The Coefficient

Equation (4.2) has the form ∇²Φ = Aρ.

The constant A must be identified.

Through The Lock:

G = 2κ / m_e² (5.1)

Therefore:

A = 4πG = 8πκ / m_e² (5.2)

and the identity reads:

∇²Φ = (8πκ / m_e²) · ρ (5.3)

The coefficient is the ratio of the fabric’s holding limit to the square of the electron mass.

The entire gravitational sector is determined by two quantities.

How much the fabric could hold (κ).

How much had to leave (m_e).

You are looking at gravity expressed as a ratio of what stayed to what escaped.

5.1 — The circularity and why it is structural

Honest disclosure.

κ is defined as Gm_e²/2.

Therefore writing G = 2κ/m_e² is, at the level of numerical computation, a tautology: G = 2(Gm_e²/2)/m_e² = G.

The coefficient has been relabelled, not independently derived.

Anyone who reads section 5 and concludes that G has been computed from first principles without empirical input is mistaken.

What HAS been done.

The form ∇²Φ = Aρ is derived from the axioms.

The five symmetry constraints in section 4 force the Laplacian, force linearity, and leave exactly one free constant A.

The form is genuinely new.

The constant A is then identified — not derived — as 4πG, or equivalently 8πκ/m_e².

5.2 — Why κ cannot be independently measured

κ is the holding limit of the pre-state — the maximum coherence the system could sustain before the break became necessary.

Measurement itself is a product of the break that κ describes.

Before the break (Axiom B), there are no records (Axiom R has nothing to order), no observers, no instruments, and no manifold (EH has nothing to embed).

The only access to κ is through its consequences — G and m_e — which are the residuals of the break.

κ is a real structural quantity with well-defined dimensions and physical meaning, but it is accessible only through its products.

Kill switch KS-I.4. If an observable is found that constrains κ without going through G, the structural inaccessibility claim is falsified and κ becomes independently testable.

You cannot measure what existed before measurement existed.

κ is the capacity of the pre-state — and the pre-state is, by definition, the state before records.

The circularity is not a bug.

It is the structure telling you what it can and cannot show you.

You are inside the break. You cannot look behind it.