Theorem: Failure of reconstruction from scheduler consistency

There are local record networks with:

1. acyclic dependency;

2. bounded degree, finite support, and finitely many local reduction shapes;

3. termination of every finite experiment;

4. identical joint records under every legal interleaving;

5. exact operational sensitivity equal to strict reachability;

6. no intervention-induced change outside the dependency future;

7. local point distinguishability and finite pasts for finite collections of records.

These properties do not imply that:

1. a one-step spatial section cannot be a Euclidean metric ball on a discrete slice;

2. a generated reachability cone is quadratic or Lorentzian;

3. interpolation or a manifold topology exists;

4. an otherwise unspecified type system enforces causal availability.

Proof. The network construction is Theorem thm:network. The ball and orthant realizations are Propositions prop:ball and prop:orthant. A two-event chain already lacks interpolation. The operational assumptions do not specify typing rules; Section sec:typing gives a refinement for which the desired availability statement can actually be proved.