From Curvature–Commutator Law to Logic of Existence: A Meta-Hamiltonian Extension of Geometric Unification

This paper, “From Curvature–Commutator Law to Logic of Existence”, reinterprets Chavis Srichan’s 2025 proposal — a single commutator equation unifying Einstein’s and Dirac’s dynamics — through the broader meta-physical and mathematical lens of Logic of Existence (LoE).

Srichan’s original law

[D_\mu, D_\nu]\Psi =

\frac{i}{\hbar}\left(

\frac{8\pi G}{c^4}\langle T_{\mu\nu}\rangle

-\Lambda_q g_{\mu\nu}

+\lambda\nabla_\mu\nabla_\nu S

\right)\Psi

LoE takes this further.

It replaces the purely geometric commutator with a meta-Hamiltonian operator acting in the field of existence:

[\nabla_\mu, \nabla_\nu]\Phi =

\frac{i}{\hbar}\,

(\alpha\hat{\mathcal{C}}

- J_{\mu\nu}\hat{\mathcal{R}}^{\mu\nu}

+ \Lambda\hat{\mathcal{L}}

+ \beta\hat{\mathcal{S}})\Phi,

In this reinterpretation:

The Einstein tensor corresponds to the symmetric projection of the LoE Hamiltonian (order and structure).

The Dirac equation arises from the antisymmetric projection (process and flow).

The entropic term is identified with the LoE τ-field, which governs the rate of emergent time through information flow.

Thus, LoE transforms Srichan’s curvature–commutator into a higher-dimensional resonance law: geometry, quantum matter, entropy, and consciousness become harmonics of one relational field.

What was an algebraic unification of physics becomes, in LoE, a unification of existence itself —

where the fundamental commutator reads:

[\text{chaos}, \text{logos}] = i\,\text{existence}.