Why it is a question
THEORY-714 now states what Ince’s I_ccs (LIT-1201) is and what it does. It is symmetric and self-redundant, it satisfies the independent identity property, and it fails Harder et al.’s identity, monotonicity and subset equality. Everything there is derived. What is not settled is whether it measures redundancy correctly, which is what the account’s former promote_when asked:
- Continuity. Ince conjectures it and checks it only locally in the examples. A sign rule makes the measure piecewise, so continuity is not automatic.
- An operational test. A system whose redundancy is fixed by mechanism, accepted by both sides of the dispute (a shared bit copied to every source, say), on which I_ccs agrees and a rival with non-negative atoms does not.
- The source-source marginal. Ince’s P̂ fixes Q(A1…An) and so lets unique information depend on it. Bertschinger et al. (LIT-1162) hold that it may not. An argument settling which is right decides between I_ccs and I_broja.
- Subset equality. The audit found it fails for I_ccs as defined, because the sign rule compares a source with a source containing it. Ince argues that subset equality, not monotonicity, is what licenses the redundancy lattice, so the failure matters for the measure’s own rationale. Would a sign rule that skips sources contained in others restore it, and at what cost to the other properties?
An answer is a proof, a counterexample, or an operational case of the kind above. Further examples judged by intuition do not settle it, nor does agreement on systems where every measure agrees.