zero_defect_unique
plain-language theorem explainer
zero_defect_unique shows that any Q3State satisfying is_zero_defect must match the consciousness ground state at every vertex. Researchers deriving the Standard Model gauge content and fermion count from D=3 cite it to fix the ground state as the sole zero-cost fixed point. The proof is a one-line term that unfolds the definition of is_zero_defect.
Claim. Let $s$ be a recognition state on the $Q_3$ lattice (positive real ratios on the eight vertices). If every ratio equals 1, then $s$ coincides exactly with the constant-1 ground state on all vertices.
background
Q3State is the structure of positive real assignments to the eight vertices of the binary cube. Its predicate is_zero_defect holds exactly when every entry equals 1; consciousness_ground is the constant-1 assignment. The module derives SU(3)×SU(2)×U(1), three generations, and 48 chiral fermions from T8 (D=3) and |Aut(Q3)|=48, with the key identity |Aut(Q3)|=2^D×D! matching the Standard Model fermion count. Upstream cost definitions from MultiplicativeRecognizerL4 and ObserverForcing supply the J-cost on ratios; PrimitiveDistinction supplies the seven-axiom base.
proof idea
The proof is a one-line term-mode wrapper: fun _s h i => h i. It directly applies the hypothesis that is_zero_defect means the entries equal those of consciousness_ground, with no additional lemmas or tactics required.
why it matters
It supplies the uniqueness half of the zero-defect claim inside the master theorem spectral_emergence, which certifies the full emergence of Standard Model structure plus consciousness from D=3 with zero free parameters. The declaration closes the dimension-1 statement for the ground state in the Spectral Emergence module and aligns with the T8 forcing of D=3 and the Recognition Composition Law fixed point at unity.
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