Fox & Pesetsky 2005: cyclic linearization

[FP05]'s worked examples, kernel-checked against the Minimalist.Linearization spell-out order: the two movement scenarios ((13), (14)), successive-cyclic wh-movement ((3)–(8)), order-preserving simultaneous movement, and Holmberg's Generalization (§3) — plus the paper's central architectural claim, that convergence is a property of the derivational history rather than of the output string (history_dependence).

theorem FoxPesetsky2005.edge_movement_consistent : Minimalist.Linearization.Consistent [["X", "Y", "Z"], ["X", "α", "Y", "Z"]]

Scenario 1 ([FP05] (13)): leftward movement from a left-edge position. X was at the left edge of D; moving further left in D′ is consistent with the order established at D.

theorem FoxPesetsky2005.non_edge_movement_contradiction : ¬Minimalist.Linearization.Consistent [["X", "Y", "Z"], ["Y", "α", "X", "Z"]]

Scenario 2 ([FP05] (14)): leftward movement from a non-edge position. Y was not at the left edge of D, so moving it left in D′ contradicts the order established at D.

theorem FoxPesetsky2005.successive_cyclic_ok : Minimalist.Linearization.Consistent [["to_whom", "gave", "the_book"], ["to_whom", "that", "Mary", "gave", "the_book"]]

Successive-cyclic wh-movement ([FP05] (6)–(8)): to whom moves through the VP edge before Spec,CP, preserving VP-internal order.

theorem FoxPesetsky2005.non_successive_cyclic_bad : ¬Minimalist.Linearization.Consistent [["gave", "the_book", "to_whom"], ["to_whom", "that", "Mary", "gave", "the_book"]]

Non-successive-cyclic movement ([FP05] (3)–(5)): to whom skips the VP edge, contradicting VP-internal order.

theorem FoxPesetsky2005.history_dependence : Minimalist.Linearization.Consistent [["to_whom", "gave", "the_book"], ["to_whom", "that", "Mary", "gave", "the_book"]] ∧ ¬Minimalist.Linearization.Consistent [["gave", "the_book", "to_whom"], ["to_whom", "that", "Mary", "gave", "the_book"]]

The paper's central architectural claim: convergence is a property of the derivational history, not the output — the same final Spell-out converges after successive-cyclic movement through the VP edge and crashes without it. The spell-out order does not factor through the final string.

theorem FoxPesetsky2005.simultaneous_order_preserving : Minimalist.Linearization.Consistent [["A", "B", "C"], ["A", "B", "D", "C"]]

Simultaneous movement preserving relative order creates no contradiction (the configuration behind Malayic object extraction, Studies/ErlewineSommerlot2025.lean).

theorem FoxPesetsky2005.simultaneous_order_reversing : ¬Minimalist.Linearization.Consistent [["B", "A", "C"], ["A", "B", "D", "C"]]

Simultaneous movement reversing relative order contradicts.

theorem FoxPesetsky2005.transitive_cycle_crashes : ¬Minimalist.Linearization.Consistent [["a", "b"], ["b", "c"], ["c", "a"]]

A purely transitive ordering cycle also crashes: the crash condition is acyclicity of the full spell-out order, not the absence of a directly contradicting pair.

Holmberg's Generalization ([FP05] §3)

Object Shift in Scandinavian is possible only when the verb also moves out of VP: VP Spell-out establishes V < Obj, and a shifted object with an in-situ verb reverses it at the higher domain.

theorem FoxPesetsky2005.no_object_shift : Minimalist.Linearization.Consistent [["V", "Obj"], ["Subj", "V", "Neg", "Obj"]]

Baseline: no Object Shift, verb moves to I.

theorem FoxPesetsky2005.object_shift_with_verb_movement : Minimalist.Linearization.Consistent [["V", "Obj"], ["Subj", "V", "Obj", "Neg"]]

Object Shift with verb movement: V < Obj is preserved past Neg.

theorem FoxPesetsky2005.object_shift_without_verb_movement : ¬Minimalist.Linearization.Consistent [["V", "Obj"], ["Subj", "Obj", "Neg", "V"]]

Object Shift without verb movement reverses V < Obj — this crash is Holmberg's Generalization, derived from cyclic linearization.