diff --git a/skills/hourlog/SKILL.md b/skills/hourlog/SKILL.md
index ebc8b45..4800510 100644
--- a/skills/hourlog/SKILL.md
+++ b/skills/hourlog/SKILL.md
@@ -48,8 +48,13 @@ time that project was actually active, plus wall-clock `total`, the day's
 `window`, and `flags`. That table is the deliverable — paste it as-is rather
 than restating it in prose.
 
-`total` is the union of active slots, so on a day with parallel sessions it is
-less than the row sum. Both numbers are true; they answer different questions.
+Overlap is divided, not double-counted: five minutes with two projects open is
+five minutes of the day, half to each. The project columns therefore add up to
+`total`, which is wall-clock presence.
+
+That division is also the ratio to submit with. The user gives the day's real
+total; you split it by these proportions. Never submit the measured numbers as
+the hours unless the user says they are right.
 
 Paste it as plain markdown in the reply. Never wrap it in a code fence: a
 fence shows the raw pipes and dashes instead of a rendered table.
diff --git a/skills/hourlog/scripts/scan-activity.py b/skills/hourlog/scripts/scan-activity.py
index fdb1d7f..73de70a 100755
--- a/skills/hourlog/scripts/scan-activity.py
+++ b/skills/hourlog/scripts/scan-activity.py
@@ -22,8 +22,9 @@ a guessed number is worse than a small true one.
 Measured time is a floor. Meetings, review and thinking leave no transcript,
 so the user adds those back; the script never does.
 
-The 'total' column is wall-clock presence, the union of active slots across
-projects, so on days with parallel sessions it is less than the row sum.
+Overlap is divided, not double-counted: five minutes with two projects open is
+five minutes of the day, half to each. So the project columns add up to the
+'total' column, which is wall-clock presence.
 """
 import argparse
 import collections
@@ -114,6 +115,21 @@ def read_session(path):
     return cwd, stamps
 
 
+def attribute(slots_of, owners, mins):
+    """Divide each slot's minutes evenly among the projects live in it.
+
+    Five minutes with two projects open is five minutes of the user's day, not
+    ten, so each project gets half. Largest remainder over whole minutes keeps
+    the parts summing to wall clock exactly.
+    """
+    exact = {p: sum(mins / owners[s] for s in ss) for p, ss in slots_of.items()}
+    floors = {p: int(v) for p, v in exact.items()}
+    left = round(sum(exact.values())) - sum(floors.values())
+    for p in sorted(exact, key=lambda p: -(exact[p] - floors[p]))[:left]:
+        floors[p] += 1
+    return floors
+
+
 def fmt_dur(minutes):
     """45 -> '45min', 155 -> '2h35', 180 -> '3h', 0 -> '—'."""
     if not minutes:
@@ -216,22 +232,27 @@ def main():
     d = since
     while d <= until:
         per = grid.get(d.isoformat(), {})
-        totals = {p: sum(len(s) for s in hrs.values()) for p, hrs in per.items()}
-        # Wall clock, not the row sum: a slot with two projects live is one
-        # minute of the user's day, counted once here and once per project.
-        union = len({s for hrs in per.values() for ss in hrs.values()
-                     for s in ss})
+        slots_of = {p: {s for ss in hrs.values() for s in ss}
+                    for p, hrs in per.items()
+                    if not p.startswith("unmapped:")}
+        owners = collections.Counter()
+        for ss in slots_of.values():
+            owners.update(ss)
+        share = attribute(slots_of, owners, mins)
         entry = {
             "date": d.isoformat(),
             "weekday": d.strftime("%a"),
-            "active_minutes": union * mins,
+            "active_minutes": len(owners) * mins,
             "projects": [],
         }
-        for proj, n in sorted(totals.items(), key=lambda kv: -kv[1]):
+        raw = {p: sum(len(s) for s in hrs.values()) * mins
+               for p, hrs in per.items()}
+        for proj in sorted(per, key=lambda p: -raw[p]):
             hrs = sorted(per[proj])
             entry["projects"].append({
                 "project": proj,
-                "active_minutes": n * mins,
+                "active_minutes": share.get(proj, raw[proj]),
+                "raw_minutes": raw[proj],
                 "first_hour": hrs[0],
                 "last_hour": hrs[-1],
                 "outside_workday": [
@@ -256,7 +277,7 @@ def main():
     print(f"{since} .. {until} — {nfiles} sessions, {mins}-min slots, "
           f"{cfg['timezone']}")
     print("measured active time, nothing extrapolated; "
-          "total is wall clock, so it can be less than the row\n")
+          "overlapping minutes split evenly between projects\n")
 
     cols = [p for p in dict.fromkeys(
         x["project"] for e in report for x in e["projects"])