I am writing one proposal for one of the funding agency and I want to write some sentence which conveys following sentiment

Although my contribution to this field will be small and not huge compare to existing knowledge, I still want to contribute with the help of your financial support.

I am thinking of writing following,

This financial support will enable to me contribute <<opposite of lion's share>> in this field.

Any suggestions? Somewhere I came across phrase 'the short end of the stick' but I don't know to to formulate formal sentence with such phrase.

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    Surely the opposite of a lion's share is something like a "runt's share". I don't know how you can make this a positive statement! Don't focus on how small your contribution will be: focus on its strengths. – Andrew Leach Jan 1 '19 at 10:41
  • I would probably say "a mere pittance". – Hot Licks Jan 1 '19 at 12:58
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    The share in lion's share is something the lion takes - not contributes. – michael.hor257k Jan 1 '19 at 13:45

You can say that the benefactors will enable you to contribute the mouse’s share. Here’s an example of such usage:

More and More Vendors Competing for the Mouse’s Share of the Business - Egnyte

However, that would sound like you aim to put in the least amount of effort possible, making the smallest possible contribution you can. It would be an effective way to alienate your donors.

If you want to be explicitly understated, as it were, consider rewording:

  • This financial support will enable me to make my humble contributions to this field.

Alternatively, just state the contribution without claiming extent:

  • This financial support will enable me to contribute [] to this field.

Any contribution you make would satisfy this assertion - including the smallest.

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    Humble contributions is perfect ! – Dexter Jan 1 '19 at 11:09

The Lion's Share is an idiomatic expression which refers to the major share of something. The phrase derives from the plot of a number of fables ascribed to Aesop.

As for an opposite, Merriam Webster gives minority share

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