T0_Logic_Forced

The module publishes the theory-only T-1 through T8 forcing spine and stops before private operator or measurement layers. In that spine, T-1 is the absolute distinguishability floor; T0 is the Boolean recognition-work split; T1 is the cost-form Meta-Principle; later steps force discreteness, ledger bookkeeping, the reciprocal cost $J$, $\phi$, the eight-tick cadence, and $D=3$.

Upstream, the bridge structure packages four facts on the Boolean floor: a nonempty recognition-work constraint certificate, cost of the consistent state equal to zero, strictly positive cost on every inconsistent Boolean configuration, and the converse that zero cost implies consistency. The unified chain states the same idea as: logic is not pre-given; at the pre-analytic floor it is exactly that zero/positive split of recognition work, the foundation beneath the Meta-Principle.

One-line abbreviation. The public name is definitionally equal to the bridge-module structure TMinus1ToT1Bridge.T0_Logic_Forced (itself aligned with the unified-chain T0 structure). No tactics, no lemmas, no new fields.

This alias is the public handle for T0 inside the complete T-1–T8 spine. Downstream it is the hypothesis type for the T0-holds witness, the T-1-to-T0 bridge, the T0-to-T1 bridge, the corollary that T1 follows from T0, the TMinus1-to-T1 certificate, and the complete forcing chain through T8. In the Recognition landmarks it is the T0 step of the forcing chain: logic as the zero/positive recognition-work split that sits under the Meta-Principle and the later uniqueness of $J$, the forcing of $\phi$, the eight-tick octave, and $D=3$. Without a stable public T0 name the spine cannot thread T-1 into T1 and beyond.