La Profilée - The Quantum Mechanics / General Relativity Boundary: A Structural Diagnosis of the Deepest Incompatibility in Theoretical Physics

The incompatibility between quantum mechanics (QM) and general relativity (GR) is the deepest unresolved problem in theoretical physics. Decades of attempts to unify the two theories have produced no experimentally confirmed quantum theory of gravity. This paper argues that the reason is structural: the incompatibility is not primarily a mathematical problem awaiting a more powerful formalism. It is a Frame-level conflict in the structural sense established by La Profilée — and one that arises from a shared incompleteness in both theories. Standard formulations of QM presuppose a fixed admissibility structure that defines the transformation space of quantum states — spacetime occupies the Frame role. In the LP reading of GR, the metric tensor is the primary carrier of transformability and therefore occupies the Module role. Frame and Module are mutually exclusive structural roles: this mutual exclusion is not asserted but derived from the structural requirement that a stable identity relation across transformations requires an invariant admissibility condition. When admissibility conditions are themselves transformation-dependent, the distinction between identity-preserving and identity-destroying transformations becomes undefined. This is formalised in Section 3 and demonstrated structurally in Appendices A and B. The deeper LP reading goes one level further: the Frame-level conflict between QM and GR arises because both theories treat spacetime — an emergent structural layer — as fundamental. QM correctly identifies it as a stable Frame at its level of description. GR correctly identifies its dynamics at the emergent level. The conflict is a level-mismatch, not a fundamental contradiction. Its resolution requires characterising F₀ — the pre-geometric structural invariant from which spacetime emerges — and showing how both QM's fixed background and GR's dynamical metric arise as structural reductions of F₀ in appropriate limits. At the Planck scale, the emergent spacetime Frame loses structural stability: the conditions under which effective distance, duration, and causal ordering constitute a stable structural layer are no longer satisfied. The breakdown is not a failure of description applied to a fixed object, but the loss of stability of the object itself — spacetime as an emergent structural layer. What remains is F₀, operating in a regime where spacetime cannot stably constitute. The paper's contribution is diagnostic and structural. It does not propose a theory of quantum gravity. It derives the structural conditions that any such theory must satisfy, explains why the major existing approaches encounter the specific difficulties they do, and identifies spacetime emergence as the structural level at which the resolution must be sought.