This manuscript formulates an Einstein–Rosen bridge branch within the L(6+7) unified variational framework. The claim boundary is deliberately strict: the classical Schwarzschild/Kruskal Einstein–Rosen bridge is preserved as a non-traversable control geometry; the work does not claim a completed physical matter-traversable wormhole, a usable portal, or controllable superluminal signaling. The paper develops a source-accounting and entropy-time classification framework in which the Einstein–Rosen object becomes a non-transport entropy-time node: a saddle configuration where geometry, effective stress-energy, entropy-flow ordering, stable-history weights, and controlled quantum-historical projections meet. The manuscript separates classical non-traversability, effective stress-energy closure, NEC/ANEC/QNEC promotion gates, Bianchi consistency, stability/matching requirements, and no-signaling boundaries. The final strengthening distinguishes matter-traversability from restricted history-projection traversability. The bridge remains non-traversable as a four-dimensional matter tunnel, but becomes passable for admissible histories, internal states, and controlled projections in the L(6+7) history-response space. A real FLAMINGO hydro/DMO response gate is added as an external data-facing constraint: three matched hydro/DMO simulation pairs support a nonzero, structured, non-factorizable response surface, with a combined coupled-response R² = 0.832 and a 41.9% improvement over an additive response model, while the matter-tunnel claim remains explicitly not tested and not claimed. The result is an exact-candidate, source-accounted, FLAMINGO-constrained Einstein–Rosen history-projection theorem paper, not a claim of a laboratory traversable wormhole.