From Documentary Audit to New Construction: Axiomatic Foundations for a History-Dependent Gravity Master Functional (Paper LXXX)

Following the frozen outcome of the LXXIX documentary genealogy audit of the History-Dependent Gravity (HDG) series, we initiate a separate new-construction program for a candidate master functional. The audit found no constructive common master realization among the documented truncations at the current evidence level, while establishing neither incompatibility nor the non-existence of a common underlying functional. The present work therefore does not attempt to reconstruct previous models via reverse engineering. Instead, it defines a top-down construction architecture in which the memory sector, its interaction operators, and the candidate master functional are specified independently, before Hessians, vertices, symmetry identities, and renormalization-group flows are derived. As a first construction choice, a spectral representation of a scalar Euclidean memory kernel is considered, with its status as an explicit new assumption clearly distinguished from the documentary evidence of earlier works. Subsequent stages are designed to test the resulting Hessian and vertex genealogy, BRST/Slavnov--Taylor consistency, modified Slavnov--Taylor identities in the presence of an FRG regulator, and controlled truncation maps to previously documented HDG structures. Recovery of legacy phenomenology is treated as a validation problem rather than an input condition. The resulting program is a constructive test of whether a consistent common master realization can be obtained, rather than a claim that such a realization has already been established.