E-LOGOS S52_Scale-Rank and Generator-Type Obstructions in a Relational-Mass Field Architecture

This preprint develops an exact structural-identifiability audit for dimensional restoration and relational-mass architectures and applies it to the frozen E-LOGOS NP0 research corpus. The analysis separates two logically independent questions. The first is whether unresolved dimensional restoration scales can be determined well enough to recover an absolute mass. The second is whether, even after those scales cancel from a same-parent mass ratio, the internal state coordinate used by the model has been physically identified with a measurable Noether generator. For an exact log-affine restoration family, y = Aθ + b, with scalar target m = t · θ + b_m, the paper proves a necessary-and-sufficient row-space criterion: the target is restoration-scale identifiable if and only if t belongs to Row(A). Whenever this condition fails, an exact null-space witness n exists such that A n = 0 while t · n ≠ 0. The witness therefore gives an explicit normalization transformation that leaves every declared readout unchanged while changing the target. This distinguishes structural non-identifiability from finite numerical precision or insufficient experimental accuracy. The theorem is applied to sixteen frozen restoration architectures in the NP0 corpus. In the base restoration chart θ = (ln L, ln Z), the ordinary-mass target has exponent t_M = (−1, 1), whereas the restored clock, radius, internal action, and Einstein-coupling rows are respectively (−1,0), (1,0), (0,1), and (−2,1). A clock and radius together determine only the common length normalization L and leave Z invisible. Although combinations involving the internal action can be algebraically full rank, the required physical current and state-map readouts are not present in the audited corpus. The same structural problem persists in several proposed extensions. An external current probe measures the product g_p Z and leaves the exact witness (0,1,−1). Minimal gauging introduces the combination η = Z g² and leaves the witness (0,−2,1). A fixed gravitational parameter α_G = Z(l_P/L)² retains the restoration homology L → aL, Z → a²Z, which changes the mass while preserving the declared gravitational combination. Algebraically sufficient augmented architectures are identified, but their independently calibrated couplings, physical readouts, or solved backreacted parent systems are absent from the present corpus. The same-parent relational-mass problem behaves differently. For two states of one frozen parent action, M_i / M_j = Ē(J_i) / Ē(J_j), and the restoration exponent of the ratio is exactly zero. The unknown L and Z therefore cancel identically. Along a differentiable fixed-coupling branch, dĒ / dJ = ω, so the relational curve remains a genuine scale-free prediction of the frozen parent model. However, scale cancellation does not establish physical generator identity. The current corpus contains no action-level, generator-preserving intertwiner between a measured physical Noether charge and the NP0 internal SO(2) action variable. Shared notation such as U(1), Q, J, or ω is not sufficient to establish equality of field content, symplectic structure, normalization, energy convention, or observable type. One direct molecular vibrational-action realization was independently screened and rejected without using observed mass data. The audit therefore closes into two independent obstruction classes: Absolute-mass obstruction — the currently admitted physical readouts leave a restoration-scale direction that changes the absolute-mass target, or else require calibrations and parent calculations not present in the frozen corpus. Relational-mass obstruction — the same-parent mass ratio is restoration-scale invariant, but the physical Noether generator and state map required to expose the theoretical relational curve to experiment remain unidentified. The negative result is intentionally bounded rather than universal. Four explicit restart certificates define the evidence required to reopen the problem: REL-Q — a physical relational-charge and generator-intertwiner certificate; Q1 — a same-parent quantum-normalization certificate; GA1 — a calibrated and fully recomputed gauged-parent certificate; GR1-A — a backreacted Einstein-anchor certificate. For every route, the required order is frozen as parent and observables → bridge and calibration → preregistered prediction → observed mass data. Observed masses may not be used to choose restoration scales, state labels, couplings, bridge functions, detector inversions, or mass types before preregistration. All sixteen architecture ranks and all declared null-space witnesses were independently reproduced with exact rational arithmetic. The audit reports 16/16 exact case-rank checks, 9/9 exact null-witness checks, and 42/42 upstream exact-rank checks. No observed particle, nuclear, molecular, or state-resolved mass enters the calculations or decisions. The result is therefore an exact current-corpus identifiability boundary and restart protocol, not an absolute-mass prediction and not a universal impossibility theorem. Its main contribution is to distinguish scale invariance, restoration-scale identifiability, and physical identification, and to specify precisely what new evidence would be required to move beyond each remaining boundary.