The Quantum Fisher Coupling in Reconstructive Dynamics

This paper clarifies the role of the quantum Fisher coupling in reconstructive dynamics. Article 5 showed that the reconstructive action reproduces the Madelung equations, and hence the Schrödinger equation, when the Fisher term carries the coupling λ = ℏ²/8m. The present article argues that the fundamental object to be analysed is not ℏ or m separately, but their natural combination:

κ = ℏ²/m.

Three results are established. First, κ is the unique coupling of dimension energy times length squared compatible with the Fisher information term in the Madelung Hamiltonian. Second, κ/2 appears as the scale of the biharmonic flow obtained by linearising the Fisher gradient flow around a flat reference state. Third, the decomposition κ = ℏ²/m requires additional geometric input: m as the inertial coefficient of Wasserstein transport, and ℏ as the prequantisation constant associated with a non-trivial symplectic loop.

In the revised architecture of the programme, this article should be read as an intermediate structural clarification. Later articles refine the status of ℏ: Article 12 identifies the action scale as forced by the Legendre–Kähler completion, Articles 15–16 relate its numerical value to the cosmological closure constant, and Articles 17–18 reinterpret it as the action quantum a₀ carried by one elementary causal succession.

The paper does not derive κ from hypotheses H1–H5. Rather, it establishes that κ is the natural single object to be derived and identifies the geometric conditions under which its decomposition into ℏ and m may become accessible.