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The CH equivalence reuses the two continuum-density Cards and adds one direct Card. Its reverse implication applies the general density obstruction without assuming a faithful separable representation; the equivalence assumes neither CH nor its negation and makes no independence claim.
1 direct Card + 2 reused prerequisites = 3 unique Cards. This count is a selected Card closure, not a source-declaration count.
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Direct references: 69 — CH and a Naimark counterexample of norm density aleph one
Reused prerequisites: 67 — Exact norm density of the fixed atomic algebra · 68 — A Naimark counterexample of continuum norm density
This separate route has one direct Card: the CH equivalence. It reuses the two density Cards as references; they remain members of the main route and are not duplicated as new selected Cards.
The forward implication substitutes into the continuum-density existence result. The reverse applies the density obstruction to an arbitrary witness and obtains . It does not assume that this witness has a faithful separable representation. The equivalence itself assumes neither CH nor its negation and is not a forcing or independence proof.
Read selected Card prerequisites before their uses. Levels are recomputed from the selected reachability-preserving projection; omitted source helpers remain traceable in the source exploration.
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Combines a cardinality bound from a faithful representation on a separable Hilbert space with a lower bound for every norm-dense subset.
MathlibAnnex.CStarAlgebra.CAR.hasDensityCharacter_atomicCounterexampleAlgebra
Immediate Card prerequisites: None in this selected scope
Used by in this scope: A Naimark counterexample of continuum norm density
Gives a C*-algebra of norm density whose nonzero irreducible representations form one unitary-equivalence class, without an identification with the compact operators.
MathlibAnnex.CStarAlgebra.CAR.existsNaimarkCounterexampleOfDensity_continuum
Immediate Card prerequisites: Exact norm density of the fixed atomic algebra
Used by in this scope: CH and a Naimark counterexample of norm density aleph one
Characterizes the continuum hypothesis by the existence of a Naimark counterexample of exact norm density .
MathlibAnnex.CStarAlgebra.CAR.continuum_eq_aleph_one_iff_existsNaimarkCounterexampleOfDensity
Immediate Card prerequisites: A Naimark counterexample of continuum norm density
Used by in this scope: None in this selected scope