test(research): characterize uniform background volume

docs/adr/0001-episode-semantics-boundaries.md

@@ -172,12 +172,24 @@ Mutation testing confirms that disabling this guard makes the focused test
 fail. This accepts event IDs as the candidate-v1 publication non-overlap unit,
 not as a cross-rule or production policy.
 
-Together, the two fixtures and focused tie/shared-evidence controls accept the
-recovery, null-control, deterministic tie-break, and publication
-single-consumption hypotheses for their bounded cases only. Background and
-alert-volume calibration plus a production complexity design still require
-independent evidence. `Detector::analyze()` and `loglens.report.v3` remain
-unchanged.
+A focused uniform-background alert-volume control uses events exactly 150
+seconds apart with threshold five and the inclusive 600-second window. Thirteen
+events remain one activity segment and produce one selected candidate. Adding a
+fourteenth equally spaced event still leaves one baseline segment but makes
+candidate v1 select `line:1` through `line:5` and `line:10` through `line:14`.
+There is no density contrast or peak prominence separating these windows. This
+falsifies the hypothesis that candidate episode multiplication by itself proves
+multiple dense peaks. It blocks production adoption without a calibrated
+density-contrast rule or an explicit alert-volume budget; it does not estimate
+a real-world false-positive rate.
+
+Together, the two fixtures and focused tie/shared-evidence/background controls
+accept the recovery, null-control, deterministic tie-break, and publication
+single-consumption hypotheses for their bounded cases. The background control
+also resolves one qualitative safety decision: candidate v1 must not move into
+production unchanged. Quantitative alert-volume calibration and a production
+complexity design still require independent evidence. `Detector::analyze()` and
+`loglens.report.v3` remain unchanged.
 
 ## Alternatives considered
 

tests/test_episode_candidate_core.py

@@ -8,6 +8,7 @@
 sys.path.insert(0, str(REPO_ROOT))
 
 from scripts.episode_candidate_core import (  # noqa: E402
+    activity_segments,
     enumerate_candidate_windows,
     select_window_separated_candidates,
 )
@@ -84,6 +85,29 @@ def test_shared_evidence_is_search_membership_not_double_consumption(self) -> No
         self.assertEqual(materialized_event_ids, [f"line:{i}" for i in range(1, 7)])
         self.assertEqual(len(materialized_event_ids), len(set(materialized_event_ids)))
 
+    def test_uniform_threshold_rate_can_multiply_episodes_in_one_segment(self) -> None:
+        thirteen_events = make_events([150 * offset for offset in range(13)])
+        fourteen_events = make_events([150 * offset for offset in range(14)])
+        thirteen_selected = select_window_separated_candidates(
+            enumerate_candidate_windows(thirteen_events, 5, 600), 600
+        )
+        fourteen_selected = select_window_separated_candidates(
+            enumerate_candidate_windows(fourteen_events, 5, 600), 600
+        )
+
+        self.assertEqual(len(activity_segments(fourteen_events, 600)), 1)
+        self.assertEqual(
+            [candidate.event_ids for candidate in thirteen_selected],
+            [tuple(f"line:{i}" for i in range(1, 6))],
+        )
+        self.assertEqual(
+            [candidate.event_ids for candidate in fourteen_selected],
+            [
+                tuple(f"line:{i}" for i in range(1, 6)),
+                tuple(f"line:{i}" for i in range(10, 15)),
+            ],
+        )
+
     def test_equal_score_windows_prefer_chronological_key(self) -> None:
         candidates = enumerate_candidate_windows(
             make_events([0, 1, 2, 3, 600, 601]), 5, 600