Harmonic Gravitation: Finite-Vantage Einstein Dynamics in Pufferfish Theory

The world is not first a box with things in it. It is what a finite world can keep of a deeper coherence object.

Harmonic Gravitation is the gravity lane of Pufferfish Theory. It enforces a strict contract: upstream, spacetime follows the ordinary Einstein run; downstream, a finite lens depth σ renders what can be stably held on spacelike slices. The lens is not a field, introduces no new degrees of freedom, and never feeds back into the run.

The paper shows why the upstream run closes where it does. Under the run-level commitments of representation independence, metric-only gravity, second-order locality, and universal coupling to a conserved stress tensor, the gravitational dynamics are fixed in four dimensions by the Einstein–Hilbert form. Matter is treated fields-first, with a default Einstein–scalar module that makes Bianchi compatibility automatic on shell.

Finite-depth visibility is then built downstream by slice holding. On each slice, the square-root Laplace generator supports Poisson holding, exact phase flow, and rebuild. The canonical gravity Cloud is the slice energy density Tμνnμnν, and its held Sea is the first coherent gravity field a finite depth can actually keep. Readout remains downstream: local posterior, expectation, baseline, one-pass anchoring, and contrast are all computed from the held field, never inserted back into Einstein’s equations.

In the Newton reporting lane, support is sourced by what the world holds, not only by what it shows. Lift-before-look yields the canonical soft-core law with an unmodified 1/r tail: singular punctures belong only to the zero-depth idealization, not to finite-depth report. In this sense, Harmonic Gravitation does not replace General Relativity with a softened cousin. It keeps the Einstein run clean and places finite-depth effects where they belong: in holding, readout, and report.

The result is not a new gravitational law, but a disciplined separation of dynamics, visibility, and reporting. Harmonic Gravitation says: run Einstein cleanly, hold on slices, read out downstream, and lift only what finite depth can honestly keep.