example for formula ID ambiguity

math_subset.xml

<mws:expr url="math.3.0">
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1" class="ltx_Math" alttext="{\displaystyle a}" display="inline" xml:id="p1.1.m1.1" xref="p1.1.m1.1.cmml">
  <semantics xml:id="p1.1.m1.1a" xref="p1.1.m1.1.cmml">
    <mi xml:id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">a</mi>
    <annotation-xml encoding="MathML-Content" xml:id="p1.1.m1.1.cmml" xref="p1.1.m1.1">
      <ci xml:id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">a</ci>
    </annotation-xml>
    <annotation encoding="application/x-tex" xml:id="p1.1.m1.1b" xref="p1.1.m1.1.cmml">{\displaystyle a}</annotation>
  </semantics>
</math>
</mws:expr>

<mws:expr url="math.4.0">
	<math xmlns="http://www.w3.org/1998/Math/MathML" id="p1.1.m1" class="ltx_Math" alttext="{\displaystyle{{\bar{\alpha}}(\theta_{i})}}" display="inline" xml:id="p1.1.m1.1" xref="p1.1.m1.1.cmml">
  <semantics xml:id="p1.1.m1.1a" xref="p1.1.m1.1.cmml">
    <mrow xml:id="p1.1.m1.1.6" xref="p1.1.m1.1.6.cmml">
      <mover accent="true" xml:id="p1.1.m1.1.1" xref="p1.1.m1.1.1.cmml">
        <mi xml:id="p1.1.m1.1.1.2" xref="p1.1.m1.1.1.2.cmml">α</mi>
        <mo stretchy="false" xml:id="p1.1.m1.1.1.1" xref="p1.1.m1.1.1.1.cmml">¯</mo>
      </mover>
      <mo xml:id="p1.1.m1.1.6.1" xref="p1.1.m1.1.6.1.cmml">⁢</mo>
      <mrow xml:id="p1.1.m1.1.6.2" xref="p1.1.m1.1.6.2.cmml">
        <mo xml:id="p1.1.m1.1.6.2a" xref="p1.1.m1.1.6.2.cmml">(</mo>
        <msub xml:id="p1.1.m1.1.6.2b" xref="p1.1.m1.1.6.2.cmml">
          <mi xml:id="p1.1.m1.1.3" xref="p1.1.m1.1.3.cmml">θ</mi>
          <mi xml:id="p1.1.m1.1.4.1" xref="p1.1.m1.1.4.1.cmml">i</mi>
        </msub>
        <mo xml:id="p1.1.m1.1.6.2c" xref="p1.1.m1.1.6.2.cmml">)</mo>
      </mrow>
    </mrow>
    <annotation-xml encoding="MathML-Content" xml:id="p1.1.m1.1.cmml" xref="p1.1.m1.1">
      <apply xml:id="p1.1.m1.1.6.cmml" xref="p1.1.m1.1.6">
        <times xml:id="p1.1.m1.1.6.1.cmml" xref="p1.1.m1.1.6.1"/>
        <apply xml:id="p1.1.m1.1.1.cmml" xref="p1.1.m1.1.1">
          <ci xml:id="p1.1.m1.1.1.1.cmml" xref="p1.1.m1.1.1.1">normal-¯</ci>
          <ci xml:id="p1.1.m1.1.1.2.cmml" xref="p1.1.m1.1.1.2">α</ci>
        </apply>
        <apply xml:id="p1.1.m1.1.6.2.cmml" xref="p1.1.m1.1.6.2">
          <csymbol cd="ambiguous" xml:id="p1.1.m1.1.6.2.1.cmml">subscript</csymbol>
          <ci xml:id="p1.1.m1.1.3.cmml" xref="p1.1.m1.1.3">θ</ci>
          <ci xml:id="p1.1.m1.1.4.1.cmml" xref="p1.1.m1.1.4.1">i</ci>
        </apply>
      </apply>
    </annotation-xml>
    <annotation encoding="application/x-tex" xml:id="p1.1.m1.1b" xref="p1.1.m1.1.cmml">{\displaystyle{{\bar{\alpha}}(\theta_{i})}}</annotation>
  </semantics>
</math>
</mws:expr>

So if the XQuery returns an xref of "math_subset.xml#p1.1.m1.1.1.cmml", then there exists ambiguity between whether it refers to math.4.0 or math.3.0

that's right
but how do you derive this math_subset.xml#p1.1.m1.1.1.cmml what's the query?

I don't think the query is relevant to my question, only the result of the query - the NTCIR format says that you return results in the following format:

<hit id="id" xref=""filename" score="score" rank="rank">
  <formula id="id" for="idref" xref="fref" score="score">
    <qvar for="name" xref="sub-fref"/>
    <qvar/>
  </formula>
</hit>

Where "for" attributes specify the query ID, and "xref" attributes specify the formula ID in the result.
NTCIR format states that the <formula> xref attribute is of form "filename#id", where ID is the formula ID.

So my question is, if the formula ID is "p1.1.m1.1.1.cmml", how do you specify which result it is using the NTCIR format? Do you use something like "filename#math.3.0#p1.1.m1.1.1.cmml"?

I think filename is the url. You are mixing the mws dump format with the NTCIR dump format here.

Probably you mix the formats since I mixed them

let me see if I can find the NTCIR dump format spec