What the reconstruction adds

The construction uses established coframe and connection mathematics. Its distinctive result is the integrated source–readout account of the historical chain, with explicit coverage, discarded information and boundary-sensitive contracts.

19. Relation to established formulations and contribution

The calibration $E$ is a coframe, its internal freedom is the Lorentz-frame freedom, and $\omega(E)$ is the usual torsion-free metric comparison in that coframe. These structures are standard, as are differential forms, the curvature product and the relation between metric and frame tensors. Reviews of gravitational actions already treat a wide family of equivalent formulations [9]. Studies of Einstein–Palatini equivalence address an independently varied connection and its additional projective structure [2]. Our dependent $\omega(E)$ construction is different in scope: it does not derive an independent connection’s stationarity or establish a new equivalence of those actions.

Boundary-sensitive work is particularly relevant. De Paoli and Speziale examine a gauge-invariant tetrad symplectic potential and its relation to metric expressions [3]. Oliveri and Speziale analyze boundary effects in tetrad variables and the resulting potential and charge distinctions [8]. Barbero G. and collaborators establish metric/tetrad covariant-phase-space relations under specified boundary formulations [1]. These results preclude interpreting a local coframe-to-metric map as an unprecedented general equivalence theorem. They also support the need to retain the variation and boundary contract rather than identify charge prescriptions solely because the bulk equations agree. We have not reconstructed their full symplectic or corner frameworks.

Similarly, covariant Noether-charge analysis has a developed treatment of Lagrangian and potential ambiguities [6]. Einstein’s chart-tagged $t$ in this paper is the specific current recovered from his first-derivative function, not a new covariant gravitational energy tensor. The contrast in (8.8) and the boundary response in (7.19) make this limitation operational.

Relative to that literature, the present contribution is an integrated conditional reconstruction of Einstein’s entire 1916 chain within a specified source–readout architecture. Its mathematical content lies in the explicit local sections and joint primitive coverage; complete residual identities before restriction; variation coverage and the distinction between gauge selection and lost trace directions; the same-realization treatment of stress, current, material fields and observations; and a correspondence register linking the historical equations to these operations. The finite-endpoint optical comparison, controlled regularized integrals, and negative witnesses make information loss and approximation scope inspectable. These calculations are proved here, but no claim is made that each individual identity or counterexample is historically unprecedented.

The source architecture contributes a discipline of joint realization and licensed projection. It does not add a new propagating field or observational prediction to the selected classical theory. If the native support were suppressed after the realization has been supplied, the coframe calculations would still recover the same classical results. Accordingly, the support is an architectural antecedent and provenance object, not an independently demonstrated microscopic explanation of gravity. This limitation is part of the theorem, not an unaddressed inference hidden by terminology. The related source–readout gravity work [11] concerns a different reconstruction route and is cited for programme context, not substituted for the proofs in this article.