The current "mainstream" answer to "How does the net proper time difference accumulate?" is that the answer to that question is, in effect, unknowable - that is no specifics can be given - see the Mainstream Response page. We would tend to agree with that answer as long as it is qualified as "unknowable in the context of Special and General Relativity".

We differ with the mainstream's reason for now contending the answer is unknowable. Using Einsteinian Relativity, the mainstream notes that different obesrvers have different views on which events on the traveling twin's worldline are simultaneous with which events on the stay-at-home twin's worldline so they allege that one cannot compare the twin's proper times when the twins are apart.. We would agree that one cannot use Special Relativity's construct of simultaneity to address the question at hand as it's based on observed time and not proper time, however, that also means that issue is a red herring. The real reason why the question, "How does the net proper time difference accumulate?", is now claimed to be unknowable by the mainstream is because Einstein Relativity does not deal with the physics of the net proper time difference and because trying to use Einstein Relativity constructs has failed to answer the question - as was shown in the Can't Be Due To Relative Velocity and the Can't Be Due To Turnaround Acceleration pages,

The current mainstream position that the answer is unknowable may seem plausible to some. However, since the data shows that asymmetric time dilation, or more accurately clock retardation, occurs and is an undeniable physical effect, it seems unlikely that the physics of that effect is inherently unknowable. In addition, using clock retardation as a function of velocity with respect to a unique physics frame (e.g., Lorentz Relativity) straightforwardly describes the physics of how the proper time difference accumulates without even a hint of a problem or paradox.

The current mainstream position that the answer is unknowable may seem to some as an unassailable, safe position. However, because there is such a disconnect between current theory and the physics of clock slowing, even this agnostic approach is fatally flawed.

Problem: We agree with the mainstream that one cannot use Special Relativity's construct of simultaneity to address the question at hand. However, since there is complete symmetry between the outbound and inbound segments except for the direction of travel, the implication is, in the context of Einsteinian Relativity, that half the net proper time difference accumulates in the outbound segment and half in the inbound segment regardless of which frame is used as the stay-at-home frame and we have seen that that contention leads to a contradiction.

If, despite the essence of Einsteinian Relativity, the mainstream tries to avoid the above problem and contends that there isn't necessarily a 50-50 split, then since the only aspect that is not symmetric between the outbound segment and the inbound segment is the direction of travel, the implication is that direction effects the physics (e.g., clock rate) of the situation. In other words, the implication is that some function affects proper time accumulation as velocity increases or decreases. This in turn implies that there is a hierarchy of frames with a unique (physics) frame being at the bottom of the hierarchy (e.g., where clocks run the fastest). We would agree with this conclusion and recommend that it be seriously investigated.