Sharp robustness of quantum marginal reconstruction under composition

This record contains the paper Sharp robustness of quantum marginal reconstruction under composition by Yasuhito Tsujimura and its finite-verification package. Uniqueness from local marginals does not determine how strongly local errors control a quantum state. For a fixed twelve-qubit product target, with all 66 two-qubit marginals observed, the paper proves that the sharp trace-norm exponent is 1/2 for states separable across the two six-qubit blocks and 1/4 for arbitrary states. Pure states of Schmidt rank two witness the latter obstruction. The paper gives sufficient structural conditions, extends the obstruction to a positive weighted family, and completely classifies one positive parameter slice, with an exceptional parameter certified by an exact two-local parent Hamiltonian. For the original product target, three-qubit marginals in one block restore the square-root exponent. These results concern deterministic marginal errors and arbitrary mixed competing states; they do not infer measurement counts, statistical estimation costs or experimental performance. The verification package provides an offline English reader guide, annotated source pages, fixed mathematical inputs, and exact-arithmetic Python checks F001-F005. Extract Quantum_Verification_v1.zip and open START_HERE.html inside quantum-verification. The guide maps the finite checks to the paper, explains what a successful run establishes, and distinguishes finite arithmetic from the general analytic arguments. The paper and verification materials are supplied together in this record. An arXiv submission is planned. The verification-use terms are in RIGHTS.txt; paper rights are stated separately in PAPER_RIGHTS.txt.