diff --git a/docs/tickets/ticket-000034-hessian-alignment-phi-linear.md b/docs/tickets/ticket-000034-hessian-alignment-phi-linear.md
index 37ba203..e679a42 100644
--- a/docs/tickets/ticket-000034-hessian-alignment-phi-linear.md
+++ b/docs/tickets/ticket-000034-hessian-alignment-phi-linear.md
@@ -171,10 +171,103 @@ across runs to detect drift in the analysis.
 
 **Open · awaiting go/no-go.** Parks until a v7 reference
 checkpoint is available; the analysis is empirical-only and
-useless without representative training data. Recommended
-deferral to v7 deployment ramp-up.
+useless without representative training data on the V7 deployment
+side. **Phase 1a (synthetic-ablation) proposed below as a way
+to land probe infrastructure ahead of v7 ramp-up — same pattern
+as #000035 Phase 1.**
 
-Closure criterion: `bench/scripts/phi_alignment_probe.py` lands
-+ a measurement run against a representative checkpoint
-produces a verdict that resolves §9.1 of `docs/soft-hash-
-channel-analysis.md`.
+### Phase 1a — synthetic-ablation probe (proposed, not landed)
+
+Mirrors the #000035 pattern: ship the deterministic primitive +
+unit tests + KAT-style verification on a synthetic input ahead
+of the real-deployment target, so the cryptographic / numerical
+infrastructure is unit-tested + bench-pinned the moment v7
+deployment provides a real checkpoint.
+
+What lands in Phase 1a:
+
+- ``bench/scripts/phi_alignment_probe.py`` (~150 LOC) per §3.1.
+  Public surface:
+
+  ```python
+  def measure_alignment(
+      W: numpy.ndarray,                  # dim_d × 256, frozen
+      hessian_eval: Callable[[numpy.ndarray], numpy.ndarray],
+                                          # closure: x → H @ x
+      *,
+      k_top: int = 100,
+      k_bot: int = 100,
+      epsilon: float = 1e-6,
+  ) -> AlignmentReport
+  ```
+
+  ``AlignmentReport`` carries top-k / bottom-k eigenvalue
+  spectra, per-eigenvector alignment scores, the aggregate
+  ``A(W, H_top) / A(W, H_uniform)`` ratio, and a verdict label
+  per §3.3 thresholds (``STRUCTURAL_ALIGNMENT`` /
+  ``NO_ALIGNMENT`` / ``ANTI_ALIGNED``).
+
+- ``bench/fixtures/phi-alignment/synthetic-checkpoints.jsonl``
+  (~30 KAT entries). Each row pins a synthetic ``(W, H)`` pair
+  with a deterministic seed AND the expected verdict. Three
+  classes:
+
+  1. **Aligned**: W's columns engineered to lie in the
+     low-eigenvalue subspace of a known-eigenstructure quadratic.
+     Expected verdict: ``STRUCTURAL_ALIGNMENT``.
+  2. **Uniform**: W ~ Gaussian(0, 1/dim_d) — the v7 reference
+     spec — measured against an isotropic Hessian. Expected
+     verdict: ``NO_ALIGNMENT``.
+  3. **Anti-aligned**: W's columns deliberately placed in the
+     high-eigenvalue subspace. Expected verdict:
+     ``ANTI_ALIGNED``.
+
+- ``tests/test_phi_alignment_probe.py``:
+
+  - Round-trip determinism (same seed → same alignment score).
+  - Verdict thresholds (engineered cases land in their expected
+    bucket; boundary cases land cleanly).
+  - Lanczos convergence on the synthetic Hessian (top-k matches
+    a known dense decomposition).
+  - Module export shape.
+  - KAT regression against the fixture.
+
+- New optional-deps block in ``pyproject.toml``:
+
+  ```toml
+  [project.optional-dependencies]
+  hessian = [
+    # Lanczos top-k / bottom-k eigendecomposition for the
+    # phi_alignment_probe (#000034). Pulled into a separate
+    # extras to keep the core install lightweight; same
+    # pattern as the [math] extras for sympy. Tests skip via
+    # pytest.importorskip when absent.
+    "numpy>=1.26",
+    "scipy>=1.11",
+  ]
+  ```
+
+  Tests fail-soft via ``pytest.importorskip("scipy.sparse.linalg")``.
+  Operators run real-checkpoint measurements via
+  ``pip install 'arborist[hessian]'``.
+
+What does NOT land in Phase 1a:
+
+- Real v7 checkpoint measurement (gates on v7 deployment producing
+  a representative checkpoint per §5 / original §7).
+- M1 / M2 implementation (separate tickets).
+- Adversarial-training experiment (out-of-scope per §4).
+
+### Phase 1b — real-checkpoint measurement (parks)
+
+Original §7 deferral preserved. When a v7 reference checkpoint
+becomes available, run ``measure_alignment`` against it; the
+verdict resolves §9.1 of ``docs/soft-hash-channel-analysis.md``
+and either closes #000018's open question (NO_ALIGNMENT) or
+escalates M1 priority (STRUCTURAL_ALIGNMENT).
+
+### Closure criterion (unchanged)
+
+Closes when Phase 1b lands a real-checkpoint measurement that
+resolves the §9.1 open question — Phase 1a is the prerequisite
+infrastructure, not closure.