The Full Nonlinear Structure

The Poisson equation (section 4) is a linearisation.

It describes the weak-field regime where the relationship between curvature and record density is approximately linear.

The full relationship is nonlinear.

The curvature depends on the density, and the density depends on the curvature.

7.1 — The topology

The eye topology describes the full nonlinear curve.

Two curves (the two sectors ℒ and 𝓟 from Axiom S, related by the involution σ) meet at a common point.

The point is 0 — the 1:1, the pre-state of perfect symmetry before the break.

The topology is closed. When folded onto a sphere, the two apparent endpoints are the same point.

7.2 — Reading the structure

At the common point (0). The two sectors meet. No separation, no break, no curvature, no records. The Poisson equation is the linearisation of the full curve near this point.

Moving outward. The break occurs. ε appears. Records accumulate. The curves separate. Curvature increases.

At maximum separation. Maximum curvature. Maximum record density. The event horizon. The extremal point relative to which the full structure is measured — relativistic in the original sense (relative to its own extremal point, not to a fixed background).

The closed topology. The quantum scale (near the common point, where ε is the break) and the cosmological scale (the full extent of the curve) are connected in the topology. The Lock’s identification of ε with the electron carries through the closure: the same electron mass that defines the gravitational coupling (G = 2κ/m_e², section 5) appears in the horizon expression at section 6.3 — because the same identification entered both. The electron is at both ends of the gravitational identity as a structural consequence of The Lock, not as an independent finding at the horizon.

7.3 — Newton vs Einstein

Newton’s gravity is the linearisation near the common point.

Curvature proportional to density, constant coefficient, valid where the fold is gentle.

Einstein’s gravity is the full curve.

The geometry and the distribution of energy-momentum locked together by a nonlinear identity.

The architecture derives both.

The linearisation is forced by symmetry constraints (section 4). The full tensor form is forced by Lovelock’s theorem (section 8).

You have now seen the full shape.

Newton saw the straight line near the origin.

Einstein saw the curve.

They are the same structure read at different distances from the common point.

The mathematics did not choose between them. It produced both.

You do not choose either. You inherit both.