The Formation of Gravity: From Ledger Record to Curvature

This work gathers, into a single chain, the formation mechanism of gravity within the framework of «Field Equations from a Common Foundation» (hereafter: the parent paper). The records of mass — charge, pattern and spin; mass itself the direction-reversal amplitude μ = m/m_P (T5) — write energy into the ledger; through the folding-consistency constraint (M4), the record writes angle deficits (δ_y) onto the d2 faces and builds a slope in the tick-rate field (Γ); bodies go straight along the bond chain (the geodesic) — what bends is the weave. The carrier of curvature is d2; d1 is traceless, it only sets the tempo. The direct proportionality of gravity to mass is the composite of three mechanisms: the unit record, linear accumulation, and non-cancellation. The address of the weakness is not the coupling — κ is fixed (8π = 4πχ [B]), the single-bond tension is the Planck force; what is small are the μ ratios [O]. Massless quanta both feel and generate gravity; a single quantum cannot build a static well; a bound record can. What bends light is not the density of matter along the route but the energy record written into the weave; three litmus tests — achromaticity, lensing in vacuum, and the gas–lens separation — rule out the medium-refraction reading. At the quantum level: quantum matter feels gravity [N✓ — COW, qBounce]; ordinary quantum field theory cannot build gravity UV-complete; the master amplitude equation (M3) contains gravity in the stationary-phase limit — its referee is BMV (T7). The Newton-limit chain is closed (§9): the lattice-Green solution of Z8 gives C = 1; the prefactor is 4π = κ/2. There is no fundamental carrier particle: the graviton is the collective mode of the weave — the quantum of the transverse deficit wave; its quantization is the open program of the M6 algebra [O]. Nor is there a graviton address in the discrete product catalogue (C(6,3) = 20; conditional on the identity-space decision). Distinctiveness statement: the work offers no distinctive new prediction; the contribution is the gathering of known results into a single ledger language and the addressing of the distinguishing channels. The text closes with pre-registered predictions and kill conditions.