margin: 0cm 0cm 0.0001pt; font-size:
                        10pt; font-family: Calibri, sans-serif;"
                        class=""><span style="font-size: 11pt;" class=""><a
                            href="mailto:james.dempsey@csiro.au"
                            style="color: purple; text-decoration:
                            underline;" class="" moz-do-not-send="true"><span
                              style="font-size: 9pt; color: rgb(5, 99,
                              193);" class="">james.dempsey@csiro.au</span></a></span><span
                          style="font-size: 9pt;" class=""> <span
                            class="Apple-converted-space"> </span></span><span
                          style="font-size: 9pt; color: rgb(0, 169,
                          206);" class="">|</span><span
                          style="font-size: 9pt;" class="">  02 6214
                          2912</span><o:p class=""></o:p></div>
                    </div>
                  </div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class=""> </span><o:p
                      class=""></o:p></div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class=""> </span><o:p
                      class=""></o:p></div>
                  <div style="border-style: solid none none;
                    border-top-width: 1pt; border-top-color: rgb(181,
                    196, 223); padding: 3pt 0cm 0cm;" class="">
                    <p class="MsoNormal" style="margin: 0cm 0cm 12pt;
                      font-size: 10pt; font-family: Calibri,
                      sans-serif;"><b class=""><span style="font-size:
                          12pt;" class="">From:<span
                            class="Apple-converted-space"> </span></span></b><span
                        style="font-size: 12pt;" class="">dal <<a
                          href="mailto:dal-bounces@ivoa.net"
                          class="moz-txt-link-freetext"
                          moz-do-not-send="true">dal-bounces@ivoa.net</a>>
                        on behalf of alberto micol <<a
                          href="mailto:amicol.ivoa@googlemail.com"
                          class="moz-txt-link-freetext"
                          moz-do-not-send="true">amicol.ivoa@googlemail.com</a>><br
                          class="">
                        <b class="">Date:<span
                            class="Apple-converted-space"> </span></b>Thursday,
                        16 February 2023 at 12:02 am<br class="">
                        <b class="">To:<span
                            class="Apple-converted-space"> </span></b><a
                          href="mailto:dal@ivoa.net"
                          class="moz-txt-link-freetext"
                          moz-do-not-send="true">dal@ivoa.net</a> <<a
                          href="mailto:dal@ivoa.net"
                          class="moz-txt-link-freetext"
                          moz-do-not-send="true">dal@ivoa.net</a>><br
                          class="">
                        <b class="">Subject:<span
                            class="Apple-converted-space"> </span></b>ObsCore
                        for velocity cubes</span><o:p class=""></o:p></p>
                  </div>
                  <div style="margin: 0cm 0cm 0.0001pt; font-size: 10pt;
                    font-family: Calibri, sans-serif;" class=""><span
                      style="font-size: 11pt;" class="">Dear ObsCorers,</span><o:p
                      class=""></o:p></div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">I have
                        received with much interest the ObsCore
                        extension for RADIO data, thanks for that very
                        clear document.</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">Would it be
                        possible to have a similar extension for cubes
                        with velocity as third axis (the other two being
                        the usual spatial ones)?</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">Let me call
                        them “velocity cubes”...</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">Here my use
                        case…</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">At ESO we need
                        to support cutouts of velocity cubes.</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">Up to now our
                        SODA interface supported spectra, images, and
                        wavelength cubes;</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">to provide the
                        user with the SODA input parameters and their
                        possible MIN/MAX values</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">we query
                        ivoa.ObsCore.</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">Now with the
                        introduction of velocity cubes, we would like to
                        get the necessary SODA input params also from
                        ObsCore.</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">We can
                        certainly do so by extending our own ObsCore
                        table (ObsCore allows to extend the table), but
                        I was wondering</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">if others have
                        similar needs, and see if we can agree with a
                        common ObsCore extension.</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">Velocity cubes
                        should come in a FITS format as described by
                        Greisen et al, 2006, so-called Paper 3.</span><o:p
                        class=""></o:p></div>
                  </div>
                  <blockquote style="margin: 5pt 0cm 5pt 30pt;" class=""
                    type="cite">
                    <div class="">
                      <div style="margin: 0cm 0cm 0.0001pt; font-size:
                        10pt; font-family: Calibri, sans-serif;"
                        class=""><span style="font-size: 11pt;" class="">Shortly
                          summarised, the velocity can be either:</span><o:p
                          class=""></o:p></div>
                    </div>
                  </blockquote>
                  <div class="">
                    <ul style="margin-bottom: 0cm;" class="" type="disc">
                      <ul style="margin-bottom: 0cm;" class=""
                        type="circle">
                        <li class="MsoNormal" style="margin: 0cm 0cm
                          0.0001pt; font-size: 10pt; font-family:
                          Calibri, sans-serif;"><span style="font-size:
                            11pt;" class="">a radio (VRAD), </span><o:p
                            class=""></o:p></li>
                        <li class="MsoNormal" style="margin: 0cm 0cm
                          0.0001pt; font-size: 10pt; font-family:
                          Calibri, sans-serif;"><span style="font-size:
                            11pt;" class="">an optical (VOPT), </span><o:p
                            class=""></o:p></li>
                        <li class="MsoNormal" style="margin: 0cm 0cm
                          0.0001pt; font-size: 10pt; font-family:
                          Calibri, sans-serif;"><span style="font-size:
                            11pt;" class="">a relativistic velocity
                            (ZOPT), </span><o:p class=""></o:p></li>
                        <li class="MsoNormal" style="margin: 0cm 0cm
                          0.0001pt; font-size: 10pt; font-family:
                          Calibri, sans-serif;"><span style="font-size:
                            11pt;" class="">a generic apparent velocity
                            (VELO).</span><o:p class=""></o:p></li>
                      </ul>
                    </ul>
                  </div>
                  <blockquote style="margin: 5pt 0cm 5pt 30pt;" class=""
                    type="cite">
                    <div class="">
                      <div style="margin: 0cm 0cm 0.0001pt; font-size:
                        10pt; font-family: Calibri, sans-serif;"
                        class=""><span style="font-size: 11pt;" class="">The
                          RESTFRQa (RESTWAVa) keyword conveys the
                          necessary reference frequency (wavelength) to
                          transform velocity into frequency or
                          wavelength. </span><o:p class=""></o:p></div>
                    </div>
                    <div class="">
                      <div style="margin: 0cm 0cm 0.0001pt; font-size:
                        10pt; font-family: Calibri, sans-serif;"
                        class=""><span style="font-size: 11pt;" class="">The
                          velocity unit is m/s.</span><o:p class=""></o:p></div>
                    </div>
                  </blockquote>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">SODA cutouts
                        on the velocity axis are usually formulated by
                        passing cuts already expressed in velocity</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">though it must
                        be possible to perform the conversions to and
                        from frequency/wavelength.</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">What would
                        then be needed in ObsCore is:</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">v_min</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">v_max</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">but also, in
                        case of radio velocity cube:</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">f_min</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">f_max (getting
                        these from the RADIO extension)</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">f_rest =
                        RESTFRQ</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">and, in case
                        of a optical or relativistic velocity cube</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">em_rest =
                        RESTWAV</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">(we already
                        have em_min, em_max)</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">The
                        em_resolv_power should then be set to:</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> lambda      
                                     freq                     c</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> ———————  =
                         ————— = —————</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> delta lambda
                                  delta freq       2 * delta_v</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">where delta_v
                        is the CD3_3 in the cube (in the example of a
                        cube with the velocity on the third axis);</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">but I would
                        also likely accept a v_pixel_scale (= delta_v).</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">The UCD for
                        the velocity should then be:</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <pre style="margin: 0cm 0cm 0.0001pt; font-size: 10pt; font-family: 'Courier New';" class="">spect.dopplerVeloc.opt<o:p class=""></o:p></pre>
                    <div class="">
                      <pre style="margin: 0cm 0cm 0.0001pt; font-size: 10pt; font-family: 'Courier New';" class="">spect.dopplerVeloc.radio<o:p class=""></o:p></pre>
                      <div class="">
                        <div style="margin: 0cm 0cm 0.0001pt; font-size:
                          10pt; font-family: Calibri, sans-serif;"
                          class=""><span style="font-size: 11pt;"
                            class="">unsure what it should be for the
                            relativistic case.</span><o:p class=""></o:p></div>
                      </div>
                    </div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">This would
                        allow us at ESO to implement SODA on top of
                        ObsCore (as already done for all other
                        parameters)</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">and would
                        allow astronomer to search the velocity cubes
                        with certain characteristics using ObsCore.</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">What do you
                        think? </span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">Is that
                        doable? I think at ESO we will simply start
                        implementing the above extra ObsCore parameters
                        (unless you suggest different names for that),</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">while waiting
                        to see if there is more interest to build a
                        proper standard.</span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class=""> </span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">Eager to know
                        what you think, </span><o:p class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">Cheers,</span><o:p
                        class=""></o:p></div>
                  </div>
                  <div class="">
                    <div style="margin: 0cm 0cm 0.0001pt; font-size:
                      10pt; font-family: Calibri, sans-serif;" class=""><span
                        style="font-size: 11pt;" class="">Alberto</span></div>
                  </div>
                </div>
              </div>
            </blockquote>
          </div>
          <br class="">
        </div>
      </div>
    </blockquote>
    <p><br>
    </p>
  </body>
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