Finite Readout, Cross Gradients, and the Newton-Core Directional Carrier: The Role of an A5 Seed

Finite Readout, Cross Gradients, and the Newton-Core Directional Carrier: The Role of an A5 Seed The paper develops a finite-readout reconstruction of the directional carrier underlying a Newton-core two-body attraction regime. The main claim is not a derivation of Newtonian gravity, but a layer-separated localization result: after one-source self-direction is excluded by witness admissibility, two-source dependence is carried by a finite quadratic Green cross-distance kernel. The cross term is not identified with force. Instead, its finite edge variation supplies a local variational edge input, while the admission of that input into an effective update channel remains an explicitly named bridge. The reconstruction separates three Newton-core axes: attractive sign, area-dominant inverse-square readout, and second-order update response. These are treated as independently auditable bridge components rather than as a single primitive force law. Source calibration, Newton’s constant, the equivalence principle, relativistic completion, and continuum/GR limits remain open bridges. The finite A5 seed is used as a closed symmetry carrier, icosahedral Green-kernel prototype, and no-bias compatibility anchor. It is not claimed to derive Newtonian gravity, general relativity, or quantum gravity by itself. The accompanying Lean 4 archive provides a machine-checkable claim-dependency audit of the mathematical and bridge-layer structure. The supplementary document describes the scope of the Lean audit, including witness admissibility, finite edge variation, scalar channel admission, open bridge \ (G ₀₃₌\), failure mode \ (F₁₀\), and the coefficient locus \ (A=AAqA\) for equivalence-principle and Newton-coupling calibration.