t7_operator_core_route_equivalence

The module Unified Forcing Chain shows that T0–T8 are forced from the cost foundation (Recognition Composition Law, normalization, calibration), not merely compatible with it. In that ladder, T7 states that the minimal ledger-compatible cycle is $2^D$; with $D=3$ this is the eight-tick octave. T8 states that $D=3$ is the unique dimension satisfying nontrivial linking, eight-tick synchronization, and gap-45 sync.

The route-equivalence record packages two bridges under those hypotheses: a canonical recognition-carrier bridge sourced only from T7, and a T7/T8-to-operator-core bridge. It then demands that the two routes agree on complexification, quarter-turn core neutrality, and the eight-tick equation, so either path presents the same operator-core surface.

Upstream, the carrier bridge is already discharged by the theorem that T7 supplies the canonical recognition carrier (eight-tick equation, inhabited carrier, shift period 8). The operator bridge is discharged by the theorem that the forced dimension/eight-tick package supplies the analytic operator core (forced eight-tick, signal availability, complexification).

Term-mode construction of the route-equivalence structure. The carrier-route field is exactly the existing theorem that T7 yields the canonical recognition-carrier bridge. The operator-route field is exactly the existing theorem that T7 and T8 yield the operator-core bridge. The three agreement fields (complexification, quarter-core neutrality, eight-tick equation) are closed by reflexivity: both routes are definitionally built from the same T7 eight-tick equation and the same complex-structure forcing facts, so the corresponding projections are definitionally equal.

This lemma sits at the T7/T8 joint of the complete inevitability chain. Downstream it is consumed by complete_forcing_chain, the unconditional assembly of T−1 through T8. Without route equivalence, the chain would carry two potentially divergent presentations of the operator core: one via the canonical carrier and one via the direct T7/T8 bridge.

In framework terms it locks the eight-tick octave (T7) and $D=3$ (T8) into a single operator-core surface used by later ledger and dynamics layers. The doc-comment states the claim directly: the canonical-carrier route and the T7/T8→OperatorCore route are the same universal construction. It does not open a new forcing step; it certifies that the two already-proved bridges are interchangeable, which is what the top-level chain needs when it wires T7 and T8 into the analytic operator core.