diff --git a/certificates/partial-swap-network.json b/certificates/partial-swap-network.json
index a72693d486..eccafa830c 100644
--- a/certificates/partial-swap-network.json
+++ b/certificates/partial-swap-network.json
@@ -1481,7 +1481,7 @@
     "scripts/partial_swap/match_positive_dag.cpp": "8a6d64e2d0ac2c69210fb0b8a5bd0d714ad40b3609f75a5fddfcba3291a3d552",
     "scripts/partial_swap/paired.py": "ddcecace3a8e04d690914cbd64873ab8dde8c0c3477a255767b0ed6f639bb0c7",
     "scripts/partial_swap/positive.py": "1dadf771226d6e4f3bf9ce3aae2e6a2ad7173f4d1c900299d0663fc4c432f3e8",
-    "scripts/partial_swap/shared.py": "7290bd639600aecff11941d3faf95c9ce95589125cc6a7f7440fb86af7a0f17c",
+    "scripts/partial_swap/shared.py": "5a0646a50b9f3e8ea55168620a78e8853b0ab810517cefc8cfb8696aedee278a",
     "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782",
     "scripts/partial_swap_producer.py": "dba07d742c68e8e4aedd1d93fc4c47a0481778268f7480997463e2b269fdd0a0"
   },
diff --git a/docs/research/partial-swap-retained-total-fix.md b/docs/research/partial-swap-retained-total-fix.md
new file mode 100644
index 0000000000..4100f361a2
--- /dev/null
+++ b/docs/research/partial-swap-retained-total-fix.md
@@ -0,0 +1,94 @@
+# Restore retained-total partial-swap verification
+
+This is a verifier regression fix, with no new κ or runtime-speedup claim.
+The reviewed starting tree is `20ecf2891d80b5acf18d980b2164fb44ea7faa90`.
+
+`partial_swap.graph.graph(h)` adds the local empty-exclusion output `()`.
+`SharedPointCircuit` lifts that output to the singleton target `(common,)`,
+representing a retained full pair-star total. The digest optimization introduced
+in [PR2039](https://github.com/CrocSwap/integer-mult-bounds/pull/2039) unpacks
+all targets as triples. Consequently even `graph(6).verify()` raises
+`ValueError: not enough values to unpack (expected 3, got 1)`. The h25 producer
+used by `make copied-fixed-reversed-producer` and `make verify` fails there too.
+Existing equivalence tests constructed exclusion-only graphs, missing this case.
+
+The repair joins the target's integer entries with commas inside the same JSON
+array delimiters. For both singleton and triple targets these are exactly the
+bytes emitted by the historical `json.dumps(..., separators=(',', ':'))`
+verifier. Sorted traversal, newline boundaries, node encoding, topology,
+disjointness, support, core and union assertions are unchanged.
+
+New tests compare whole receipts to the pre-optimization verifier on retained-total
+graphs of sizes 6, 8, 10 and 25, and compare h25 against the frozen
+`research/copied-fixed-reversed/producer-input-25.json` scalar receipt. A negative
+control replaces a full retained total with a proper excluded-pair sum and
+requires both verifiers to reject it. Existing exclusion-only equivalence and
+support-corruption controls remain in place.
+
+The live partial-swap certificate is regenerated with its own generator. Exactly
+one source hash changes; all mathematical values remain byte-identical. The two
+existing optimization test suites and package verifiers bind the repaired source
+hash. Their frozen baseline files, provenance manifests, performance receipts,
+and historical source commits remain unchanged. No archived mathematical
+certificate or expected circuit digest is edited.
+
+## Reproduction
+
+From the repository root, with Python 3.12 (the producer also needs a C++17 compiler):
+
+```sh
+python3.12 -B scripts/partial_swap_network.py
+python3.12 -B -m unittest discover -s tests -p 'test_partial_swap*.py'
+python3.12 -B scripts/research_package.py --package research/partial-swap-digest
+python3.12 -B scripts/research_package.py --package research/partial-swap-init
+make copied-fixed-reversed-producer
+```
+
+The package checks include h46 receipt equivalence, optimized-Python digest
+checks and certificate pin-only comparisons. Production support assertions are
+historically disabled by `python -O`; the negative controls run without `-O`.
+This repair does not alter that inherited interface.
+
+## Validation on the repaired source
+
+- Python 3.14.7 focused suite: 16 tests pass, including the new negative control.
+- Python 3.12.11 registered `partial-swap-digest` and `partial-swap-init`
+  packages: both pass their complete normal/optimized verification and tests.
+- `make copied-fixed-reversed-producer`: exit 0. Fresh h25 DAG, all 96,273
+  distinct matrix profiles, five-prime reconstruction, positive labels,
+  matching and the separate copied CRT audit pass.
+- `make verify`: exit 2 after the repaired producer and full geometry checks
+  pass. The next historical witness rejects its old source pin (see below).
+- `git diff --check`: pass.
+
+The unchanged h25 scalar digest is
+`69283632099c012ae00cf1e9ab5b1f0757912944ff0708aa6cbf7633d841fd88`;
+the exported DAG hash is
+`ab28c3eba56b4b494f659b833c5aba4bb3e1e2225c3294411edf51a3999f1d03`.
+The repaired source hash is
+`5a0646a50b9f3e8ea55168620a78e8853b0ab810517cefc8cfb8696aedee278a`.
+
+The broad historical sweep next fails in
+`research/copied-fixed-reversed/witness.py:verify_sources`: its frozen manifest
+requires `shared.py` hash `81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34`,
+whereas pinned main already contains
+`7290bd639600aecff11941d3faf95c9ce95589125cc6a7f7440fb86af7a0f17c`.
+Comparing the manifest and source directly at the pinned main commit confirms
+this mismatch predates this repair. The manifest remains unchanged; this PR does
+not claim that the complete historical sweep passes. The selected cold replay,
+Lean and unrelated historical sweeps were not rerun for this verifier-only change.
+
+Open next question: separately reconcile historical witness provenance with live
+tooling, retaining explicit equivalence evidence and immutable original pins.
+
+## Scope and credit
+
+Douglas R. Colkitt authored the shared-point and exclusion circuits; icekylinx
+adapted the partial-swap producer; Wentao Li (VictorLiwentao) contributed the
+PR2039 optimizations. The h25 producer credits the PR36/PR21 base-two graph,
+PR32 structured profiler and Zhihao Chen's PR29 label audit. All existing license
+and attribution notices are preserved. SovereignSteak prepared this repair with
+OpenAI Codex assistance.
+
+No asymptotic construction, conditional hypothesis or selected record changes.
+Finite verification here does not prove the full conditional multiplication theorem.
diff --git a/research/partial-swap-digest/verify.py b/research/partial-swap-digest/verify.py
index b659164f63..557efa007f 100644
--- a/research/partial-swap-digest/verify.py
+++ b/research/partial-swap-digest/verify.py
@@ -27,7 +27,7 @@
 BASE_COMMIT = "0b1cccf86e2f5132ed286a26ef0a681a495740ea"
 ORIGINAL_BLOB = "a2f0190704db83bd8ef48e46e723c49b925804fe"
 ORIGINAL_SHA256 = "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34"
-OPTIMIZED_SHA256 = "7290bd639600aecff11941d3faf95c9ce95589125cc6a7f7440fb86af7a0f17c"
+OPTIMIZED_SHA256 = "5a0646a50b9f3e8ea55168620a78e8853b0ab810517cefc8cfb8696aedee278a"
 BASE_CERT_SHA256 = "f3c4be597b2f2136da4ae2cc80c7454f63c90aa01f84e5b8131cee4dd55de815"
 CERT_REL = "certificates/partial-swap-network.json"
 SOURCE_REL = "scripts/partial_swap/shared.py"
diff --git a/research/partial-swap-init/verify.py b/research/partial-swap-init/verify.py
index fd2290bff7..02b3a3d39f 100644
--- a/research/partial-swap-init/verify.py
+++ b/research/partial-swap-init/verify.py
@@ -28,7 +28,7 @@
 BASE_COMMIT = "3b29a00f972bd15871baac0acf5ac204740a9863"
 ORIGINAL_BLOB = "77a3672dce3b377eee30a6c3e993a63c2d3840d5"
 ORIGINAL_SHA256 = "b27c8bfe1de3f7d2d5fb19ac742adf11597c2aaa7add68430443119997e646e8"
-OPTIMIZED_SHA256 = "7290bd639600aecff11941d3faf95c9ce95589125cc6a7f7440fb86af7a0f17c"
+OPTIMIZED_SHA256 = "5a0646a50b9f3e8ea55168620a78e8853b0ab810517cefc8cfb8696aedee278a"
 BASE_CERT_SHA256 = "6e6ebabf06ee125e58f6871748aaa1fddc4cbf5e70338c61742bca85b9b3e7d4"
 FULL_SIZE_SHA256 = "b0402f9eaaf138129939521c2a2ef1c3e8230b730de0a7bdea3596eb415dd173"
 CERT_REL = "certificates/partial-swap-network.json"
diff --git a/scripts/partial_swap/shared.py b/scripts/partial_swap/shared.py
index 9a48086000..44a0e454c7 100644
--- a/scripts/partial_swap/shared.py
+++ b/scripts/partial_swap/shared.py
@@ -168,10 +168,10 @@ def verify(self):
         for (common,target),node in sorted(self.outputs.items()):
             excluded=tuple(sorted(points[common].index(x) for x in target if x!=common))
             assert support_in(node,common)==local_support[local_outputs[excluded]]
-            t0,t1,t2=target
+            target_text=','.join(map(str,target))
             # Byte-identical to json.dumps((common,target,node),
             # separators=(',',':'))+'\n'
-            update(encode(f'[{common},[{t0},{t1},{t2}],{node}]\n'))
+            update(encode(f'[{common},[{target_text}],{node}]\n'))
         return dict(h=self.h,inputs=len(self.inputs),partial_outputs=len(self.outputs),
                     additions=self.additions,roles=self.additions+len(self.outputs),
                     merged_additions=self.merged,
diff --git a/tests/test_partial_swap_digest.py b/tests/test_partial_swap_digest.py
index 409e07e282..edf131a2b6 100644
--- a/tests/test_partial_swap_digest.py
+++ b/tests/test_partial_swap_digest.py
@@ -14,9 +14,10 @@
 sys.path.insert(0, str(ROOT / "scripts"))
 
 from partial_swap import shared as production  # noqa: E402
+from partial_swap.graph import graph  # noqa: E402
 
 ORIGINAL_SHA256 = "81e9af92cdf38243a540cdcff2062778e449467848d444da37a9553c12ca4c34"
-OPTIMIZED_SHA256 = "7290bd639600aecff11941d3faf95c9ce95589125cc6a7f7440fb86af7a0f17c"
+OPTIMIZED_SHA256 = "5a0646a50b9f3e8ea55168620a78e8853b0ab810517cefc8cfb8696aedee278a"
 
 
 def load_baseline():
@@ -74,6 +75,30 @@ def test_small_circuit_receipts_match(self):
                 circuit.verify(),
             )
 
+    def test_retained_total_receipts_match(self):
+        # graph() adds an empty-exclusion local output, lifted to (common,).
+        for h in (6, 8, 10, 25):
+            with self.subTest(h=h):
+                circuit = graph(h)
+                self.assertEqual(sum(len(t) == 1 for _, t in circuit.outputs), h)
+                receipt = circuit.verify()
+                self.assertEqual(self.baseline.SharedPointCircuit.verify(circuit), receipt)
+                if h == 25:
+                    frozen = json.loads((ROOT / "research/copied-fixed-reversed/producer-input-25.json").read_text())
+                    self.assertEqual(receipt, frozen["scalar"])
+
+    def test_wrong_retained_total_rejected(self):
+        circuit = graph(8)
+        key = next(key for key in circuit.outputs if len(key[1]) == 1)
+        common = key[0]
+        # A proper excluded-pair sum cannot replace the full retained total.
+        circuit.outputs[key] = next(node for (c, t), node in circuit.outputs.items()
+                                    if c == common and len(t) == 3)
+        with self.assertRaises(AssertionError):
+            circuit.verify()
+        with self.assertRaises(AssertionError):
+            self.baseline.SharedPointCircuit.verify(circuit)
+
     def test_support_rejection_preserved(self):
         circuit = production.SharedPointCircuit(8)
         node = next(n for n in circuit.active if circuit.args[n])
diff --git a/tests/test_partial_swap_init.py b/tests/test_partial_swap_init.py
index 23f0505a28..76d641d069 100644
--- a/tests/test_partial_swap_init.py
+++ b/tests/test_partial_swap_init.py
@@ -19,7 +19,7 @@
 
 BASE_COMMIT = "3b29a00f972bd15871baac0acf5ac204740a9863"
 ORIGINAL_SHA256 = "b27c8bfe1de3f7d2d5fb19ac742adf11597c2aaa7add68430443119997e646e8"
-OPTIMIZED_SHA256 = "7290bd639600aecff11941d3faf95c9ce95589125cc6a7f7440fb86af7a0f17c"
+OPTIMIZED_SHA256 = "5a0646a50b9f3e8ea55168620a78e8853b0ab810517cefc8cfb8696aedee278a"
 
 
 def load_baseline():