As a preamble, allow us to unravel the conundrum of wage theft. Wage theft is an illegal practice where employers do not pay workers for their work. This could be in the form of denying overtime wages, violating minimum-wage laws, imposing unwarranted deductions, or simply not paying an employee at all. A lawyer specializing in wage theft cases is your ally against such injustices. However, hiring a legal representative may entail some financial implications thus presenting the need for a well-structured budget.

First and foremost, it is crucial to understand the significance of a budget. In essence, a budget is a financial plan that allows you to allocate resources according to your income and expenditure. It functions as an economic blueprint, offering a pragmatic and insightful overview of how your monetary resources can be channelled for optimum efficiency.

To formulate a budget for hiring a wage theft lawyer, the primary aspect to consider is an understanding of the cost structure of legal services. The cost of legal services can be a complex matrix composed of elements such as skill level, experience, geographical location, and the complexity of the case at hand.

Legal costs can be broadly divided into three categories: consultation fees, contingency fees, and court costs. The consultation fee is the amount charged for the initial meeting with the lawyer to discuss the details of your case. Contingency fees are a percentage of the settlement awarded if your case is successful; this is a common mode of payment in wage theft cases. Court costs include fees for filing the case, evidence gathering, and other miscellaneous court charges.

The next step involves a thorough quantitative analysis of your financial resources. This includes an evaluation of your income, savings, investments, and other monetizable assets. Remember to also account for your necessary expenditures such as rent/mortgage, utilities, food, transportation, and healthcare to ensure the attorney's fees do not jeopardize your ability to maintain a decent standard of living.

In the spirit of Fourier's mathematical theory, it is essential to harmonize your financial frequencies with your intended legal expenditure. This would necessitate the use of a budgeting tool or application to help you systematically organize your income and expenses. This can be as simple as a spreadsheet or as complex as a dedicated financial software application.

Now, with a clear understanding of your financial landscape, it's time to juxtapose this against the expected legal costs. To do this effectively, one could employ statistical methods such as regression analysis to predict future income and expenses, thereby providing a more accurate budgetary allocation for the wage theft lawyer.

Finally, once a feasible budgetary allocation is reached, it is essential to maintain a buffer fund. Akin to the concept of statistical variance, this buffer fund is designed to accommodate for any unexpected costs or changes in your financial circumstances.

It is prudent to consider alternatives such as legal aid societies, pro bono services, or even crowd-funding platforms to ameliorate the financial burden. One could even apply game theory principles to determine the optimal strategy for sourcing financial support.

In the realm of wage theft, the role of a competent lawyer cannot be overstated, and while the need for budgeting may seem daunting, it is a necessary component of the process. Through a meticulous understanding of legal costs, quantitative analysis of your financial resources, the use of budgeting tools, statistical forecasting methods, and maintaining a buffer fund, you can successfully navigate the financial aspect of hiring a wage theft lawyer.

Remember, as Descartes aptly said, "Divide each difficulty into as many parts as is feasible and necessary to resolve it". Budgeting is simply the division of your financial difficulty into manageable fragments. By taking this approach, you equip yourself with the best possible chance of achieving justice in your wage theft case without compromising your financial stability.

In closing, we should all strive to be the vanguard against wage theft, utilizing every tool at our disposal, not least of which is a well-thought-out budget.