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At first glance, how you react to the headline figure from NHS Test and Trace's first set of published figures might seem to depend on whether you're a glass half full or half empty sort of person.

Or, to be more precise, a glass two-thirds full or one-third empty, because those are the ratios that come out of these statistics.

Is it an impressive achievement to have reached 67% of people who tested positive and asked for details of recent contacts?

Or is it a concerning failure to have been unable to reach 33%?

Sadly, it is hard to give a definitive answer, because these statistics do not permit much interrogation.

Take the headline figure that 8,117 people who tested positive for coronavirus between 28 May and 3 June had their case transferred to the contact tracing system.

The government's own figures would suggest that around 13,000 people tested positive that week. So why is there a discrepancy?

Asked about this, Baroness Dido Harding said there were "some errors in the data" and Professor John Newton said that there was "quite a lot of double counting" in the government figures.

Professor Newton added: "We are confident we have included all the people who have been tested positive."

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But while we should be able to trust what he says, we should also be able to verify it - and at the moment we can't.

Perhaps more worryingly, it is not clear that granular data is being provided to local public health teams, who are clearly going to be responsible for a large part of this effort.

Can a local director of public health find out quickly, in real time, how many cases have been identified and traced in a particular postcode? Can a GP?

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Right now, it seems they cannot.

A sign of this disconnect can be seen in the data released today.

The figures for the time it takes to ask someone to isolate, one of the most crucial measures of success for contact tracing, suggest that 85% of contacts were asked to isolate within 24 hours.

But this only applies to 5,278 of the 26,985 contacts reached and advised to self-isolate.

The other 21,707 people were, we are told, managed by "local public health teams".

Why don't we have statistics for how quickly they managed to do this?

Given that local public health teams take on so-called "complex cases", jargon for cases involving emergency service workers and anyone else who has been in contact with lots of people, it is crucial that both the public and the Test and Trace system itself can see what is going on.

These early numbers suggest that complex cases may make up the bulk of the contact tracing activity.

That means that even if the national system is working perfectly, it won't mean much if the local outbreak response isn't just as good.

Local directors of public health tell me they are still working on their response plans for local outbreaks.

Should the two-metre social distancing restriction be reduced?

Have they been given enough resources to take on such a burden? Should we be easing lockdown before they're ready?

The disconnect between local and national systems has been a constant feature for the national response during this crisis.

It is concerning that at this early stage that fault line is showing up in Test and Trace.