diff --git a/complete/2026/07/delaunay-frozen-tables-gradient.md b/complete/2026/07/delaunay-frozen-tables-gradient.md
new file mode 100644
index 00000000..c80faeb6
--- /dev/null
+++ b/complete/2026/07/delaunay-frozen-tables-gradient.md
@@ -0,0 +1,133 @@
+## delaunay-frozen-tables-gradient
+- completed: 2026-07-26
+- branch: `claude/rectangular-mesh-gradients-mh1j0z` (PyAutoArray + autolens_workspace_test + autolens_workspace_developer; PR/merge pending with the rest of the session's mesh-gradients work — no issue was opened, the task was conceived and executed in the same session)
+- key commits: PyAutoArray `feat: unlock jax.grad through the Delaunay mesh via frozen integer tables` + `docs: state the sense in which the Delaunay mesh is autodifferentiable`; autolens_workspace_test `test: jax_grad FD certification for the Delaunay mesh`
+- verdict: SHIPPED — the Delaunay mesh is autodifferentiable (a.e.-exact frozen-tables gradient)
+- summary: |
+    The 2026-07-09 audit's "Delaunay is hard-undifferentiable" verdict was
+    stale: the visibility-walk refactor had moved every differentiable
+    quantity (point location, barycentric weights, dual areas, split points)
+    in-graph, leaving the host qhull `pure_callback` returning only int32
+    connectivity tables. Those tables are piecewise-constant in the vertex
+    positions — their true derivative is zero between triangle-flip events —
+    so wrapping the callback input in `jax.lax.stop_gradient` (one line in
+    `_jax_delaunay_tables`) yields the EXACT almost-everywhere derivative,
+    not an approximation. Values are bit-identical (primal untouched): the
+    jax_likelihood delaunay regression literal passes unchanged.
+
+    Certification (new `autolens_workspace_test/scripts/imaging/jax_grad/delaunay.py`,
+    production shape: Hilbert image mesh + circle edge zeroing +
+    reg.AdaptSplit(0.1, 10), 14-param truth-centred lens): all params live,
+    eager==jit, FD-step-sweep with lens light at 1e-8..1e-10 and mass/shear
+    at 1e-5..2e-3 (documented rtol=1e-2 — the scatter is FD steps straddling
+    flip events, the measure-zero jump seams where no method has a gradient;
+    AD differentiates the branch the point is on).
+
+    THE SENSE IN WHICH IT IS AUTODIFFERENTIABLE (now in the Delaunay class
+    docstring): ReLU-network territory — piecewise-smooth, smooth within
+    each triangulation topology, measure-zero jump discontinuities at flips.
+    Contrast the kernel-CDF rectangular meshes: C-infinity by construction,
+    no seams — still the cleanest gradient-inference choice; Delaunay is the
+    scientifically exact piecewise-smooth alternative.
+
+    REMAINING TRADE (documented, not fixed): the tables callback is
+    `vmap_method="sequential"` — one host qhull call per vmap lane — so the
+    KNN meshes keep the batched-throughput niche until the callback is
+    batched (delaunay_research.md option B territory).
+
+    Lore: the audit README's "Why Delaunay gradients are infeasible" section
+    assessed the PRE-walk architecture (callback returned float split_points
+    /mappings, where freezing would have dropped real terms); its point 3
+    (the frozen gradient is the correct a.e. derivative) is what this ships.
+    Probe pattern for the unlock: monkeypatch stop_gradient, value_and_grad,
+    FD sweep — 30 minutes from hypothesis to evidence.
+
+## Original prompt
+
+# Delaunay frozen-tables gradient — unlock jax.grad with stop_gradient on the tables callback
+
+Type: feature
+Target: autoarray
+Repos:
+- PyAutoArray
+- autolens_workspace_test
+- autolens_workspace_developer
+Difficulty: medium
+Autonomy: supervised
+Priority: high
+Status: draft
+
+## The finding (probed 2026-07-26, wrap-up of the mesh-gradients assessment)
+
+The Delaunay mesh's "hard-undifferentiable" verdict (2026-07-09 audit) is
+**stale**: since the visibility-walk landed, the JAX path
+(`jax_delaunay` in `autoarray/inversion/mesh/interpolator/delaunay.py`) runs
+everything differentiable **in-graph** — point location, barycentric weights,
+dual areas, split points — and the `pure_callback` returns only int32
+triangulation tables (`simplices`, `neighbors`, `vertex_simplex`). Those
+tables are piecewise-constant in the vertex positions (their true derivative
+is zero between re-wiring events), so freezing them is NOT an approximation:
+it is the exact almost-everywhere derivative of the likelihood.
+
+The unlock is one line — the callback input just needs to be excluded from
+differentiation:
+
+```python
+def _tables_stopgrad(points):
+    return _orig_tables(jax.lax.stop_gradient(points))
+```
+
+Probe (monkeypatch, jax_test 14-param fiducial, full production shape:
+Hilbert image mesh + circle edge zeroing + `reg.AdaptSplit(0.1, 10)`):
+
+- `value_and_grad` finite, non-zero, mass/shear live on all 14 params.
+- eager == jit (rtol 1e-10).
+- FD-step-sweep: **median rel err 9.6e-6, max 2.1e-3** (worst:
+  `mass.ell_comps_0`) — the residual scatter on mass params is FD stepping
+  across re-wiring events (measure-zero discontinuities, same class as the
+  KNN meshes' neighbour swaps and the certified branch flips of
+  PyAutoArray#377), while lens-light params match at 1e-8–1e-10.
+
+Probe script pattern: `jax_grad/knn.py` composition with
+`mesh=al.mesh.Delaunay(pixels, zeroed_pixels)`; the monkeypatch above.
+
+## Task
+
+1. Ship the unlock in `_jax_delaunay_tables` (stop_gradient on `points`
+   before the callback — or an equivalent `custom_jvp` zero rule if
+   stop_gradient interacts badly with anything). Values are bit-identical
+   (the primal is untouched); only differentiation behaviour changes, from
+   "raises" to "exact a.e. gradient".
+2. Certification: add a Delaunay variant to
+   `autolens_workspace_test/scripts/imaging/jax_grad/` (mirror `knn.py`;
+   FD-step-sweep, documented tolerance for the re-wiring FD scatter —
+   probe suggests rtol 3e-3 or per-param exclusions à la the os_pix=1
+   einstein_radius precedent). Re-run the delaunay jax_likelihood scripts
+   (imaging, interferometer, datacube, multi) to confirm values unchanged.
+3. Update `imaging/jax_grad/knn.py`'s docstring + the audit README's
+   Delaunay narrative ("Why Delaunay gradients are infeasible today" —
+   points 1–2 are superseded; point 3's a.e. analysis is what the probe
+   confirms) — partially done 2026-07-26 (row + findings-log updated;
+   the section prose still says infeasible).
+4. Samplers caveat to document: gradient-based searches see measure-zero
+   value discontinuities at re-wiring events (the interpolant jumps when a
+   containing triangle's diagonal flips) — same practical class as the
+   XLA branch flips (#377), but geometric in origin and mesh-density
+   dependent.
+
+## Why this matters
+
+Delaunay is the flagship source reconstruction (exact spatial locality,
+every vertex guaranteed simplex membership — the property whose absence
+sank the KNN-barycentric wildcard, PyAutoArray#317). This makes it
+gradient-capable at zero science cost. The remaining Delaunay-vs-KNN trade
+is batched throughput only: the tables callback is
+`vmap_method="sequential"` (one host qhull call per vmap lane), so KNN
+meshes stay preferable for heavily-vmapped samplers until the callback is
+batched (delaunay_research.md option B territory).
+
+## Constraints
+
+- The unlock must not change values (it cannot — primal untouched); the
+  jax_likelihood regression literals are the gate.
+- Library unit tests numpy-only; JAX validation via workspace_test jax_grad.
diff --git a/complete/index.md b/complete/index.md
index 02b9620b..3a77dec6 100644
--- a/complete/index.md
+++ b/complete/index.md
@@ -6,7 +6,7 @@ Token-light navigation over the finished-work records (schema:
 only then grep a dated bucket. Curators: edit the band between the CURATED
 markers; everything below GENERATED is rebuilt.
 
-739 records across 6 buckets.
+741 records across 6 buckets.
 
 <!-- CURATED:START -->
 ## Highlights
@@ -95,6 +95,7 @@ _(curate hard-won records here — survives regeneration.)_
 - [cti-resurrection-phase5](2026/07/cti-resurrection-phase5.md) — closed
 - [database-latent-wheel-load](2026/07/database-latent-wheel-load.md) — database scripts failed on release wheels loading latent variables → AssertionError. Release-tail item D. Corr…
 - [defunct-grids-yaml-removal](2026/07/defunct-grids-yaml-removal.md) — Deleted the 10 orphan `config/grids.yaml` copies plus 3 references (2 library `config/README.md` bullets, 1 `a…
+- [delaunay-frozen-tables-gradient](2026/07/delaunay-frozen-tables-gradient.md)
 - [delaunay-qhull-callback](2026/07/delaunay-qhull-callback.md)
 - [delete_pyautoheart_shim](2026/07/delete_pyautoheart_shim.md)
 - [desktop-acceptance-mcp](2026/07/desktop-acceptance-mcp.md)
@@ -259,6 +260,7 @@ _(curate hard-won records here — survives regeneration.)_
 - [prior-config-cache](2026/07/prior-config-cache.md) — The aggregator arc's "deeper follow-up" — cProfile showed 77% of per-result summary/model load was Model.__ini…
 - [prior-width-safety](2026/07/prior-width-safety.md) — Phase 2 of #1331 — RelativeWidthModifier abs(mean)+opt-in absolute_floor, default-path width guard (parameter-…
 - [priors-messages-fixes](2026/07/priors-messages-fixes.md) — Phase 1 of #1331 priors/messages batch — 7 fixes (01/02/04/10 + decisions 1/3/4), 12 regression tests, Fable m…
+- [profiling-dataset-auto-simulate](2026/07/profiling-dataset-auto-simulate.md) — PR #89
 - [profiling-mirror-taxonomy](2026/07/profiling-mirror-taxonomy.md) — profiling#85 + Brain#161
 - [profiling-preopt-campaign](2026/07/profiling-preopt-campaign.md) — Phase-3 (likelihood_runtime) leg of the polish.md PreOptimizationTimes campaign, frozen "done enough" at user …
 - [psf-convolution-docstring](2026/07/psf-convolution-docstring.md) — Normalized PSF-convolution docs across 41 simulator.py (both workspaces). Tier A (3 reference files: imaging/s…
diff --git a/draft/feature/autoarray/regularization_jax_gradient_gaps.md b/draft/feature/autoarray/regularization_jax_gradient_gaps.md
new file mode 100644
index 00000000..6a609dad
--- /dev/null
+++ b/draft/feature/autoarray/regularization_jax_gradient_gaps.md
@@ -0,0 +1,80 @@
+# Regularization JAX gradient gaps — xp-ports + kernel-scheme linear algebra
+
+Type: feature
+Target: autoarray
+Repos:
+- PyAutoArray
+- autolens_workspace_test
+Difficulty: medium
+Autonomy: supervised
+Priority: normal
+Status: draft
+
+## Context (2026-07-26 regularization × mesh gradient sweep)
+
+A full sweep of every `al.reg` scheme against the gradient-capable meshes
+(`RectangularAdaptDensity` os_pix=4; `KNearestNeighbor`/`KNNBarycentric`
+Hilbert + edge zeroing) mapped the JAX-gradient compatibility surface. The
+matrix and measurements live in
+`autolens_workspace_developer/jax_profiling/gradient/README.md`
+("Regularization × mesh gradient matrix"); positive certifications are
+pinned by `autolens_workspace_test/scripts/imaging/jax_grad/regularization.py`
+and the mesh-family negatives by `jax_grad/knn.py`. Three actionable gaps
+fell out — none blocks current production paths, so this is one prompt to
+be split or trimmed at start-dev if any leg grows:
+
+## 1. xp-ports — DONE
+
+*Both legs shipped 2026-07-26 on `claude/rectangular-mesh-gradients-mh1j0z`:
+`ExponentialKernel` (xp threaded through the covariance build, NaN-safe
+`sqrt(d²+1e-20)` distances) and `BrightnessZeroth` (the `pixel_signals_from`
+call site now threads `xp`). JAX gradients verified on both. Legs 2 and 3
+below remain the open work of this prompt.*
+
+## 2. Kernel-scheme linear algebra: avoid the explicit `C^-1` (the real one)
+
+`MaternKernel`/`MaternAdaptKernel`/`GaussianKernel` build
+`H = coefficient * inv_via_cholesky(C)` — an explicit dense inverse. On
+well-spaced vertices (rectangular mesh: cond(C) ≈ 3e5 at nu=2.5) this is
+fine and `MaternKernel(nu=2.5)` is strict-FD-certified (2.2e-4). On TRACED
+(clustered) mesh vertices (KNN meshes: min pairwise separation ~7e-3 vs
+median ~9e-2 → cond(C) ≈ 1.4e9 at nu=2.5) the explicit inverse puts a
+~1e-6..4e-5 absolute numerical noise floor on the likelihood itself
+(measured as eager-vs-jit LL differences), which caps FD verifiability at
+~1e-3..1e-2 relative and adds the same noise to sampler-visible likelihoods.
+
+Reformulation candidates (in the spirit of the opt-in slogdet, PyAutoArray#391):
+
+- Keep `H` implicit through the Cholesky of `C`: `s^T H s` via
+  `cho_solve(L, s)`, `log det H = -2 Σ log diag L` — no explicit inverse,
+  one factorization, strictly more accurate and faster. Requires the
+  inversion interface to accept an implicit/functional `H` (today it
+  consumes a dense matrix — check `curvature_reg_matrix` assembly).
+- Cheaper interim: scale the fixed `1e-8` diagonal jitter with the kernel's
+  dynamic range / N, and expose it as a kwarg.
+
+Gate any change on the `regularization.py` jax_grad script re-passing and
+on FoM parity on the numpy path.
+
+## 3. Split-family shape guard on rectangular meshes (papercut)
+
+`ConstantSplit`/`AdaptSplit`/`AdaptSplitZeroth` on a rectangular mesh fail
+with a raw broadcasting `TypeError` ((784,784) vs (3808,3808)): the split
+machinery assumes 4-cross-per-pixel splits, while the rectangular
+interpolator reuses its per-query 4-corner mappings for
+`_mappings_sizes_weights_split`. Either raise a clear
+"split regularization requires a Delaunay-family mesh" exception at
+composition time, or implement true pixel-centre crosses for the
+rectangular geometry (relates to
+`draft/feature/autoarray/rectangular_adapt_constant_split_guard.md` if that
+covers the same surface — merge at intake if so).
+
+## Out of scope
+
+- `ConstantZeroth` dead code — already filed
+  (`draft/bug/autoarray/constant_zeroth_broken_dead_code.md`).
+- `CurvatureMask`/`FourthOrderMask` — dpsi (potential-correction) schemes,
+  correctly incompatible with source meshes; nothing to fix.
+- Making neighbour-based schemes (`Constant`/`Adapt`) JAX-traceable on the
+  Delaunay mesh family (kNN-derived neighbours) — bigger design question,
+  only worth filing if a production pipeline needs it.