Bare Tower Dimension Classification
Abstract
A bare orthogonal Hilbert tower is classified by the Hilbert dimensions of its initial block, every shell, and its terminal residual.
Theorem 1.1 (Block dimensions classify bare towers).
Proof. Machine-checked in Lean as D5/S3/Observer/Completion/BareTowerDimensionClassification.bare_tower_dimension_classification (✓ std3). ∎
Source. Repository-derived.
Commentary.
The block index has one initial coordinate, one coordinate for every natural-numbered shell, and one terminal residual coordinate. The ambient carrier is their canonical square-summable Hilbert sum.
Tower equivalence is witnessed by a global unitary together with its unitary computation rule on every canonical block embedding.
Two blocks have the same Hilbert dimension when each admits a Hilbert basis on one common index type. Basis representations construct the block unitaries, and the local square-summable bridge assembles them into the global unitary.
References
- Truth anchor:
D5/S3/Observer/Completion/BareTowerDimensionClassification.bare_tower_dimension_classification