diff --git a/tests/test_third_door_blueprint_fidelity.py b/tests/test_third_door_blueprint_fidelity.py
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+"""Third-Door blueprint-fidelity ledger.
+
+The ADR-0239 geometry suite (``test_adr_0239_dynamic_manifold.py``) only ever
+exercises the *identity + single-plane rotor* regime — the one input class where
+``rotor_power`` does not hit its non-simple-bivector identity fallback, and where
+several assertions are tautologies (``residual >= 0``, ``reconstruction_residual
+>= 0``). This file exercises the operators on realistic *composed* conformal
+versors (products of rotations on distinct planes — what a real field state
+looks like) and encodes the properties the Super-Blueprint / R&D-Revised
+blueprints actually REQUIRE.
+
+The blueprints are the rigorous artifact; the landed code substitutes heuristics.
+So the spec-property tests here are marked ``xfail(strict=True)`` with reasons
+citing the blueprint section + audit finding. When an operator is implemented to
+spec, its xfail flips to xpass (strict) and CI forces the marker's removal.
+
+Empirical findings (2026-07-11 audit, reproduced deterministically below):
+  #1  supervised_blend is a no-op for interior alpha on composed versors
+      (rotor_power returns identity for the non-simple transition rotor);
+      versor_condition stays ~1e-16 and masks it.
+  #2  cartan_iwasawa_factorize raises "factor R not closed" on composed
+      conformal versors (~45% of the time), instead of the "mathematically
+      exact, guaranteed" decomposition the Super-Blueprint §2.2 specifies.
+
+See PR description and the fidelity table for the full spec-vs-impl ledger.
+"""
+
+from __future__ import annotations
+
+import numpy as np
+import pytest
+
+from algebra.cl41 import geometric_product
+from algebra.rotor import make_rotor_from_angle
+from core.physics.dynamic_manifold import cartan_iwasawa_factorize
+from core.physics.goldtether import GoldTetherMonitor
+
+
+def _identity() -> np.ndarray:
+    v = np.zeros(32, dtype=np.float64)
+    v[0] = 1.0
+    return v
+
+
+def _composed_versor(planes: tuple[int, ...], seed: float) -> np.ndarray:
+    """A realistic multi-plane conformal versor.
+
+    The product of >=3 rotations on distinct bivector planes is a *non-simple*
+    even versor (its grade-2 part squares to more than a scalar). This is the
+    generic case for any field state built from a sequence of word-versors —
+    and the case the ADR-0239 tests never cover.
+    """
+    v = _identity()
+    for k, idx in enumerate(planes):
+        angle = 0.3 + 0.13 * k + 0.05 * seed
+        v = geometric_product(v, make_rotor_from_angle(angle, bivector_idx=idx))
+    return v
+
+
+# --- Finding #1: supervised_blend geodesic ----------------------------------
+
+def test_supervised_blend_currently_degenerates_on_composed_versors():
+    """CHARACTERIZATION of finding #1 — locks the current (defective) behaviour.
+
+    On a composed pair, the "geodesic" collapses onto the source for every
+    interior alpha while closure stays green. This test PASSES today. When
+    supervised_blend is fixed to spec it SHOULD start failing — at which point
+    delete this test and drop the xfail on the spec test below.
+    """
+    a = _composed_versor((6, 7, 8, 10, 11), seed=1.0)
+    b = _composed_versor((6, 7, 8, 10, 11), seed=2.0)
+    m = GoldTetherMonitor()
+    for alpha in (0.25, 0.5, 0.75):
+        mid = m.supervised_blend(a, b, alpha)
+        assert np.allclose(mid, a, atol=1e-12), "no-op degeneration expected (finding #1)"
+
+
+@pytest.mark.xfail(
+    reason=(
+        "Finding #1 / R&D-Revised §2.3: supervised_blend applies rotor_power to the "
+        "whole (non-simple) transition rotor B*rev(A); rotor_power returns identity "
+        "for non-simple bivectors, so the blend is a no-op for interior alpha and only "
+        "reaches the target via the explicit alpha>=1 shortcut. versor_condition passes "
+        "and cannot detect it. Spec requires a genuine BCH-free geodesic (Cartan-Iwasawa "
+        "factor-wise slerp) that interpolates strictly between the endpoints."
+    ),
+    strict=True,
+)
+def test_supervised_blend_should_interpolate_composed_versors():
+    a = _composed_versor((6, 7, 8, 10, 11), seed=1.0)
+    b = _composed_versor((6, 7, 8, 10, 11), seed=2.0)
+    mid = GoldTetherMonitor().supervised_blend(a, b, 0.5)
+    # Spec: a midpoint interpolation is strictly between the endpoints.
+    assert float(np.linalg.norm(mid - a)) > 1e-9, "mid collapsed onto source"
+    assert float(np.linalg.norm(mid - b)) > 1e-9, "mid collapsed onto target"
+
+
+# --- Finding #2: Cartan-Iwasawa decomposition -------------------------------
+
+def test_cartan_iwasawa_currently_raises_on_composed_versor():
+    """CHARACTERIZATION of finding #2 — locks the current (defective) behaviour.
+
+    Deterministic composed versor that the heuristic factorizer cannot close.
+    PASSES today (asserts the raise). Delete when the spec algorithm lands.
+    """
+    v = _composed_versor((6, 7, 8), seed=0.0)
+    with pytest.raises(ValueError, match="not closed"):
+        cartan_iwasawa_factorize(v)
+
+
+@pytest.mark.xfail(
+    reason=(
+        "Finding #2 / Super-Blueprint §2.2: cartan_iwasawa_factorize is specified as a "
+        "'mathematically exact, non-iterative' decomposition that 'guarantees perfect "
+        "decomposition' via the action of V on n_o / n_inf. The landed grade-projection "
+        "heuristic instead raises 'factor R not closed' on composed conformal versors "
+        "(~45% at 3-4 planes). Spec: factorization must succeed and R*T*D must "
+        "reconstruct V to < 1e-6."
+    ),
+    strict=True,
+)
+def test_cartan_iwasawa_should_reconstruct_composed_motion():
+    v = _composed_versor((6, 7, 8), seed=0.0)
+    fac = cartan_iwasawa_factorize(v)  # spec: must not raise
+    recon = geometric_product(geometric_product(fac.R, fac.T), fac.D)
+    assert float(np.linalg.norm(recon - v)) < 1e-6