T1_MetaPrinciple_Forced
plain-language theorem explainer
T1 packages the cost-form Meta-Principle on the Boolean recognition floor: inconsistent configurations carry strictly positive recognition-work cost, zero cost forces consistency, and the marked inconsistent bit is positive. Foundation authors cite it when closing the T-1→T1 bridge and when exporting the Meta-Principle into the T-1→T8 spine. As a Prop structure it is the interface discharged by the T0 corollary, not a free-standing proof.
Claim. The Meta-Principle T1 on the Boolean configuration space with recognition cost $C$ asserts: (i) if $a$ is inconsistent then $C(a)>0$; (ii) if $C(a)=0$ then $a$ is consistent; (iii) the marked inconsistent configuration satisfies $C(\mathsf{true})>0$.
background
This module isolates the first three levels of the forcing chain without importing the analytic $J$-cost surface. T-1 is the absolute floor of distinguishability; T0 is the minimal recognition-work cost interface; T1 is the cost-form Meta-Principle that inconsistent floor states cannot be selected at zero cost.
A configuration space supplies an empty configuration, a binary join, a consistency predicate, and an independence relation. On the Boolean floor the concrete recognition-work cost is $C(\mathsf{false})=0$ and $C(\mathsf{true})=1$, so consistency marks the zero-cost bit as the only consistent state.
The Boolean cost is defined in this bridge and re-exported for the public T-1 through T8 spine. The structure packages the three inequalities that turn T0's logic-forced cost interface into the Meta-Principle statement used downstream.
proof idea
This declaration is a Prop structure, not a proved theorem. It names three fields any witness of T1 must supply: positivity on inconsistent configurations, consistency of zero-cost configurations, and positivity of the marked inconsistent Boolean. Discharge is deferred to the T0 corollary, which copies the matching fields from a T0 hypothesis and specializes the inconsistency-positive clause at true.
why it matters
T1 is the first contentful Meta-Principle step after the absolute floor and the logic-forced cost interface. Downstream, the T0-to-T1 bridge records that T0 supplies T1; t1_holds asserts T1 once T0 holds; and the compact certificate bundles T-1 through T1 for the first forcing bridge. The longer T-1→T8 spine re-exports the same Prop as its T1 alias.
In the Recognition Science forcing chain this is the pre-analytic seed of later uniqueness results (T5 $J$-uniqueness, T6 $\varphi$, T7 eight-tick octave, T8 $D=3$). The module deliberately stops short of the analytic $J$-cost; the bridge only forces that inconsistent recognition-work cannot be free.
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