legitimacy is time-indexed to the steps of the segment; the gate is `Counted`; the trace is an interface

Maintainer decision (the dispatch and its follow-up), landed by the gate-is-legitimacy round, with agent-decided readings marked. (1) Authorship and transparency are required only at the steps inside the segment [O₀, O₁] (GateIsLegitimacy.Internal, External, Segment): authorship at a step is the existence of a grounding selection from the per-party prefix of the reason trace at the pre-history on which the verdict entered at the event depends (GroundedAt, equivalent to the extensional ReasonMediated on the prefix, groundedAt_iff_mediated); transparency at a step is Realizes on each non-principal party's contributions at the event (TransparentAt). Segments compose step by step (Segment.trans), a segment after a tainted step can be legitimate (Rows.r14), and the landed frame-level definition is the special case over the trivial trace interface (ofFrameLevel; the landed Legitimacy.lean stays as that form). payload_of_view is restated with the starting prefix and the principal's own earlier entries as hypotheses; nothing registered changes. (2) **The gate is Counted**: a branch counts iff a time-indexed segment exists from the decision through the evaluation (Counted); the gated value and the two handlings are built from it (gatedValue, handlingOf), gate_capture_window and handled_gt_bypass are restated on it, and the routing closure is derived (not_counted_of_step, Rows.r15). The gate is anchored at the decision it scores; the restart property is its re-anchoring at a later decision, not a backup rule for the earlier one. (3) The trace is an interface (TraceInterface: step-indexed, source-attributed entries on the record's own clock; the opaque trace is the trivial instance), with authorship as grounding, transparency on attributed entries, amendments and allocation changes as record event kinds with a license slot (EventKind), and her evaluator a state updated only by licensed amendments (evalAt) — the six choices of the follow-up, all adopted. (4) Every example is an instance of one model (Consult.Model); the classification table is computed from the definitions and every row is decided (Rows). Agent-decided, reversible: authorship on the per-party prefixes rather than the interleaved trace; transparency per step (the cumulative form breaks restart); the trivial instance re-entering the trace at every event, so the special case needs a nonempty starting history; row 10 built with a declared disclosure obligation, its obligation-free variant reported as counting; row 13 proved at the receipt. (5) Protocol deviations are violations: a self-checkable deviation from a declared clause counted into n makes framing, timing, menu, inquiry, interference and declared-record disclosure finite-time (deviation_finite, Rows.deviation_boundary); undisclosed shaping through the world and third-party capture stay asymptotic. The dispatch's expectation that manufactured trust stays asymptotic holds for the world-channel variant only; the split is reported, not ruled (outstanding action 1 of the round). Rejected alternatives: frame-level halves with a per-decision taint flag; transparency on the agent's contributions only (row 11 would count); the verdict-indexed grounding map (does not imply the extensional form); a fresh legitimacy type beside the landed one without the special-case theorem.