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Curoiser and curioser...

You are playing in the semifinal of the top flight regional KO bracket against a well know pro and his client.  You play precision and pick up this hand:  

North
Q106
AKJ
AJ96
QJ2
W
N
E
S
1
2
P
3
P
P
X
P
P
P

Partner's first pass is ambiguous - either penalty for 2 or 0-7 HCP.  So there is some ambiguity about partner's reopening double.  It could be a penalty double in in which case you would expect to be short in in the first place, or it shows 5-7 HCP (BoP) and a desire to compete without clear direction.  Some might call this a DISP or Optional T/O double.  Your cards tell you which of the two options is more likely.  

Partner leads a to this Dummy:

West
8
Q1063
108743
K82

Spots are approximate (no hand records). 

You play 3 rounds of and declarer ruffs the third round then plays A and ruffs a spade.  Declarer calls for a small from the board and you duck your A.  Partner wins their Q and leads their 4th .  You ruff the Q with your J.

Declarer pauses.  Tanks. Then he looks at you and asks - "Was your partner's double a takeout double?"

How do you answer?

You know partner can double if they want to reopen (top of pass range) or if they had a penalty double in the first place.  So you explain that the double is balance of power and can be penalty oriented (optional takeout).  

Declarer overruffs, but when the hand ends you set declarer one for +200.

The pro is outraged.  How can you possibility tell me that your partner made a penalty double when you knew you held the QJx?  This is a director call.

I asserted that my duty is to describe our agreement not my holding.  That didn't satisfy this person.  He insisted I purposely tried to mislead him as the double was clearly takeout and I knew it.  

The crux of the issue for me is that both takeout and optional penalty are live possibilities absent information from my hand.  What is certain at the point the double is made is that we own the balance of power.  

Am I supposed to peek into my hand and tell LHO that "of course, partner is short in "?  Am is supposed to explain that this double is simply reopening (and leave it at that)?  Am I supposed to say that since partner denies a biddable 5-card suit we have no LoTT safety at the 3 level so I tend to convert these doubles to penalty when my hand seems right?

Or is all of this so obvious that the question asked by LHO is suspect in its own right?   

Going round and round on this one....

(FWIW, they never asked about the alert of partner's initial pass).  

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