diff --git a/docs/EDCM_MATHEMATICS.md b/docs/EDCM_MATHEMATICS.md
index 6c0c203..85c1a62 100644
--- a/docs/EDCM_MATHEMATICS.md
+++ b/docs/EDCM_MATHEMATICS.md
@@ -294,20 +294,27 @@ N_t=\operatorname{clamp}\left(
 \right).
 $$
 
-### Confidence polarity
+### Scope motion compatibility carrier
 
-Let $o_t$ and $u_t$ be overconfidence and under-confidence marker hits:
+Bare $O$ is a legacy scalar carrier, not a canonical metric identity. The
+maintained baseline binds it explicitly to
+`edcm.behavioral.O_scope`; `edcm.behavioral.O_confidence` remains a distinct
+canonical axis and is not produced by `RoundMetrics`.
 
-$$
+Let $e_t$ and $c_t$ be hits from the frozen `scope_expansion` and
+`scope_containment` marker categories:
+
+$
 O_t=
 \begin{cases}
-0,&o_t+u_t=0,\\
-2\dfrac{o_t}{o_t+u_t}-1,&o_t+u_t>0.
+0,&e_t+c_t=0,\\
+2\dfrac{e_t}{e_t+c_t}-1,&e_t+c_t>0.
 \end{cases}
-$$
+$
 
-Positive is overconfident, negative is under-confident. This baseline zero is
-a within-domain no-hit value; it must not be reused as typed absence.
+Positive is scope expansion/overextension and negative is scope
+contraction/containment. This baseline zero is a within-domain no-hit value; it
+must not be reused as typed absence.
 
 ### Coherence loss
 
@@ -628,9 +635,13 @@ The field reader retains `previous_field_hash->current_field_hash` and appends
 the motion-presence flag and the three exact read tuples. This is a
 runtime-language identity contract, not a portable canonical-JSON signature.
 
-The axis registry also names $C,R,D,I,F,E,O_{scope},O_{confidence},L_{load},
-L_{loss},L_{resistance},N,P,\kappa$ and the six projections. Registration does
-not make an axis canonical.
+The axis registry names distinct canonical identities
+$O_{scope}\ne O_{confidence}$ and
+$L_{load}\ne L_{loss}\ne L_{resistance}$ alongside the remaining axes and
+projections. A bare symbol is not canonical identity. The maintained legacy
+round-vector carriers bind $O\rightarrow O_{scope}$ and
+$L\rightarrow L_{loss}$; those compatibility bindings do not alias the sibling
+axes.
 
 ## 10. Implemented v0.3.1 architecture layer
 
diff --git a/docs/metric-origin-domain-claim.md b/docs/metric-origin-domain-claim.md
index 51e9586..f5a0b66 100644
--- a/docs/metric-origin-domain-claim.md
+++ b/docs/metric-origin-domain-claim.md
@@ -25,12 +25,18 @@ neighboring_terms:
   - semantic trajectory
 known_collisions:
   - UCNS geometric origin remains separate
-effective_version: metric-origin-v0
-supersedes: none
+  - legacy single-letter O and L carriers are noncanonical identities
+effective_version: metric-origin-v0.1
+supersedes: metric-origin-v0
+resolved_identity_split:
+  - O_scope != O_confidence
+  - L_load != L_loss != L_resistance
+legacy_carrier_targets:
+  O: edcm.behavioral.O_scope
+  L: edcm.behavioral.L_loss
 unresolved:
   - authority provenance for the originating operator declaration
-  - O naming conflict: Overextension versus Overconfidence
-  - L naming conflict: Load versus Coherence Loss
+  - lawful observed-construct to semantic-origin projection/distance
 ```
 
 The circularity firewall is binding:
diff --git a/edcm/measurement/metrics/matrix.py b/edcm/measurement/metrics/matrix.py
index 1b63c23..3ffbe4e 100644
--- a/edcm/measurement/metrics/matrix.py
+++ b/edcm/measurement/metrics/matrix.py
@@ -17,7 +17,7 @@
 Notes on invariants
 -------------------
 - All Layer 1 metrics except O are [0, 1].
-- O is [-1, 1]: positive = overconfident, negative = under-confident.
+- O is [-1, 1]: positive = scope expansion/overextension, negative = scope contraction/containment.
   It is the only signed metric.  Callers that need [0, 1] should use
   abs(O) or (O + 1) / 2 as appropriate; the signed range is preserved
   here for full fidelity.
@@ -94,8 +94,8 @@
 #   marker_C      MarkerHits(C, contradiction)       (÷token_count before use)
 #   marker_R      MarkerHits(R, refusal)             (÷token_count before use)
 #   marker_I      MarkerHits(I, integration-fail)    (÷token_count before use)
-#   marker_O_over MarkerHits(O, overconfidence)      (signed, see O row)
-#   marker_O_under MarkerHits(O, under-confidence)   (signed, see O row)
+#   marker_O_expand MarkerHits(O, scope_expansion)  (signed, see O row)
+#   marker_O_contain MarkerHits(O, scope_containment) (signed, see O row)
 #   loop_risk     composite (rep_b, rep_ngram, cosine_ab) — see risk.py
 #   entropy_gain  ΔH between rounds                  (for P)
 # ---------------------------------------------------------------------------
@@ -136,11 +136,11 @@
         "I": {
             "marker_I": 1.0,
         },
-        # O: overconfidence — signed [-1, 1]
-        #    O = (over - under) / (over + under); weights are directional
+        # O: legacy carrier for canonical O_scope — signed [-1, 1]
+        #    O = (expansion - containment) / (expansion + containment)
         "O": {
-            "marker_O_over":  +1.0,
-            "marker_O_under": -1.0,
+            "marker_O_expand":  +1.0,
+            "marker_O_contain": -1.0,
         },
         # L: coherence loss — repetition + low novelty
         "L": {