A scoped construction on the definite-order sector, with coherent-control composition left open. Paper 70 typed the order-sector candidate layer demanded by Paper 34's radical-precedence stay — the OrdSecSpec normal form and a decidable admission test — but withheld its composition theorems by displayed rule ("grammar not equal to theorem"; "flagged not equal to auditioned") and reserved the audition for a successor. This is that audition: panel P-B of the Twentieth Grouping, whose charter Paper 71 fixed. The charter had chartered P-B "over the P-A background-free support functor"; but P-A yielded no constructed support instance, so by the charter's routing law that variant is empty by routing, and the charter routes "a purely order-sector candidate not consuming the P-A support object separately. " This paper takes that survive path. The foil is the Global Composer — "Composer supplies composition; Chronologist supplies the candidate structure" — the authority that would supply an order-sector algebra's own composition from outside the candidate class. Paper 70's seven OrdSecSpec fields are instantiated as a self-standing normal form consuming no P-A support object, and the composition is auditioned on the definite-order (conditioned) sector of the one row Paper 70 admitted at skeleton grade — the process-matrix / quantum-switch family on Paper 34's controlled-order subdomain — with the switch's own coherent order left uncomposed. The audition is ordered: (1) associativity/closure is constitutive (it makes the declared class an algebra) and is audited first; (2) spacelike independence is a property of an already-associative class, audited second. The result is honestly narrow. On the definite-order class D — Paper 34's conditioned, record-relative definite orders, defined intrinsically as deterministic combs — (1) constructs: the sequential composition is the link product, closed and associative on D as a strict operator identity, imported at stated validity from the quantum-network framework (Chiribella, D'Ariano, and Perinotti 2009: the link product Definition 2 / Eq. (14) ; associativity Theorem 2 Property 2 under the empty-triple-intersection condition; the deterministic-comb normalization hierarchy Theorem 3 / Eq. (25) ; the connection of two networks Section III. C, Corollary 2 / Eq. (37), under the no-loop condition) and reducing form-to-form to Paper 58's undressed slab composition (Lemma Rᵈ). On D's spacelike-separated juxtapositions, (2) constructs by strict recovery to Paper 58's Theorem T-a. The genuinely order-sector-specific extensions — composition across coherent control and the commutation of record-conditioning with composition — are not claimed; they are named-open, as are all-orders dressed composition (Paper 58's (d5) ) and the physical measurement model (Paper 70's (m5) ). The verdict is CompletionStatus (order-sector construction) = scoped: an associative, spacelike-independent order-sector algebra on the definite-order class, the general order-sector algebra open, the dressed-over-P-A variant an honest empty-by-routing null. No composition rule is supplied by an external ALAC authority or by a Global Composer; the composition is the O1 framework's own link product, imported as established mathematics (L1-M) at stated validity; the canonical chronology appears only in the reduction map's codomain. The Composer is retired on the definite-order class, and nowhere claimed beyond it. The audition domain is the definite-order class only; the coherent-control composition, the conditioning-composition commutation, and the general order-sector algebra are not claimed. H1 (no causal loop / valid network) and H2 (no system shared by three operators) are admissibility conditions under which the imported link-product theorem applies, not physical assumptions. Only the boolean absence-of-instance is routed from Paper 71 (element 9) ; the K3-DG obstruction and all F1/F3/DG internals are not consumed. No framework selected, no calibration, no datum scored, zero L3-A acts, no physics evaluated.
Tomoyuki Uchida (Tue,) studied this question.