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 \ (D ₁\), mediated residual circulation through ₁ () =180 (ᵧ-I), reinjection through ₁=Y\, Uₑ₄ₓₔₑ₍| ₇ₑ, the dynamically active unreinjected residual source term\ Gₑ₄ₒ (t) =\|Q ₁\, e^tE ₁\, D ₁\, M\|². theorem then classifies the conditional propagation results introduced in TA40 and TA41: boundary-surface propagation through the operator\ P_ (): HR L² (B), inverse-square weak-field scaling under the assumptions of linear propagation, localized source structure, and radial symmetry, \|ₑ₄ₒ (r) |= Mₑ₄ₒ4 r². 42 explicitly states that no theorem in the TA36-TA41 arc establishes the identification\ₑ₄ₒ gravity. , 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.
Craig Edwin Holdway (Sat,) studied this question.