diff --git a/.github/time/sync.py b/.github/time/sync.py
index d1019fa..d81f8fc 100644
--- a/.github/time/sync.py
+++ b/.github/time/sync.py
@@ -14,9 +14,10 @@ cloud session's branch on the copy), and a pull mirror makes the receiving repo
   like any other; the landed work then flows back out with main. A branch already in main, or one whose PR was closed
   at the same commit, is left alone.
 - Back: Time itself commits to an imported branch in one case, merging the base into an approved PR that fell behind.
-  When the home's branch is ahead of the copy's (the copy's tip is in it), those commits go back to the copy
-  fast-forward, so the copy's next session builds on them instead of overwriting them. When both sides have commits of
-  their own, the copy wins, as its writer: Time merges the base again on a later beat.
+  When the home's branch is ahead of the copy's by Time's merges and nothing else, they go back to the copy
+  fast-forward (and only if the copy's branch hasn't moved since it was read), so the copy's next session builds on
+  them instead of overwriting them. Anything else ahead on the home (the copy rewound its own branch, or someone pushed
+  to it at the home) is not sent out: the copy, the writer, wins, and Time merges the base again on a later beat.
 
 time/sync.json:
     {"repos": [{"repo": "teahubxyz/time", "out": ["main"],
@@ -138,6 +139,16 @@ def landed(work: str, ref: str, base: str) -> bool:
     return git("merge-base", "--is-ancestor", ref, base, cwd=work, check=False).returncode == 0
 
 
+def times_merges(work: str, copy_ref: str, home_ref: str) -> bool:
+    """The home's branch is ahead of the copy's by update_branch's merges alone: every first-parent commit between them
+    is a two-parent merge authored by Time. The copy rewinding its own branch leaves the home ahead too, by the
+    copy's own withdrawn commits, and those must not go back; nor must a human's or a worker's push at the home."""
+    if not landed(work, copy_ref, home_ref):
+        return False
+    rows = git("log", "--first-parent", "--format=%an%x09%P", f"{copy_ref}..{home_ref}", cwd=work).stdout.splitlines()
+    return bool(rows) and all(r.split("\t")[0] == tm.TIME_GIT_NAME and len(r.split("\t")[1].split()) == 2 for r in rows)
+
+
 CARD_BRANCH = re.compile(r"^claude/card-(\d+)(?:\b|-)")   # a cloud session building card N (router.py's cloud lane)
 
 
@@ -261,10 +272,12 @@ def sync_repo(entry: dict, home_url: str, force: bool = False) -> dict:
                     continue
                 git("fetch", "-q", url, f"+refs/heads/{branch}:refs/copy/{branch}", cwd=work)
                 moved = mine.get(branch) != sha
-                if moved and mine.get(branch):
-                    git("fetch", "-q", home_url, f"+refs/heads/{branch}:refs/back/{branch}", cwd=work)
-                    if landed(work, f"refs/copy/{branch}", f"refs/back/{branch}"):   # the home is ahead: Time's merge
-                        p = git("push", "-q", url, f"refs/back/{branch}:refs/heads/{branch}", cwd=work, check=False)
+                if moved and mine.get(branch):   # the home's branch may be ahead by Time's merge of the base
+                    got = git("fetch", "-q", home_url, f"+refs/heads/{branch}:refs/back/{branch}", cwd=work, check=False)
+                    if got.returncode == 0 and times_merges(work, f"refs/copy/{branch}", f"refs/back/{branch}"):
+                        read = git("rev-parse", f"refs/copy/{branch}", cwd=work).stdout.strip()
+                        p = git("push", "-q", f"--force-with-lease=refs/heads/{branch}:{read}", url,
+                                f"refs/back/{branch}:refs/heads/{branch}", cwd=work, check=False)
                         if p.returncode == 0:
                             r.setdefault("back", []).append(branch)
                         else:   # the copy moved meanwhile: the next run sorts it out