recognition_from_balanced_floor_ledger

In the Unified Forcing Chain, T-1 through T8 are forced from the Recognition Composition Law plus normalization and calibration. T4 (Recognition) is the step that turns a discrete ledger into an actual recognizer: something that can pair states as observed-versus-observer.

The Boolean floor is the minimal configuration space. Its recognition-work cost is the two-valued function $C(\mathsf{false})=0$, $C(\mathsf{true})=1$. Balance of the empty ledger is exactly $C(\mathsf{false})=0$. Upstream, balanced_floor_recognition packages that hypothesis into a record whose recognition field is the pair $\langle\mathsf{false},\mathsf{false}\rangle$: the empty consistent state recognizing itself.

Recognize Bool Bool is the Recognition Science type of a recognizer on that floor. Nonemptiness of that type is the existence claim T4 needs at the Boolean level before the chain lifts further.

One-line term proof. Apply the upstream package balanced_floor_recognition to the balance hypothesis $C(\mathsf{false})=0$, then project the .recognition field. That field is already a proof of Nonempty (Recognize Bool Bool), built as $\langle\langle\mathsf{false},\mathsf{false}\rangle\rangle$. No further algebra or case analysis.

This is the T4 existence arrow at the Boolean floor: balanced empty ledger implies a recognition witness. Downstream, t4_corollary_of_t2_t3 feeds it the T3 empty-balance fact and obtains T4_Recognition_Forced. The same extraction appears in the T2/T3→T4 bridge certificate, which ties the witness to the ledger rather than inserting recognition as a free sibling.

In the forcing chain this closes the T3→T4 link (Ledger + observables → Recognition). T2 supplies the two-point distinction; T3 supplies empty balance; this lemma turns that balance into the inhabited recognizer type. Later steps (unique $J$, $\varphi$, eight-tick, $D=3$) sit above T4 and inherit that the floor is already recognizing.