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poms1349-sup-0001-appendixS1-S8.docxWord document336KAppendix S1: Proof of Proposition 1 Appendix S2: Proof of Proposition 2 Appendix S3: Proof of Propositions 3 and 4 Appendix S4: Proof of Theorem 2 Appendix S5: Proof of Theorem 3 (1) Appendix S6: Proof of Theorem 3 (3) Appendix S7: Proof of Theorem 4 Appendix S8: Derivation of Eq. (9)

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