variational_to_measurement_bridge_holds

The module UnifiedForcingChain proves that T-1 through T8 are forced from the Recognition Composition Law plus normalization and calibration. Measurement sits after the variational ledger dynamics: once configurations evolve by defect-nonincreasing successors, one must recover the standard measurement package (deterministic outcomes, permanent correlations, Born weights).

VariationalLayer_Forced packages that dynamics without extra axioms: for every positive $N$ and configuration $c$, a variational successor exists, every such successor weakly decreases total defect, and the unity configuration is an equilibrium. Variational_To_Measurement_Bridge is the Prop-structure that turns those facts, together with subsystem/observer projections, into measurement dynamics.

Upstream, MeasurementMechanism already proves the concrete projection lemmas (unique outcome, same-state same-outcome, subsystem underdetermination, correlation creation and permanence, positivity and Born structure of the J-cost weight). The bridge does not re-derive them; it certifies that the variational layer is enough to unlock that package inside the forcing chain.

Term-mode structure construction. Each field of Variational_To_Measurement_Bridge is filled by the matching lemma from MeasurementMechanism:

• outcome_is_determined, same_state_same_outcome, subsystem_cannot_know_whole are direct applications of the corresponding MeasurementMechanism theorems.
• measurement_creates_correlation and correlation_is_permanent pass through the variational-step and trajectory hypotheses unchanged.
• jcost_weight_pos and jcost_born_structure cite the J-cost weight lemmas (positivity of $\exp(-\mathrm{total_defect})$ and its maximality on variational successors).
• The final measurement field is the already-proved measurement_layer_holds certificate.

The hypothesis _hvar : VariationalLayer_Forced is unused in the term (underscore); the bridge is available once that layer is in scope, and the real work lives in MeasurementMechanism.

This bridge is one link in the complete inevitability chain. Downstream, complete_forcing_chain assembles T-1 through T8 by threading successive bridges; this declaration supplies the variational-to-measurement step so the chain can treat measurement as forced rather than postulated.

In the framework map it sits after T3/T4-style ledger and recognition structure and before the unique-J / $\phi$ / eight-tick / $D=3$ stretch (T5-T8). The Born-structure fields connect the J-cost $J(x)=(x+x^{-1})/2-1$ to measurement weights, so the same cost that forces the ledger also forces the probabilistic readout. No open scaffold remains here: claim status is proved, and the parent chain consumes it unconditionally once the variational layer holds.