Population: inhabitance claim over the real row + declared runtime task

dag/gunbc/plans/native_obligation_population.dag

@@ -110,6 +110,7 @@ fn native_obligation_population_body() -> List<MarkdownBlock> {
     ol(items: [
       li(text: "Ruled 2026-10-09: the frontier is observed from a run, never reasoned from source."),
       li(text: "Ruled 2026-10-10 (operator, relayed by smart-gull-336): the denominator is the derived universe -- green identities, exactly one observed frontier and typed exclusions/refusals -- and the green set alone is never a production-admission denominator; the first frontier's subject is a stable qualified identity or a derived single-member target with a cardinality assertion, never \"the smallest member\"."),
+      li(text: "Runtime task, declared: typed refusal reasons for the population predicates (`native_member_is_eligible`, `native_member_is_a_subject_row`). They return Bool today, admitted for the first fold with an empty green set; the trigger is the first non-empty green set."),
       li(text: "Deferred: widening the universe from one identity to all of `v2.test.*`; trigger is M1 landed with a terminal that the driver can pass."),
     ]),
   ]

dag/gunbc/roadmap/roadmap_authority.dag

@@ -936,6 +936,7 @@ fn declared_roadmap_nodes() -> List<RoadmapNode> {
           "a_host_judged_member_is_ineligible" as NonEmptyStr,
           "the_population_is_disjoint_from_the_emitted_subject_rows" as NonEmptyStr,
           "the_denominator_is_the_derived_universe_not_the_green_set" as NonEmptyStr,
+          "the_real_subject_rows_derive_the_supplied_labels_and_each_refuses_as_a_member_the_real_route" as NonEmptyStr,
         ],
       )),
       parent: in_project(project: "native-route-to-live", contribution: "This is the shape the native route takes on the required path: the drop v2_native_route_off_the_merge_path retires only when this population is judged on a landing, and D10 admission reads its green set as the subject denominator."),

dag/test/claim/native/native_obligation_population_witness_test.dag

@@ -1,9 +1,11 @@
 module test.claim.native.native_obligation_population_witness_test
 
-import std.types { Bool, String, List }
+import std.types { Bool, String, List, list_length }
+import v2.std.algebra { any }
+import gunbc.emitted_subject_build_gate { emitted_subject_build_rows, emitted_subject_build_label_text }
 import v2.std.live_tree { LiveTreeDisposition, SubstrateInputsOnly }
 import gunbc.plans.native_obligation_population {
-  native_denominator_is_the_universe, native_member_is_eligible, native_member_is_a_subject_row,
+  native_denominator_is_the_universe, native_population_green_set, native_member_is_eligible, native_member_is_a_subject_row,
 }
 
 data live_tree_disposition: LiveTreeDisposition = SubstrateInputsOnly
@@ -31,3 +33,20 @@ test fn the_denominator_is_the_derived_universe_not_the_green_set() -> Bool {
     && !native_denominator_is_the_universe(universe: ["a", "b", "c"], green: ["a"], frontier: ["b", "c"], exclusions: [])
     && !native_denominator_is_the_universe(universe: ["a", "b"], green: ["a"], frontier: ["b"], exclusions: ["z"])
 }
+
+// INHABITANCE: the real route, and it can go red today. The real emitted_subject_build_rows derive exactly
+// the two labels the disjointness control above supplies (the two compiler products, operator ruling
+// 2026-10-09: emitted_subject_build_rows stays the two products), and each of them refuses as a population
+// member through the real predicate -- so deleting the label fold, changing the subject roster, or breaking
+// native_member_is_a_subject_row reds this claim. The last two conjuncts run the same predicates over the real
+// native_population_green_set; that row is empty until the first native adjudication lands (the plan's declared
+// trigger), so they are the real path's last execution for the green set and carry no weight of their own yet.
+test fn the_real_subject_rows_derive_the_supplied_labels_and_each_refuses_as_a_member_the_real_route() -> Bool {
+  let labels = emitted_subject_build_rows() |> map(r => emitted_subject_build_label_text(row: r))
+  list_length(labels) == 2
+    && any(labels, l => l == "//gunbc/instruments:self-host")
+    && any(labels, l => l == "//gunbc/instruments:v2-native-cli")
+    && !any(labels, l => !native_member_is_a_subject_row(member: l, subject_labels: labels))
+    && !any(native_population_green_set, m => !native_member_is_eligible(member: m))
+    && !any(native_population_green_set, m => native_member_is_a_subject_row(member: m, subject_labels: labels))
+}