t0_to_classical_logic_and_unique_minimizer_bridge_holds
plain-language theorem explainer
Given that logic is forced at the cost floor (T0), the classical-logic and unique-minimizer bridge holds: no configuration satisfies P ↔ ¬P, stabilization is decidable, and the unique RS-existent is unity. Anyone assembling the complete forcing chain or the extended inevitability surface cites this packing step. The proof is a pure structure assembly that wires existing BiconditionalSelfNegation and OntologyPredicates lemmas into the bridge fields.
Claim. If T0 holds (logic forced by recognition-work cost: consistent Boolean floor states cost zero, inconsistent ones cost positive), then the classical-logic and unique-minimizer bridge holds: there is no self-negating configuration with $(\mathrm{defect}=0)\leftrightarrow\neg(\mathrm{defect}=0)$, no general predicate-level biconditional self-negation, every real configuration has definite stabilization status, there is a unique RS-existent and it equals $1$, and the bundled classical-logic-plus-closure theorem holds.
background
The Unified Forcing Chain module shows that T0–T8 are forced from the Recognition Composition Law plus normalization and calibration. T0 is the claim that logic itself is not pre-given: at the pre-analytic floor, consistent configurations have zero recognition-work cost and inconsistent ones have positive cost.
The bridge structure packages classical-logic facts with a substantive uniqueness fact. Despite an older name that spoke of “Gödel dissolution,” the content is only that $P\leftrightarrow\neg P$ has no inhabitant (in two formulations), that the stabilization predicate is decidable, and that the unique RS-existent is $x=1$ (the T5 unique-minimizer fact).
Upstream, no_self_negating_config is the two-line classical fact that no real configuration satisfies $(\mathrm{defect},c=0)\leftrightarrow\neg(\mathrm{defect},c=0)$; the general-predicate form is the same contradiction at the predicate level. The complete classical-logic-and-closure bundle conjoins those impossibilities with unique existence of the RS-existent at unity.
proof idea
Term-mode structure construction under the T0 hypothesis. Each bridge field is filled by a named upstream lemma:
no_self_negating_configandno_general_self_negating_predicatefrom BiconditionalSelfNegation (classical $P\leftrightarrow\neg P$ impossibility).definite_stab_statusfromstab_decidable(excluded middle on stabilization).rs_closure_unique_existentandrs_existent_iff_onefrom OntologyPredicates (unique RS-existent is $1$).classical_logic_theorem_holdsandcomplete_classical_logic_bundlefrom the corresponding BiconditionalSelfNegation theorems that already package those facts.
No new arithmetic or case analysis occurs here; the T0 hypothesis is carried only as the bridge parameter.
why it matters
This is the T0-side packing step in the complete inevitability chain. Downstream, complete_forcing_chain threads T−1 through T8 by calling the successive bridges; this theorem supplies the classical-logic and unique-minimizer bundle once T0 is in hand. It also feeds spine_to_extras_bridge_holds (extras drawn from spine nodes), the deprecated Gödel-named aliases, and ultimate_inevitability_extended, whose surface explicitly includes the no-self-negation conjuncts.
In framework terms it sits at T0 (logic forced by cost) and imports the T5 unique-minimizer fact ($x=1$) into the same bundle, so later steps that need both classical consistency and the unique cost minimum can cite one object. The doc-comment and deprecation notes deliberately correct the historical “Gödel dissolution” framing: the bundle does not refute Gödel’s first incompleteness theorem; it only records classical biconditional impossibility plus unique minimization.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.