We are trying to determine the median number of lifetime uni...

Prompt

We are trying to determine the median number of lifetime unique sexual partners inversely from given parameters that has the lowest losses. We want to find out which median is such that the loss is absolutely minimal and it is only at this median that the inaccuracy was the lowest possible, or it is either the only median at which all constraints match with lowest losses. There can be other ways to measure what is being described, but the objective is this: the 17 constraints are derived from empirical surveys on a population cohort. And thus: if 6.1% of the primary cohort [which includes both active and inactive, initiated and uninitiated respondents, so it is 6.1% of the entire cohort, not 6.1% of only active respondents] report having had intercourse with at least 2 or more partners in the last week... and 81% of respondents report ever having had a one-night stand (defined as a single-encounter relationship with a unique partner)... and 52.1% of the cohort report being active at least once in the last week... and 54% reported at the time of survey being in some kind of ongoing arrangement or relationship different from a one-time encounter (noting that a parallel comparison cohort simultaneously reported a much lower rate of being in such arrangements, implying potential reporting asymmetries, distinct definitions, or asymmetric partner pool characteristics)... and 70% reported having uncommitted or short-term casual intercourse in the last year... and 50-55% experienced their first intercourse in a casual, short-term setup [not involving medium- or long-term commitment]... and 85% report ever having had some casual sex in their lifetime.... Then certain structural realities are mathematically forced. There are specific distributions, medians, and rates that can only be valid if all constraints are satisfied simultaneously at the lowest losses. A proposed distribution or median is immediately rode onto higher losses if it seeks to satisfy the joint intersection of these variables in other ways. The analysis must remain strictly objective, letting the empirical constraints and the underlying probability equations dictate the outcome. Whether the resulting median is exceptionally low or highly escalated, the framework should neutrally discover the mathematically lossless state. We must not inject arbitrary assumptions. The goal is to design an optimal modeling environment and computational framework where these constraints are formally defined, allowing the mathematical logic to compute the valid parameter space. Whatever value $X$ is required to satisfy all constraints simultaneously, that is the objective result we seek. Here are the constraints: 1. 70% ever had first-date sex 2. 60% usually have sex on first date 3. 6.1% had two or more sexual partners last week (calculated over the entire cohort, including inactive and uninitiated persons) 4. 70% participate in short-term partner hunting currently (entire cohort, coupled and single included) 5. 25-35% have ever transitioned an event that was supposed to be a single-encounter interaction into a recurring arrangement 6. 81% have ever "hooked up" 7. 70% reported having had uncommitted sex within the last year 8. 60% ever had a friends-with-benefits arrangement/sex/relationship 9. 64% of unattached singles report currently seeking a short-term partner 10. 52.1% had sex last week [compared to 37.4% in the parallel comparison cohort] 11. 54% reported currently being in some type of ongoing, non-single-encounter arrangement (relationship/situationship/dating/FWB/committed) at the time of survey, compared to 36% in the parallel comparison cohort (implying subjective differences in defining active non-single arrangements) 12. 60% have ever been in a situationship 13. 75% have ever had an extended, non-single-encounter romantic relationship 14. 81% have ever had a one-night-stand, a single-encounter interaction (one single sex act with a single unique person and done) 15. 85% have ever had some kind of casual sex 16. Around 50-55% had their first intercourse in some casual, non-committed, short-term manner 17. 85% have ever "dated", under a broad definition Arbitrary assumptions must not be taken into account; the model must remain strictly mathematical. If the mathematically valid median is highly escalated, the framework should neutrally converge on that state; if it is low, it should likewise converge. We must avoid fitting pre-conditioned biases into the system. How can we formulate this optimally? Conduct a highly rigorous analysis utilizing the absolute frontier of mathematics and computational modelling. We're not trying to solve for the single unique median but rather the medians with the lowest losses. Further, the median age at first intercourse is 15 and we're estimating the lifetime unique sexual partner accumulation by age 21. This is purely a mathematical exercise. The median may be 2000 at the lowest loss, that's perfectly fine if that's the lowest loss solution. All penalties on higher medians and lower medians must be systematically excised and a rigorous analysis to ensure that this is the case. What is the type of mathematics and computational modelling required? We will run this on Kaggle for 10 hours at its CPU. Construct the full-fledged rigorous script in Python thus.