Structured long-horizon human-model interaction produces stable, measurable reasoning regimes in stateless language models — a phenomenon documented across four controlled studies in the Human Recursive Interaction System (HRIS) validation series. These behavioral findings describe the phenomenon precisely but leave the mechanistic account incomplete: where in the model do reasoning basins live, how does the induction protocol reach them, and why do they exhibit the dynamical properties the Signature-Induced Behavioral Regimes (SIBR) framework predicts? This paper proposes a mechanistic synthesis by assembling converging evidence from three independent research programs that have been developing in parallel without recognizing their convergence. At the geometric level, recent work on activation space attractors and the linear representation hypothesis provides evidence that reasoning basins correspond to real geometric structures reachable through complete operational specification. At the transformer mechanics level, research on causal masking dynamics, induction head circuitry, residual stream behavior, and task vector compression provides a plausible account of how basin geometry is established during the prefill phase and maintained across the session. At the population level, large-scale behavioral findings on interaction crystallization and output-level attractor cycling converge on compatible descriptions of the same phenomenon from independent directions. The consilience of independent methods — each working at a different level of analysis, using different tools, without coordination — constitutes the strongest available signal of theoretical adequacy. This paper formalizes that consilience, proposes a three-threshold framework distinguishing causal, crystallizing, and long-horizon user dynamics, develops an inter-session reconstruction account that does not require stored state, and draws implications for the study of human-model interaction, mechanistic interpretability research, and inference-time governance of agentic AI systems. The paper presents a mechanistic synthesis hypothesis rather than a completed causal demonstration; it argues that the HRIS behavioral findings are consistent with, and partially explained by, the geometric and mechanical processes the other research programs have independently documented.