GPU kernel registry

One row per kernel version. A result records the kernel that produced it (MetalKernelIdentity: name, version, source digest, pipeline variant, and a fingerprint over both), so any saved phase, export, or benchmark line can be traced to a row here.

Rules

• One production kernel per job. When a faster version is validated, it replaces the older one; the older one is retired, not kept as a silent fallback. Any case the new kernel cannot serve is named below and in code.

• Version on change. Editing a kernel’s .metal source or its numerical contract requires a new version here and in SSBKernelRegistry. SSBKernelRegistryTests fails when a shipped source digest does not match its registered version, or when this page lacks the version or digest.

• Active means measured. A version becomes active only with parity tests passing and both benchmark and in-app headed timings recorded with date, device, and dataset. Retired versions stay listed with their last numbers.

Timings are median / p90 ms per reconstruction. Device for all rows: MacBook Pro, Apple M5 Max, 40-core GPU, 128 GB, macOS 26.4. Data: a thick-crystal acquisition (the first below), 512 × 512 × 192 × 192, 8,806 bright-field pixels, 300 keV, 30 mrad; 256² rows use the same acquisition’s full detector at a 256² scan (docs/performance/ssb/reports/2026-10-24-native-metal-ssb-redraw.md).

Native SSB reconstruction (MetalSSBKernels)

Kernel	Status	Source digest	Serves	Validated	Fifth order, 512², 3×	Low order, 512², 3×	Fifth order, 256², 3×	Parity	Replaced by	Retired
ssb-redraw v0.3	active (in-app headed timing pending)	73dc413569c7	phase_of_mean (method ssb), 1–4×	2026-10-25	benchmark 30.8 / 31.4 (v0.2 30.5 / 31.3, runs alternating, paired median +0.1 ms); in app not yet measured	benchmark 39.9 (v0.2 40.3, alternating under background load; minimum 29.8 vs 29.4)	benchmark 10.3 / 10.7 (v0.2 10.1 / 10.3)	SSBRedrawReconstructionTests (per-term and double-precision references; testRedrawResolvesNearlyCancellingSidebands: 3.7e-8 rad rms where v0.2 is 4.5e-3); five measured acquisitions × eight optics sets × 1×, 2×, Auto against CUDA and a float64 definition: native−definition ≤ 1.08 and native−CUDA ≤ 1.13 times CUDA’s own error (v0.2: up to 2.45 / 2.53), report	—	—
ssb-redraw v0.2	retired (low-frequency precision; superseded by v0.3)	b20d7914811d	phase_of_mean (method ssb), 1–4× (also complex_wave until its retirement, 2026-10-25)	2026-10-24	benchmark 33.7 / 33.9; in app 30.3–33.0 (median ≈ 31.3, ≈ 32 FPS)	benchmark 31.2 / 31.5; in app 32.5–34.9	benchmark 9.9 / 10.0	SSBRedrawReconstructionTests (per-term and double-precision fifth-order references); SSBComplexWaveTests until 2026-10-25	ssb-redraw v0.3	2026-10-25
ssb-per-term v0.3	retired (test reference; explicit 8× only)	886e139608e3	8×; v0.2 without the deleted objective kernel fifth_agreement in the shared ssb_fifth_order source; per-term kernels unchanged	2026-10-25	as v0.1	as v0.1	as v0.1	reference for ssb-redraw v0.3; outputs bitwise those of v0.2 on the synthetic test scene (agreements, derivatives, gradients, reconstructions, drag previews, full fit; 2026-10-25)	ssb-redraw v0.2	2026-10-24
ssb-per-term v0.2	retired (test reference; explicit 8× only; superseded by v0.3, same kernels)	05177e0c2cde	8×; v0.1 without the retired complex_wave amplitude kernel, per-term kernels unchanged	2026-10-25	as v0.1	as v0.1	as v0.1	reference for ssb-redraw v0.2 and v0.3	ssb-redraw v0.2	2026-10-24
ssb-per-term v0.1	retired (test reference; explicit 8× only)	1c390cc7b833	1–4× before 2026-10-24; 8× now	before 2026-10-24	benchmark 214.9 / 223.8; in app ≈ 320	benchmark 60.4 / 64.3	benchmark 67.9 / 69.3	reference for v0.2	ssb-redraw v0.2	2026-10-24
ssb-mean-phase v0.1	retired (estimator removed)	4aa7c1da6391	mean_phase (C10/C12 only)	before 2026-10-24	n/a (no higher orders)	not remeasured	not remeasured	joint tests until 2026-10-25	phase / complex (ssb-direct); methods are ssb, phase, complex	2026-10-25

The first render after a fit costs about 100–130 ms in the app (pipeline variant compilation and warm-up); the steady drag rate above excludes it. In-app timings are MetalSSBJointPhase.wallSeconds on an otherwise idle GPU with one app instance on the built-in display.

Native regularized direct reconstruction (MetalSSBKernels)

Methods phase and complex of MetalSSBJointModel.reconstruct(_:upsamplingFactor:method:regularization:) (SSBDirectSolver, ssb_direct.metal), the port of the CUDA PreparedDirect: per scan frequency the normal equations of every supported output alias (direct_normal_equations: the weak-object transfer per BF pixel in float32 with CUDA’s expressions, products of open alias pairs, float32 batch sums met in float-float across BF batches), then float64 Cholesky solves of the damped systems on the CPU, then one inverse FFT of the packed eta + i phi spectrum (direct_wave). The layout (frequencies, aliases, priors, detector weights, dose) is kept per data, factor, prior and weighting; the prepared normal equations per optics, one per method (a complex system also serves phase), so a damping change only solves again.

Wall ms on an Apple M5 Max (metal-ssb-fit-benchmark --direct-parity / --fixture-parity, 2026-10-25): a measured 512 × 512 acquisition (9,298 BF pixels, 0.373 Å step, Auto 3×, 3–6 aliases per frequency) and a 0.525 Å-step one (9,289 BF pixels, Auto 4×, 7–12 aliases). “Optics change” is a call at new optics (layout and kernels kept: prepare + solve + wave; GPU prepare in brackets); “damping change” reuses the prepared system. The first call of a process adds the layout (3–7 ms) and kernel specialization (about 50–80 ms). In the app (headed, 2026-10-25): a C10 edit with Complex selected 484 ms, Phase’s first render 353 ms.

Kernel	Status	Source digest	Serves	Validated	Optics change 1× / 2× / 3× (0.373 Å)	Optics change 4× (0.525 Å)	Damping change	Parity	Replaced by	Retired
ssb-direct v0.4	active	817bc577037c	as v0.3; the k-only aperture term A(k) is CUDA’s square-pixel thick_probe_geometry (alpha^2 = r^2 wl^2, one fma for the edge), as the transfer’s A(k +- q)	2026-10-25	as v0.2	as v0.2	as v0.2	SSBDirectMeasuredParityTests (SSB_DIRECT_ALL=1) on two measured fixtures within 2x CUDA’s own error	—	—
ssb-direct v0.3	retired (A(k) from the general aperture formula, about 1 ulp from CUDA at the edge)	5ab966bbda82	as v0.2: v0.2 with the deleted agreement kernels removed from the shared ssb_joint and ssb_fifth_order sources; direct kernels unchanged	2026-10-25	as v0.2	as v0.2	as v0.2	outputs bitwise those of v0.2 on the synthetic test scene (agreements, derivatives, gradients, reconstructions, drag previews, full fit; 2026-10-25)	ssb-direct v0.4	2026-10-25
ssb-direct v0.2	retired (superseded by v0.3, same kernels)	4e0355f889a5	methods phase and complex, 1–4×, and their drag windows	2026-10-25	phase 45–50 / 118–123 / 165–175; complex 47–64 / 153–161 / 167–190 (one thread per frequency and alias for complex systems of two or more aliases, direct_normal_tiled)	not remeasured (the tiled kernel serves complex)	as v0.1	as v0.1 on every reconstruction of the five fixtures (see the parity record); drag previews within 1e-6 of the exact image’s std inside their window (SSBDirectDragWindowTests, --direct-drag)	ssb-direct v0.3	2026-10-25
ssb-direct v0.1	retired (direct_normal_equations alone; it still serves phase and 1× complex in v0.2)	8d1237658f22	methods phase and complex, 1–4×	2026-10-25	phase 53 / 128–148 / 175–183 (GPU 170); complex 54–57 / 204–210 / 280–287 (GPU 272–278)	phase 468 (GPU 450); complex 1228 (GPU 1201)	phase 0.7–4.7, complex 0.9–7.0 at 1–4×; 15 at 4× complex	five measured acquisitions × their optics × 1× and Auto × 5–7 regularization presets against CUDA (182 reconstructions): phase rms 4e-8–1.8e-7 rad, correlation ≥ 0.9999999999, complex amplitude relative rms ≤ 1.6e-7; against a float64 oracle the same size as CUDA’s own error; SSBDirectReconstructionTests (synthetic, in-test float64 reference)	ssb-direct v0.2	2026-10-25

Drag previews (v0.2, buildDragWindow / dragPreview, design note maintainer/2026-10-25-ssb-direct-drag-windows.md): a Chebyshev series of the prepared entries along the dragged control from 29 exact preparations (50 for an azimuth). At 3× a window builds in about 5 s; a preview frame takes 5–9 ms in the benchmark and, in the app while dragging C10 or C12, 5.4–5.9 ms (phase) and 9.8–10.4 ms (complex) per render with a render every 16–21 ms; it agrees with the exact image to about 1e-6 of its standard deviation.

Native SSB fit (MetalSSBKernels)

The primary (low-order) fit’s trust-region Newton climbs on the exact gradient and Hessian of the agreement in C10, C12 (two Cartesian components), the sample tilt and the depth spread (ssb_low_order_derivatives.metal, SSBLowOrderDerivatives). It replaces the finite-difference stencil of 13 or 28 objective evaluations per Newton iteration. v0.2 evaluates in stages: a value pass (the objective’s sums; the same 256-pixel partials and expressions as v0.1’s pass 1, with the soft-aperture shortcut, fast sincos, Markstein quotients and real anchor branches of ssb-joint-agreement v0.2), then, where the Newton uses them, the derivatives. Their pass forms 29 k-sums instead of v0.1’s 51 by two exact reductions: the depth-sinc weights depend on the tilt only through q·θ (so the tilt row and column derivatives are qx and qy times one derivative), and the C10/C12 phase slopes are linear in k (each sum over them is two k-moments, each product of two is three). The combine expands them to v0.1’s 51 per band frequency. For Newton centers whose derivatives it will use (every iteration but the pruned second one), a fused pass forms the value sums (bitwise those of the value pass) and the 43 derivative sums that need no model sum N, projected on conj N in the combine. No derivatives are formed at a rejected step or for the starts that the second iteration’s pruning stops.

GPU ms per center (median of seven calls, command-buffer GPU time; metal-ssb-fit-benchmark --objective-bench on the kept low-order fit of each app-matched case and three seeded random centers near it), Apple M5 Max, 2026-10-25. The v0.2 numbers were taken with heavier background GPU load than v0.1’s: the unchanged ssb-joint-agreement v0.2 single candidate measured 8.5 / 9.1 / 17.4 ms with v0.1 and 9.8 / 11.7 / 19.7 ms with v0.2. Fits (median of three, interleaved with the v0.1 build): Newton 0.91 → 0.34 s (first), 1.47 → 0.57 s (second acquisition), 1.83 → 0.74 s (third); same centers per start, same kept branch, low-order parameters within 2e-6 nm / 3.2e-5° / 1e-6 mrad.

Kernel	Status	Source digest	Serves	Validated	First (8,807 BF, 44,247 q)	Second (9,298 BF, 44,255 q)	Third (8,930 BF, 77,842 q)	Parity	Replaced by	Retired
ssb-low-order-derivatives v0.4	active	bd5adb61d4b7	as v0.3: v0.3 with the deleted agreement kernels removed from the shared ssb_joint source; derivative kernels unchanged	2026-10-25	as v0.3	as v0.3	as v0.3	outputs bitwise those of v0.3 on the synthetic test scene (agreements, derivatives, gradients, reconstructions, drag previews, full fit; 2026-10-25)	—	—
ssb-low-order-derivatives v0.3	retired (superseded by v0.4, same kernels)	0158114dc413	as v0.2: v0.2 with the retired mean_phase kernels removed from the shared ssb_joint source; derivative kernels unchanged	2026-10-25	as v0.2	as v0.2	as v0.2	as v0.2	ssb-low-order-derivatives v0.4	2026-10-25
ssb-low-order-derivatives v0.2	retired (superseded by v0.3, same kernels)	6178f0ed1613	primary-fit Newton (value, gradient, Hessian)	2026-10-25	fused 29.4 (one center) / 27.6 (three); value pass 11.2 + derivative pass 24.4	fused 27.5 / 26.2; value 12.0 + derivatives 25.9	fused 49.8 / 45.1; value 19.5 + derivatives 44.0	SSBModelReconstructionTests.testLowOrderDerivativesMatchFiniteDifferences (Richardson differences: gradient ≤ 3.8e-5, Hessian ≤ 3.5e-4 relative; value against the agreement objective ≤ 9e-7; fused and two-stage value bitwise equal, derivatives ≤ 7e-6; v0.1 value ≤ 2.2e-7, derivatives ≤ 1.3e-5), SSBAgreementSearchTests.testStagedExactNewtonMatchesOneStage; measured on the three acquisitions: value within 5.3e-10 of v0.1	ssb-low-order-derivatives v0.3	2026-10-25
ssb-low-order-derivatives v0.1 (ssb_low_order)	deleted 2026-10-25 (was the test reference of v0.2 and v0.3)	40da0bd64def	primary-fit Newton before 2026-10-25	2026-10-25	53.7 / 53.8 (pass 1 ≈ 16 + pass 2 ≈ 38)	57.2 / 58.5	101.6 / 104.3	reference for v0.2	ssb-low-order-derivatives v0.2	2026-10-25

Native SSB fifth-order gradient (MetalSSBKernels)

The exact-gradient search’s calls, GPU ms per call (command buffer; the wall time of a call exceeds it by about 0.3 ms), one candidate unless noted, at the app-matched kept rotation: the value pass, the gradient pass after it, and both together on all BF pixels; the same on every 8th BF pixel (coarse stage); the start Hessian batch (29 candidates on every 64th BF pixel). Min / median over 27 calls from three short runs alternating with v0.1 (the GPU throttles under sustained load and shows about 38% background use from the desktop, so long single runs read up to 1.8x slower). Data as below: the first, a thick-crystal acquisition (8,807 BF pixels, 44,247 band frequencies), the second (9,298, 44,255) and the third acquisition (8,930, 77,842). Benchmark: metal-ssb-fit-benchmark --objective-bench RUN.json --search-kernels-only, 2026-10-25.

Kernel	Status	Source digest	Serves	Validated	First	Second	Third	Parity	Replaced by	Retired
ssb-fifth-gradient v0.3	active (SSBModelFit.HigherOrderSearch.exactGradient*)	16e118d89846	as v0.2: v0.2 with the deleted fifth_agreement removed from the shared ssb_fifth_order source; gradient kernels unchanged	2026-10-25	as v0.2	as v0.2	as v0.2	outputs bitwise those of v0.2 on the synthetic test scene (agreements, derivatives, gradients, reconstructions, drag previews, full fit; 2026-10-25)	—	—
ssb-fifth-gradient v0.2	retired (superseded by v0.3, same kernels)	9a751b5a12ba	exact gradient of the fifth-order agreement (28 z: coefficients, depth, tilt) on all BF pixels or every n-th, after the ssb-fifth-agreement v0.3 value pass (fifth_gradient_scale, fifth_gradient_rows)	2026-10-25	all BF: value 9.8 / 11.0, gradient 16.5 / 18.4, both 27.8 / 29.2; every 8th: 1.35 / 1.40, 2.11 / 2.25, 3.45 / 3.63; Hessian batch 10.7 / 11.9	all BF: 10.2 / 11.5, 17.9 / 19.7, 28.5 / 31.6; every 8th: 1.38 / 1.49, 2.21 / 2.33, 3.60 / 3.97; Hessian 11.3 / 12.6	all BF: 18.4 / 18.8, 30.6 / 32.8, 49.1 / 52.9; every 8th: 2.21 / 2.50, 3.61 / 4.32, 5.97 / 7.06; Hessian 19.9 / 21.4	SSBFifthOrderGradientTests (double-precision central differences of all 28 z: worst 2.9e-6 of max|g| on all BF pixels, 2.6e-6 on every 3rd; value pass bit-identical to fifthOrderAgreements); measured against v0.1 at the same points: gradients within 3.5e-6 of max|g| at the search starts (within 4.6e-5 at the optima, where the gradient is float32 noise), agreements within 1.9e-7	ssb-fifth-gradient v0.3	2026-10-25
ssb-fifth-gradient v0.1	retired	dc8d80c38d16	before 2026-10-25 (value pass: fifth_agreement and its strided copy fifth_strided_agreement; BF- or band-subsampled agreement)	2026-10-25	all BF: 22.4 / 23.4, 33.0 / 35.4, 57.1 / 59.6; every 8th: 2.76 / 3.05, 4.15 / 4.25, 7.10 / 8.03; Hessian 22.4 / 23.6	all BF: 23.1 / 24.5, 35.3 / 38.0, 60.5 / 62.9; every 8th: 2.93 / 3.08, 4.34 / 4.68, 7.44 / 7.97; Hessian 23.6 / 24.8	all BF: 40.0 / 42.0, 60.1 / 64.3, 101.2 / 107.1; every 8th: 4.72 / 5.90, 7.25 / 9.66, 12.5 / 14.4; Hessian 39.7 / 43.1	SSBFifthOrderGradientTests (worst 3.6e-6 of max|g|)	ssb-fifth-gradient v0.2	2026-10-25

v0.2 evaluates the per-pair terms of the ssb-fifth-agreement value pass (band tiles, row-collapsed Horner phases, the exact soft-aperture shortcut, fast::sincos and Markstein division) and needs no per-pair basis: chi is a polynomial of degree at most 6 in k, so the coefficient gradient is linear in the monomial sums T_a = sum 2w [alpha1 ((k - q)^a - k^a) + alpha2 ((k + q)^a - k^a)], and by the binomial expansion (the k^a terms cancel exactly) T_a = sum over a’ < a of C(a, a’) q^(a - a’) [alpha2 + (-1)^|a - a’| alpha1] k^a’. Each thread (one band frequency) accumulates the 15 even and 21 odd moments of k (36 vector FMAs per pair against monomials shared in threadgroup memory; v0.1 evaluated three 28-term bases per pair) and shifts them by its q once; the host maps the 25 monomial sums to the 28 packed coefficients in double. A BF subsample keeps at least 32 pixels.

Fifth-order stage of the full native fit (metal-ssb-fit-benchmark --cache CASE --repeats 3, median, runs alternating with v0.1 on the same busy machine): first 0.91 → 0.46 s, second 1.31 → 0.60 s, third 1.36 → 0.68 s; same kept branch and rotation; Double-summed final agreement relative to v0.1 +1.5e-7, −1.5e-8, −2.6e-8 (float32 rounding of the reassociated value pass; C10 within 3.5e-4 nm).

Fit objectives (MetalSSBJointModel agreement)

GPU ms per candidate objective (median of three calls; command-buffer GPU time, which the wall time of the call exceeds by at most 0.3 ms) at a fit’s kept rotation. Fifth order: one candidate, four seeded random candidates, the 57-point Newton diagonal stencil, 64 random candidates. Low order: one candidate, eight (one search-trial batch) and 64 random candidates. Data: the first, a thick-crystal acquisition (8,805 BF pixels, 44,247 band frequencies), a second 512² acquisition (9,296 BF, 44,255) and a third (8,928 BF, 77,842), all 300 keV, 30 mrad. Benchmark: metal-ssb-fit-benchmark --objective-bench RUN.json, 2026-10-25.

Kernel	Status	Source digest	Serves	Validated	First	Second	Third	Parity	Replaced by	Retired
ssb-fifth-agreement v0.4	active	1c42b235b1d7	as v0.3: v0.3 with the deleted fifth_agreement (v0.1) removed from ssb_fifth_order; agreement kernels unchanged	2026-10-25	as v0.3	as v0.3	as v0.3	outputs bitwise those of v0.3 on the synthetic test scene (agreements, derivatives, gradients, reconstructions, drag previews, full fit; 2026-10-25); SSBFifthOrderNumericsTests.testRowsKernelMatchesDoublePrecisionDefinition (within 1.2e-6 of the float64 objective)	—	—
ssb-fifth-agreement v0.3	retired (superseded by v0.4, same kernels)	2d385e96d9c4	fifthOrderAgreements (fifth-order fit, stencil Newton, gradient check) and the value pass of ssb-fifth-gradient v0.2 on all BF pixels or every n-th	2026-10-25	as v0.2 (10.7 / 6.3 / 5.9 / 7.5 back to back with v0.2 at 10.9 / 6.3 / 7.0 / 7.6)	as v0.2	as v0.2	v0.2’s per-pair code plus a BF stride: bit-identical to v0.2 on every candidate set of the three acquisitions; SSBFifthOrderGradientTests (every 3rd BF pixel against the float64 objective)	ssb-fifth-agreement v0.4	2026-10-25
ssb-fifth-agreement v0.2	retired (superseded by v0.3, same per-pair terms)	f2f700147e47	fifthOrderAgreements before the BF stride	2026-10-25	11.0 / 6.6 / 5.6 / 6.6	11.1 / 7.2 / 5.8 / 6.9	18.4 / 11.5 / 9.8 / 12.0	SSBFifthOrderNumericsTests (v0.1 and the float64 objective); measured: within 3.1e-7 of v0.1 on all three acquisitions	ssb-fifth-agreement v0.3	2026-10-25
ssb-fifth-agreement v0.1 (fifth_agreement in ssb-per-term)	deleted 2026-10-25 (was the test reference of v0.2 and later)	1c390cc7b833	before 2026-10-25	before 2026-10-25	24.4 / 19.6 / 20.8 / 21.2	25.4 / 21.4 / 23.3 / 22.9	41.3 / 36.6 / 37.9 / 37.5	reference for v0.2	ssb-fifth-agreement v0.2	2026-10-25
ssb-joint-agreement v0.4	active	f0192e7d0589	as v0.3: v0.3 with v0.1 (joint_objective_angle_sums) and the per-term agreement (joint_objective_batch, joint_trial_probe, the SSBAgreementKernel.perTerm option) deleted from ssb_joint; agreement kernels unchanged	2026-10-25	as v0.3	as v0.3	as v0.3	outputs bitwise those of v0.3 on the synthetic test scene (agreements, derivatives, gradients, reconstructions, drag previews, full fit; 2026-10-25); SSBFifthOrderNumericsTests.testLowOrderAngleSumsMatchDoublePrecisionDefinition (within 4.7e-6 of the float64 objective on the synthetic scene)	—	—
ssb-joint-agreement v0.3	retired (superseded by v0.4, same kernels)	6283577c146a	as v0.2: v0.2 with the retired mean_phase kernels removed from the shared ssb_joint source; agreement kernels unchanged	2026-10-25	as v0.2	as v0.2	as v0.2	as v0.2	ssb-joint-agreement v0.4	2026-10-25
ssb-joint-agreement v0.2	retired (superseded by v0.3, same kernels)	d698aa9cb17a	agreements with .angleSums (low-order search trials, branch scores)	2026-10-25	8.7 / 5.1 / 5.1	10.2 / 5.9 / 5.8	16.3 / 9.5 / 9.8	SSBFifthOrderNumericsTests.testLowOrderAngleSumsMatchReference; measured: within 1.3e-8 of v0.1	ssb-joint-agreement v0.3	2026-10-25
ssb-joint-agreement v0.1 (joint_objective_angle_sums in ssb_joint)	deleted 2026-10-25 (was the test reference of v0.2 and later)	4aa7c1da6391 (with ssb-mean-phase)	before 2026-10-25	before 2026-10-25	35.3 / 8.9 / 9.4	41.1 / 10.3 / 10.9	65.3 / 18.2 / 17.8	reference for v0.2	ssb-joint-agreement v0.2	2026-10-25

Both v0.2 kernels (and ssb-fifth-agreement v0.3, which adds the BF stride) evaluate the per-pair float32 terms of v0.1:

• The soft aperture of joint_geometry_xy is exactly 1 inside and 0 outside conservatively rounded radii; the full expression runs only for SIMD groups with a lane in the one-pixel edge ring (a one-trip simd_ballot loop, since the compiler if-converts plain uniform branches). Divisions use the correctly rounded reciprocal with a Markstein correction, which reproduces IEEE division. The edge, alpha^2 and the depth-sinc arguments are bitwise those of v0.1 on every (k, q) pair of the first and third acquisitions.

• fast::sin / fast::sincos equal precise:: with fast math off except for 1-ulp differences in about one argument in 1e7, at less than half the cost.

• A threadgroup computes one to four candidates per thread with no padding candidates.

The fifth-order kernel also reassociates chi(k -/+ q), its only change of rounding: a threadgroup owns band frequencies of at most two band rows and collapses the bivariate chi polynomial (built in double precision from the same packed float32 terms) once per BF pixel and row, so each sideband is one degree-6 Horner evaluation instead of the 14-term harmonic sum. Candidates with equal depth and tilt share depth-sinc weights. On the synthetic test scene both fifth-order kernels are about 1e-6 from the float64 objective and v0.2 is no less accurate.

Retired native engine (MetalSSBEngine, ssb.metal)

The engine’s own non-model SSB and its phase-variance fit, retired 2026-10-25: native SSB fits and reconstructs with the joint model only. These kernels were never registered in SSBKernelRegistry (the rows below have no version), so trimming ssb.metal changed no registered digest. ssb.metal keeps counts_to_complex, the row FFTs (fft_rows_radix8, fft_rows_small_mixed_radix), transpose_complex32 and extract_hermitian_half, which prepare the Fourier evidence of every joint model, and ssb_object_phase, which shows a reopened .ssb run. Last measurements (2026-08-19, private 512² uint8 fixture native-ssb-fullbf-512-u8-v2, Apple M5 Max, migration record).

Kernels	Status	Served	Last measured	Replaced by	Retired
ssb_gamma_accumulate, ssb_gamma_accumulate_half, ssb_gamma_accumulate_half_aberrations, ssb_gamma_accumulate_full_aberrations, ssb_finalize_fourier_sum, ssb_precompute_cross_trig	retired (non-model engine removed)	MetalSSBEngine.reconstruct(aberrations:scanDetectorRotationDegrees:): SSB without tilt or depth, C10/C12 plus manual higher orders	warm reconstruction 8.9 ms p50, 512²	ssb-redraw (joint model, method ssb)	2026-10-25
ssb_precompute_chi_trig, ssb_correct_half_ifft_small, ssb_ifft_small_phase_moments, ssb_correct_half_column_ifft512_hermitian, ssb_ifft512_nyquist_correction, ssb_ifft512_rows_hermitian_phase_moments, ssb_correct_full_for_phase_loss, ssb_accumulate_phase_moments, ssb_transpose_half_to_column_major, ssb_transpose_half_to_row_major	retired (phase-variance fit removed)	MetalSSBEngine.phaseVariance and optimize (SSBOptimizer: 200 seeded TPE trials, Nelder–Mead); SSBFitOptions(objective: .phaseVariance)	exact loss 25.1 ms p50; 200-trial fit 6.06 s p50, 512²	ssb-joint-agreement, ssb-low-order-derivatives, ssb-fifth-agreement, ssb-fifth-gradient (model agreement)	2026-10-25