Complexity of Quadratic Bosonic Hamiltonian Simulation: $\mathsf{BQP}$-Completeness and $\mathsf{PostBQP}$-Hardness

This project is a theoretical physics research paper rather than a software product. In the context of competitive intelligence, its value lies in providing the mathematical foundation for why certain quantum simulations are hard or easy, which directly informs the roadmap for photonic quantum computing companies (like Xanadu or PsiQuantum). The defensibility is low from a software perspective because it is a public theoretical framework, but it represents a high-novelty breakthrough in quantum complexity theory. Frontier labs (OpenAI, Anthropic) have zero interest in this niche theoretical physics domain, as it does not currently intersect with LLM scaling or general-purpose AI. The '3 forks' on a 19-day-old repo with 0 stars likely indicates academic interest or researchers mirroring the source for verification. The displacement risk is 'unlikely' because mathematical proofs of complexity classes are foundational and do not 'expire' like software, though they may be refined by future theoretical work.