Column-Matroid Backbone (Paper II)
A Structural Identity and Its Corollaries
Under the stated construction, the deficit is the observable-column corank and admits the reported pairwise formula.
Abstract
The coherence fee equals the corank of the observable column set in the linear matroid on the full coboundary columns. This structural identity yields a closed-form pairwise formula fee(A,B) = U(A) + U(B) + |shared_dims(A,B)| and proves additive decomposition as matroid direct-sum additivity. An empirical density law localizes the connecting homomorphism strictly in the interior of its attainable range on all 240 nontrivial compositions tested.
Evidence and record
Which matroid identity underlies the disclosure deficit?
fee(G) = corank_M(O): the backbone theorem with closed-form pairwise formula verified on 703 real-schema compositions
The former hierarchical-fee/lean evidence path did not exist. Adjacent checked rank identities are narrower than the whole paper; its corank identification is a written mathematical claim, not cleared here by those declarations.
A counterexample under the exact construction and stated hypotheses.
not requested
- narrows The Coherence Fee Paper I
- is formalized by Signed-Incidence Structure