fix(analysis): _expected_ticks usa ceiling division (no off-by-one)

Il piano originale aveva `floor(span/15) + 1` che over-conta a span allineati
(span=60min → 5 invece di 4). Il primo fix dell'implementer (`floor(span/15)`)
under-conta a span non-allineati (span=16min → 1 invece di 2). Solo
`ceil(span/15)` è corretto in entrambi i casi. Aggiunti 2 test che
coprono gli scenari non-allineato e boundary-esatto per impedire
regressioni. Plan doc allineato.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

docs/superpowers/plans/2026-05-12-data-quality-audit.md

@@ -246,8 +246,12 @@ def _expected_ticks(since: datetime, until: datetime) -> int:
         )
     if first_tick >= until:
         return 0
-    span = until - first_tick
-    return int(span.total_seconds() // (_TICK_INTERVAL_MIN * 60)) + 1
+    # Count ticks in [first_tick, until): the count is
+    # ceil(span_minutes / 15). floor() under-counts at non-multiple
+    # spans; floor()+1 over-counts at aligned multiples. Only
+    # ceil() works for both. Requires `import math` at the top.
+    span_seconds = (until - first_tick).total_seconds()
+    return math.ceil(span_seconds / (_TICK_INTERVAL_MIN * 60))
 ```
 
 - [ ] **Step 4: Run tests to verify they pass**

src/cerbero_bite/analysis/data_audit.py

@@ -12,6 +12,7 @@ parameters. To tune a threshold, edit this file.
 
 from __future__ import annotations
 
+import math
 import sqlite3
 import statistics
 from dataclasses import dataclass, field
@@ -117,5 +118,9 @@ def _expected_ticks(since: datetime, until: datetime) -> int:
         )
     if first_tick >= until:
         return 0
-    span = until - first_tick
-    return int(span.total_seconds() // (_TICK_INTERVAL_MIN * 60))
+    # Count ticks in [first_tick, until): the largest k with
+    # first_tick + k*15min < until is ceil(span/15) - 1, so the
+    # count is ceil(span_minutes / 15). floor() under-counts at
+    # aligned multiples and would mis-count non-aligned spans.
+    span_seconds = (until - first_tick).total_seconds()
+    return math.ceil(span_seconds / (_TICK_INTERVAL_MIN * 60))

tests/unit/test_data_audit.py

@@ -26,3 +26,20 @@ def test_expected_ticks_unaligned_since_rounds_up() -> None:
     until = datetime(2026, 5, 12, 12, 30, tzinfo=UTC)
     # First aligned tick after 12:07 is 12:15, then 12:30 is excluded
     assert _expected_ticks(since, until) == 1
+
+
+def test_expected_ticks_non_multiple_span_uses_ceiling() -> None:
+    # Span = 16 min (12:00 → 12:16): ticks 12:00 AND 12:15 are < 12:16.
+    # floor(16/15) = 1 would under-count; the correct answer is 2.
+    since = datetime(2026, 5, 12, 12, 0, tzinfo=UTC)
+    until = datetime(2026, 5, 12, 12, 16, tzinfo=UTC)
+    assert _expected_ticks(since, until) == 2
+
+
+def test_expected_ticks_exact_quarter_boundary_is_excluded() -> None:
+    # Until landing exactly on a */15 tick: that tick is NOT counted
+    # because the window is half-open on the right.
+    since = datetime(2026, 5, 12, 12, 0, tzinfo=UTC)
+    until = datetime(2026, 5, 12, 12, 45, tzinfo=UTC)
+    # Ticks at 12:00, 12:15, 12:30 → 3 (12:45 excluded)
+    assert _expected_ticks(since, until) == 3