Gravity-Candidate Source Classification Theorem

TA42 is a classification theorem establishing the epistemic status of the residual-gradient architecture developed in TA36-TA41. The theorem separates mathematically derived operator structure from conditional propagation assumptions and speculative physical interpretation. The solid structural results established by the transport architecture are: forced residual extraction through \(DB\), mediated residual circulation through\[EB(λ)=1/80λ(σ_y-I),\]admissible reinjection through\[CB=Π_Y\, Uᵣₑₜᵤᵣₙ|H_R,\]and the dynamically active unreinjected residual source term\[ Gᵣₑₛ(t)=\|QB\,e^{tEB}\,DB\,ψ_M\|^2.\]The theorem then classifies the conditional propagation results introduced in TA40 and TA41: boundary-surface propagation through the operator\[ P∂(τ): H_R→ L^2(∂ B),\]and inverse-square weak-field scaling under the assumptions of linear propagation, localized source structure, and radial symmetry,\[|∇Φᵣₑₛ(r)|={α Mᵣₑₛ}{4π r^2}.\]TA42 explicitly states that no theorem in the TA36-TA41 arc establishes the identification\[Φᵣₑₛ gravity.\]Instead, the theorem proves only that the residual-scattering architecture generates a mathematically defined gravity-candidate source term exhibiting inverse-square weak-field behaviour under conditional propagation assumptions. Whether this object corresponds to gravity, part of gravity, an effective correction, or a distinct residual interaction remains unresolved pending dimensional calibration, propagation-geometry derivation, coupling normalization, and observational correspondence. Status: solid for the operator-level residual ecology and source-term structure; conditional for boundary propagation and inverse-square weak-field behaviour under explicit assumptions; speculative for any physical identification with gravity or established gravitational theory.