The paper was intended to contain five sections. In the first section of the paper, Ducant explains change and the parameters of change, and examines the patterns of change within specified systems. He successfully reduces all forms of bifurcation to a single variant and eliminates non-autonomous oscillation. In the second section, he explains the concept of a random universe in which any single point may change in stability, regardless of the values of parameters, the local stability of an identified pattern, or any external stimulus active on that point. In effect, he argues that parameters and patterns are illusions, and stimuli are irrelevant, and that bifurcation as described occurs for its own reasons. Some academics have argued that these two sections represent the whole of Ducant's work on the paper, and Ducant himself would later claim this. The third section, which was never written, would have explained the redundancy of trying to identify and control parameters in order to ensure that no point in a system reaches a critical threshold. The fifth section would have proposed methods of achieving the goals set out in the latter third of section four, and contained Ducant's conclusions on the nature and importance of bifurcations. The most significant arguments are to be found in section four. It is here that Ducant suggests that as stability changes randomly, it can be intentionally changed by, and only by, simple action rather than careful variation. He also argues that if bifurcations do not exist, it is necessary to create them, and explains why they should be created and the effect of such creation. When the paper was first published there were widespread claims that this portion is at odds, both stylistically and philosophically, with the rest of the text. Many have alleged that this material was added by the Darrow Foundation, particularly given the Foundation's subsequent pioneering use of these theories during the Orbital Wars. Ducant himself denied writing this material, but this was almost certainly a duplicitous turn due to his own change of opinion, and the arguments in this section are clearly a logical progression from his prior arguments.
Supporters of these theories can point to the Orbital Wars as proof. It is an observed fact that once a turning-point in the conflict was identified, either in the past or in the future, competing factions rushed to place agents at that point; and that no faction placed agents except at identified turning-points. The argument asserts that in pursuing this strategy, the relative factions created each identified turning-point; that the placement and action of agents created a physical point of bifurcation in the spacetime continuum. This happened both retroactively, in the case of turning-points that had already happened, and proactively, in the case of turning-points that had been predicted. It therefore follows that not only did all actions within the conflict create points of bifurcation, but that all points not affected by such actions were not points of bifurcation. Unenlightened detractors have argued that the relationship between points of bifurcation and the placement of agents are examples of reactionary behaviour, and any productive connection is actually coincidence (in the case of turning-points that have already happened) or hysteresis and self-fulfilling prophecy (in the cases of predicted turning-points).
The final theory contained in the paper, that branches formed by bifurcation would be incidentally influenced by the intent of the manipulator, rather than the nature of the manipulation, is thought to have lead to characteristic tactics employed during the Orbital Wars, described in the Bifurcative Spacetime Strategy Theory. This theory argues that the various factions in the war were all pursuing a "third way" between the traditional determinist theory, that that points in spacetime are inherently stable or unstable, and Ducant's theory that bifurcations can be created. The strategy employed was based on an assumption that certain points in the continuum were natural points of bifurcation, but that the nature of the branch could be influenced. These strategic manoeuvres rejected Ducant's principle that points of bifurcation were merely the product of strategic manoeuvres and the stability or instability of points is the product of agents and not inherent. However, the final winning strategy of the Wars, the innovative Homotopy Campaign, was engendered by the assumption that the inherent stability or instability of a point was irrelevant, and therefore represented the tacit triumph of the Case for Bifurcation in the face of continued intellectual resistance.
Ducant left the Case for Bifurcation unfinished, embarking upon the journey described in the [Non-Wanderer's Tale]? in order to prove his theories. In his absence, and in light of massive public interest in the theories Ducant had been discussing, the Darrow Foundation managed to secure access to the incomplete text and published it as was, without the intended third and fifth chapters. This edition was to form the only record of the Case for Bifurcation. When Ducant finished his journey and returned to Earth during the Orbital Wars, he attacked the Darrow Foundation, not for publishing his work in an incomplete form or without his permission, but for publishing it at all. It has been suggested that his own status, as an active agent at the [Qirel Encounter]?, whilst confirming his theories about the nature and creation of points of bifurcation, had soured his whole attitude towards the subject. Ducantís subsequent work, the inferior, sentimental and hastily-written Case for Branches, both an academic thesis and a legal argument in which he contradicted and attacked the Case for Bifurcation, would suggest that his intellect had indeed given way to his emotions. Others have suggested that this Alexander Ducant was a different Alexander Ducant, and though there is no evidence for this claim it is certainly a comforting notion. Ducant used the Case for Branches to successfully sue for punitive damages against both the Darrow Foundation and the grandson of the editor of the published edition of the Case for Bifurcation, although he was thankfully unable to secure a court order to destroy all existing copies. The Case for Permanent Cryptostability, his later civil action against himself for intellectual irresponsibility and criminal intent, was thrown out of court.