diff --git a/tests/test_engine_loop_proof.py b/tests/test_engine_loop_proof.py
new file mode 100644
index 00000000..129f38db
--- /dev/null
+++ b/tests/test_engine_loop_proof.py
@@ -0,0 +1,139 @@
+"""
+tests/test_engine_loop_proof.py
+
+Minimum executable proof that the CORE engine loop exists in running code:
+
+    inject -> generate -> final_state -> vault.store -> vault.recall
+
+This is intentionally narrow. It is not a benchmark suite and not a behavior
+quality test. It proves the refined engine contract after the generation seam,
+state immutability, backend routing, and assistant-final-state storage fixes.
+"""
+
+from __future__ import annotations
+
+import ast
+from pathlib import Path
+
+import numpy as np
+
+from algebra.versor import unitize_versor, versor_condition
+from generate.result import GenerationResult
+from generate.stream import generate
+from ingest.gate import inject
+from persona.motor import PersonaMotor
+from session.context import SessionContext
+from vault.store import VaultStore
+from vocab.manifold import VocabManifold
+
+
+ROOT = Path(__file__).resolve().parents[1]
+
+
+def _basis_versor(blade: int, scalar: float = 1.0) -> np.ndarray:
+    """Small deterministic construction helper for valid Cl(4,1) versors."""
+    v = np.zeros(32, dtype=np.float32)
+    v[0] = scalar
+    v[blade] = 0.25
+    return unitize_versor(v)
+
+
+def _minimal_vocab() -> VocabManifold:
+    """
+    Build a tiny deterministic manifold with non-identical entries.
+
+    Each entry is construction-unitized before insertion; VocabManifold owns
+    points only and does not build transition operators.
+    """
+    vocab = VocabManifold()
+    vocab.add("logos", _basis_versor(1))
+    vocab.add("arche", _basis_versor(2))
+    vocab.add("pneuma", _basis_versor(3))
+    vocab.add("truth", _basis_versor(4))
+    return vocab
+
+
+def test_minimum_engine_loop_is_deterministic_and_stores_generated_state() -> None:
+    vocab = _minimal_vocab()
+    persona = PersonaMotor.identity()
+    tokens = ["logos", "arche"]
+
+    initial = inject(tokens, vocab)
+    assert versor_condition(initial.F) < 1e-6
+
+    result = generate(initial, vocab, persona, max_tokens=3)
+    assert isinstance(result, GenerationResult)
+    assert isinstance(result.tokens, tuple)
+    assert result.tokens
+    assert result.final_state.step == initial.step + 3
+    assert not np.array_equal(result.final_state.F, initial.F)
+
+    repeated = generate(inject(tokens, vocab), vocab, persona, max_tokens=3)
+    assert repeated.tokens == result.tokens
+    np.testing.assert_array_equal(repeated.final_state.F, result.final_state.F)
+
+    vault = VaultStore()
+    stored_idx = vault.store(result.final_state.F, metadata={"role": "assistant"})
+    assert stored_idx == 0
+
+    recalled = vault.recall(result.final_state.F, top_k=1)
+    assert recalled[0]["metadata"]["role"] == "assistant"
+    assert recalled[0]["index"] == stored_idx
+    np.testing.assert_allclose(recalled[0]["versor"], result.final_state.F)
+    assert not np.array_equal(recalled[0]["versor"], initial.F)
+
+
+def test_session_context_respond_preserves_and_vaults_final_state() -> None:
+    session = SessionContext(vocab=_minimal_vocab())
+    initial = session.ingest(["logos", "arche"])
+
+    result = session.respond(max_tokens=3)
+
+    assert isinstance(result, GenerationResult)
+    assert session.state == result.final_state
+    assert not np.array_equal(result.final_state.F, initial.F)
+
+    recalled = session.vault.recall(result.final_state.F, top_k=1)
+    assert recalled[0]["metadata"]["role"] == "assistant"
+    np.testing.assert_allclose(recalled[0]["versor"], result.final_state.F)
+    assert not np.array_equal(recalled[0]["versor"], initial.F)
+
+
+def test_hot_path_modules_route_through_backend_boundary() -> None:
+    """
+    Production hot paths must route through algebra.backend for dispatch.
+
+    Direct algebra.cga/algebra.versor imports here would bypass Rust/Rayon when
+    available and violate the acceleration boundary established by Commit 2.
+    """
+    checked = {
+        "field/propagate.py": {
+            "required": {("algebra.backend", "versor_apply")},
+            "forbidden_modules": {"algebra.versor", ".versor"},
+        },
+        "vocab/manifold.py": {
+            "required": {("algebra.backend", "cga_inner")},
+            "forbidden_modules": {"algebra.cga", ".cga"},
+        },
+        "vault/store.py": {
+            "required": {("algebra.backend", "vault_recall")},
+            "forbidden_modules": set(),  # null_project may remain on algebra.cga.
+        },
+    }
+
+    for rel, rule in checked.items():
+        tree = ast.parse((ROOT / rel).read_text(encoding="utf-8"), filename=rel)
+        imports: set[tuple[str, str]] = set()
+        forbidden_hits: list[str] = []
+
+        for node in ast.walk(tree):
+            if isinstance(node, ast.ImportFrom):
+                module = node.module or ""
+                if module in rule["forbidden_modules"]:
+                    forbidden_hits.append(f"{rel}:{node.lineno}:{module}")
+                for alias in node.names:
+                    imports.add((module, alias.name))
+
+        missing = rule["required"] - imports
+        assert not missing, f"{rel} missing backend imports: {sorted(missing)}"
+        assert not forbidden_hits, "Forbidden hot-path imports:\n" + "\n".join(forbidden_hits)