IFO Gravity: A Conditional Weak-Field Reconstruction from Causal-Knot Variables

## Abstract The Informational-Foundational Ontology (IFO) models physical reality strictly from directed causal relations, treating continuous spacetime as an emergent macroscopic construct. Within an emergent 3+1-dimensional Lorentzian narrow-sense layer, this paper presents a conditional reconstruction of weak-field gravitation. Localized matter is parametrized by its invariant causal phase rewrite rate $\Omega_M \equiv Mc^2/\hbar$ and rate density $q_M \equiv \rho c^2/\hbar$. Adopting a minimal isotropic Poisson bridging ansatz and conditioning the infrared sector on the Infrared Tensor-Spectrum Hypothesis (`H-S2`)—where the dominant unsuppressed, gapless long-wavelength response coupled to matter is a massless helicity-$\pm 2$ mode—the coupling between the causal rewrite rate and the dimensionless stitching potential $\psi = \Phi/c^2$ is mediated by the causal-geometric area scale $\ell_P^2/c = G\hbar/c^4$. Under these explicit assumptions, the standard isotropic weak-field metric of General Relativity with post-Newtonian parameter $\gamma = 1$ is recovered from the Fierz–Pauli action normalized to the Newtonian limit. While $\hbar$ cancels algebraically in classical macroscopic observables, it maintains a microscopic Compton–Schwarzschild reciprocal identity $r_s \bar{\lambda}_C = 2\ell_P^2$. We examine four weak-field consistency sectors: gravitational redshift, light deflection and Shapiro time delay, bound-system mass defect, and the translational gravitomagnetic component $h_{0i}$ with the characteristic spin-2 prefactor of 4. We emphasize that this paper establishes a parametric correspondence and consistency bridge rather than an unconstrained first-principles derivation. The dynamical origin of the attractive Poisson kernel, the spectral suppression of scalar modes, and the microscopic calculation of Newton's constant $G$ remain open foundational debts. ## Remarks on series status This paper can be read alone as a conditional weak-field result. It assumes the effective 3+1 Lorentzian background of IFO-Spacetime and the operationalenergy / actualization language of IFO-Energy. It does not re-derive those contracts. - IFO-Energy: [DOI:10.5281/zenodo.22010214](https://zenodo.org/records/22010214)- IFO-Spacetime: [DOI:10.5281/zenodo.22095559](https://zenodo.org/records/22095559)- IFO-Entry (optional, pedagogical only): [DOI:10.5281/zenodo.21203277](https://zenodo.org/records/21203277) Claim of this paper: under the unique healthy massless spin-2 infrared hypothesis (A-S2*), the static weak-field metric has γ = 1. Deriving A-S2* and Newton’s constant G from retargeting remains open.