What Is AP08’s, and What Remains

The fourth sentence is carried as an upstream claim. The dual is owed.

The picture gives three of general relativity’s four sentences, at the register §§2– 4 state. The equivalence (§2). The landscape setting the crossing (§3). The source (§4). The fourth is how much the landscape bends per what has landed. That is AP08’s, and it has been read. AP08 derives the form of Einstein’s field equations with cosmological constant from the four axioms: the weak-field limit from four axiom-derived constraints, the tensor form from five covariant constraints and Lovelock’s theorem, with N = 3 from AP10. The coefficient is identified, not derived, through the Lock, and AP08 discloses the circularity (KS-I.3, KS-I.4). The source is record density, identified as matter density conditional on the Lock (AP08 §3.2; KS-I.5). The manifold is accumulated record structure, not a pre-existing container (AP08 §2). That last sentence is the connection this paper needs, and AP08 already made it: AP08’s manifold is this paper’s landscape; its record density is what has landed (§4); its curvature is the change of slope (§3); and the metric it inherits is AP10’s Lorentzian signature, fenced there at KS-D.4, which AP52 pays at the structural register. So the fourth sentence is not owed. It is AP08’s, with AP08’s own open items: the coefficient’s circularity (KS-I.3, KS-I.4), the source identification (KS-I.5), Λ’s value (KS-I.7), and the bridge from record monotonicity to covariant conservation, which AP08 §8.1 names as a bridge step and not a completed derivation (KS-I.8). If that bridge fails, AP08’s tensor form fails at its third constraint, and the fourth sentence is owed again. This paper adds no equation to it.

What the corpus owes in either case is the dual. AP43 names two pulls on the now. One from what has been written. One from what could be written: the gravity of possibilities, the pull toward the high-amplitude branch before actualisation. AP43 §7 closes its Newtonian limit: a Poisson equation on configuration space, the Born weight as source, α as the coupling. Its relativistic form is AP43-D1. Owed. This paper does not pay it. It says where it sits in the picture: the potential side pressing on the neck (§5). If the picture can give D1, it will give it there: as the rate at which the potential side’s press sets what lands next, compounded over the gates. That derivation is not attempted here. The relation between the two pulls — whether AP08’s curvature moves the press, and the press moves where grains land — is not specified here. It waits on D1.

Grade. AP08: verified; the form derived there, the coefficient and the source identified there; read here as the landscape and the change of slope. AP43-D1: owed, unchanged; its place in the picture named.

The landed side has its equation. The potential side does not yet. The picture says where to look.