required_floor: admit test.claim.seed_growth_admission_witness to the required gate

dag/gunbc/seed_growth_admission.dag

@@ -460,12 +460,26 @@ fn seed_growth_live_lookup(live: Map<String, Bool>, key: String) -> Bool? {
 }
 
 fn seed_growth_stale_justifications(live_items: List<DeclarationRef>) -> List<String> {
+  seed_growth_stale_declarations(live_items: live_items)
+    |> map(r => declaration_ref_display_key(ref: r))
+}
+
+// THE ROSTER BINDING IS ONE STEP AND THE KEY RENDERING ANOTHER. The real-roster binding is its own
+// function so a witness can hold it to the COMPLETE roster (every row reported stale against a live
+// population that names none of them) without paying the display-key render of every row, which is
+// the expense and which no completeness assertion inspects.
+fn seed_growth_stale_declarations(live_items: List<DeclarationRef>) -> List<DeclarationRef> {
+  seed_growth_stale_over(roster: seed_growth_roster_all_declarations(), live_items: live_items)
+}
+
+// THE STALENESS RELATION OVER A SUPPLIED ROSTER. A witness of the relation's shape supplies a
+// small roster (DESIGN section 3, a witness discriminates at one interface).
+fn seed_growth_stale_over(roster: List<DeclarationRef>, live_items: List<DeclarationRef>) -> List<DeclarationRef> {
   let live = seed_growth_live_set(live_items: live_items)
   filter(
-    xs: seed_growth_roster_all_declarations(),
+    xs: roster,
     predicate: fn(r) { !seed_growth_live_has(live: live, r: r) }
   )
-    |> map(r => declaration_ref_display_key(ref: r))
 }
 
 fn seed_growth_unjustified_additions(added: List<DeclarationRef>) -> List<String> {

dag/test/claim/seed_growth_admission_witness_test.dag

@@ -6,6 +6,8 @@ import gunbc.seed_growth_admission {
   seed_growth_forward_freeze_policy_note,
   seed_growth_unjustified_additions,
   seed_growth_stale_justifications,
+  seed_growth_stale_declarations,
+  seed_growth_stale_over,
   seed_growth_roster_all_declarations,
   seed_growth_roster_mechanical_checks_holds,
   seed_growth_roster_well_formed_gate_holds
@@ -22,19 +24,45 @@ test fn seed_growth_roster_mechanical_checks_hold() -> Bool {
 
 // THE JOIN IS SPLIT AND THE SPLIT IS THE ASSERTION. Under the single-candidate-set form these two
 // calls were one, so the population that found an unjustified addition was the same one that
-// declared every untouched roster row stale. Here the SAME candidate list goes to both functions
-// and they must answer differently: the rogue is an unjustified addition, and passing it as the live
+// declared every untouched roster row stale. Here the SAME candidate goes to both functions and
+// they must answer differently: the rogue is an unjustified addition, and passing it as the live
 // population makes every real roster row stale rather than none. A reimplementation that collapsed
-// them again reds on the second conjunct.
-test fn seed_growth_join_refuses_unknown_declaration() -> Bool {
-  let rogue = DeclarationRef {
+// them again reds on the second claim. The two answers are independent, so they are two claims
+// rather than one conjunction paying both under one budget (DESIGN section 3, a witness
+// discriminates at one interface).
+fn seed_growth_rogue_declaration() -> DeclarationRef {
+  DeclarationRef {
     module_path: "v1_compiler.cli_run",
     decl_name: "totally_unjustified_hand_rust_symbol",
     field: WholeDeclaration
   }
-  length(xs: seed_growth_unjustified_additions(added: [rogue])) == 1
-    && length(xs: seed_growth_stale_justifications(live_items: [rogue]))
-      == length(xs: seed_growth_roster_all_declarations())
+}
+
+test fn seed_growth_join_refuses_unknown_declaration() -> Bool {
+  length(xs: seed_growth_unjustified_additions(added: [seed_growth_rogue_declaration()])) == 1
+}
+
+// THE ROSTER IS SUPPLIED, THE RELATION IS REAL. Rendering every roster row's display key put the
+// whole-roster form of this claim over the new-witness cost requirement (re-derive:
+// claim_executor --required-floor, its COMPLETED-OVER-COST-REQUIREMENT line), and the assertion
+// inspects none of the keys. The generic relation is discriminated here on a supplied roster; the
+// next claim holds the real binding to the complete roster.
+test fn an_unknown_live_population_reports_every_roster_row_stale() -> Bool {
+  let roster = [
+    DeclarationRef { module_path: "v1_compiler.a", decl_name: "first", field: WholeDeclaration },
+    DeclarationRef { module_path: "v1_compiler.b", decl_name: "second", field: WholeDeclaration }
+  ]
+  length(xs: seed_growth_stale_over(roster: roster, live_items: [seed_growth_rogue_declaration()])) == 2
+    && length(xs: seed_growth_stale_over(roster: roster, live_items: roster)) == 0
+}
+
+// THE REAL BINDING RANGES OVER THE COMPLETE ROSTER. Against a live population that names no roster
+// row, every row is stale -- so a staleness function bound to an empty roster or any strict subset
+// reds here, which a_live_roster_declaration_is_not_reported_stale cannot detect (an empty binding
+// also reports nothing stale). seed_growth_stale_justifications is this list rendered to keys.
+test fn the_real_staleness_binding_covers_every_roster_row() -> Bool {
+  length(xs: seed_growth_stale_declarations(live_items: [seed_growth_rogue_declaration()]))
+    == length(xs: seed_growth_roster_all_declarations())
 }
 
 // A ROSTER ROW THAT STILL NAMES A LIVE ITEM IS NOT STALE. Without this control the staleness

src/v2/workflow/required_floor.dag

@@ -899,6 +899,11 @@ fn required_gate_prefixes() -> List<String> {
 // in today but would silently widen if a sibling is ever planted. Its claims run through the census
 // probe over planted fixture sources (no live-tree read, SubstrateInputsOnly in spirit -- the
 // fixture sources are supplied strings), priced at NewWitnessTier.
+// THE SEED-GROWTH ADMISSION WITNESS (operator ruling, escalation msg_341a9785, approved
+// 2026-10-03). `test.claim.seed_growth_admission_witness` carries the seed-growth roster's
+// duplicate-key and well-formed checks and the addition/staleness join; it matched no family prefix,
+// so those reds executed on no merge lane. Admitted at exact module grain for the same reason as the
+// test-reference wall: a family prefix would silently widen to any future sibling.
 fn required_gate_authored_modules() -> List<String> {
   [
     "test.claim.runner_capacity_plan_witness",
@@ -916,6 +921,7 @@ fn required_gate_authored_modules() -> List<String> {
     "test.claim.discovery_census_witness",
     "v2.test.claim.effect_demand.effect_demand_floor_join_test",
     "test.claim.test_reference_wall_witness",
+    "test.claim.seed_growth_admission_witness",
   ]
 }