CPU dense decision and diagnostic evidence

The eight-accumulator CPU candidate was rejected at the fixed-work preflight. Its first configuration converged with different iterations and matvecs even though both revisions passed true-residual checks. No candidate CPU A/B timing campaign was started, so this is neither a measured slowdown nor a demonstrated speedup. Keep the baseline production arithmetic; retain useful independent boundary, cancellation and non-finite coverage. CPU 2048 prepared optimization remains open.

This report records diagnostics from baseline 84c88c98c895103395e1b6d6e98f7618848a14d3 and rejected candidate abd655a20a6835b6b95b2e6c3aeae2b69b9957aa. It is not a current-main NumPy/PyTorch scorecard. The 5% adoption threshold is unchanged. Fresh API, Session and prepared scopes remain separate; no backend, fusion or size AUTO policy is introduced.

Fixed-work rejection

The refined source was frozen before candidate performance outcomes. The first configuration is CPU-release, dense float64, native kernel, standard CG without preconditioner, fused operations, fresh API, one CPU thread. For dense-64, two checks each reproduce baseline 49/51/0 versus candidate 48/50/0 (iterations/matvecs/restarts). Both true residuals pass the original tolerance. Rounding-group changes are numerically valid here but ineligible for this declared same-work optimization trial. There is no work normalization, selective size exception, timing comparison, or relaxed tolerance.

All checks from the two completed first-configuration workers

Revision

Case

Implementation

I/M/R

Checks

Maximum true residual

Minimum threshold

baseline

dense-64

native

49/51/0

2

1.8582645e-06

3.0576161e-06

baseline

dense-64

numpy-out

49/51/0

2

1.8734617e-06

3.0576161e-06

baseline

dense-64

torch-eager-out

49/51/0

2

1.9437482e-06

3.0576161e-06

baseline

dense-256

native

67/70/1

2

4.8815545e-06

5.0262292e-06

baseline

dense-256

numpy-out

67/70/1

2

4.8752604e-06

5.0262292e-06

baseline

dense-256

torch-eager-out

67/70/1

2

4.8872893e-06

5.0262292e-06

baseline

dense-1024

native

70/73/1

2

9.6567151e-06

1.0405785e-05

baseline

dense-1024

numpy-out

70/73/1

2

9.6567151e-06

1.0405785e-05

baseline

dense-1024

torch-eager-out

70/73/1

2

9.6567151e-06

1.0405785e-05

baseline

dense-2048

native

70/73/1

2

1.2911386e-05

1.4810685e-05

baseline

dense-2048

numpy-out

70/73/1

2

1.2911386e-05

1.4810685e-05

baseline

dense-2048

torch-eager-out

70/73/1

2

1.2911385e-05

1.4810685e-05

current

dense-64

native

48/50/0

2

2.307155e-06

3.0576161e-06

current

dense-64

numpy-out

49/51/0

2

1.8734617e-06

3.0576161e-06

current

dense-64

torch-eager-out

49/51/0

2

1.9437482e-06

3.0576161e-06

current

dense-256

native

67/70/1

2

4.9381732e-06

5.0262292e-06

current

dense-256

numpy-out

67/70/1

2

4.8752604e-06

5.0262292e-06

current

dense-256

torch-eager-out

67/70/1

2

4.8872893e-06

5.0262292e-06

current

dense-1024

native

70/73/1

2

9.6567151e-06

1.0405785e-05

current

dense-1024

numpy-out

70/73/1

2

9.6567151e-06

1.0405785e-05

current

dense-1024

torch-eager-out

70/73/1

2

9.6567151e-06

1.0405785e-05

current

dense-2048

native

70/73/1

2

1.2911385e-05

1.4810685e-05

current

dense-2048

numpy-out

70/73/1

2

1.2911386e-05

1.4810685e-05

current

dense-2048

torch-eager-out

70/73/1

2

1.2911385e-05

1.4810685e-05

The enclosing preflight manifest remains failed; later declared configurations were not completed by this aborted CPU trial. The full per-check values and source identities are preserved in the accompanying structured audit.

Actual code-generation inspection

GNU C++ 16.0.1 used -O3 -DNDEBUG -std=c++20 -fPIC -Wall -Wextra -Wpedantic. All inspected helpers use 128-bit SSE2, without AVX or FMA. The refined low/high four-element arrays preserve the first eight-accumulator prototype’s per-lane recurrence and balanced reduction, but change association relative to the four-accumulator baseline. Static instruction and frame counts do not establish runtime performance, cache behavior or bandwidth.

Actual serial two-row helper observations

Observation

Baseline

713c8ae

abd655a

Packed accumulation chains

4

8

8

Distinct bulk-loop XMM register names

7

13

13

Bulk-loop FP stack references

0

0

0

Instructions per eight columns

36

34

34

Unconditional frame bytes

0 on multiple-of-four path

168

104

Entry array-zeroing bytes

0

128

64

Post-bulk FP stores before optional four-column tail (bytes)

0

64

64

Two-row helper symbol bytes

475

918

835

Whole dense object .text bytes

3774

4667

4539

The refinement partially reduces setup and footprint; its unconditional frame, canary and post-loop stores remain. No further source variant was selected from performance outcomes. Earlier rejected four-row and four-accumulator unroll experiments are separate evidence and are not repeated or relabelled here.

Previously preserved actual object SHA256 identities

Representation

Preserved object

SHA256

Baseline

codegen-halves/baseline.o

9315d269ab22598ddd4227a0fa6080681569b9fdf5c0b2baff07a4b43cbfdf95

713c8ae

codegen/current-713-stage.o

778f5045420972e87161c5dd291a1f269ad6b5da807273ade4734c0563454b6b

abd655a

codegen-halves/current.o

5b82b88229d0dcfd998974b5bc926413f08aae25dc4d3e1b7589cda18c7d7284

These object hashes were checked in the earlier static audit; report rendering does not rehash binaries. The full frame/instruction audit remains preserved as cpu-codegen-halves-note.rst.

Baseline same-call engine attribution

The exact shared solver engine and actual CPU backends are instrumented on the same dense-2048 fixture (seed 20261017). There are 24 ordinary captures and six additional provider-wrapped captures, each in a fresh process with three warmups and ten measured engine calls. Every warmup and sample has a converged status, stable I/M/R within its capture, and an independent wider-long-double true residual check outside timing. Jacobi preparation, workspace allocation, x reset, Python dispatch and public solve validation are outside these engine intervals.

The matvec-entry percentage is the median of each call’s summed apply, apply_and_dot and residual_squared_norm times divided by its engine time. Composite entries include vector arithmetic. The nested private CBLAS timer isolates actual provider-entry elapsed time inside those composites; it includes provider checks/dispatch and timer overhead, rather than exclusive microkernel CPU time. Provider time must not be added to entry sums. All percentages below come from same-call ratios; separate capture medians are not subtracted.

All engine captures; times are medians in milliseconds

Capture

I/M/R

Engine ms

Entry sum ms

Remainder ms

Matvec-entry %

Nested provider %

Maximum true-residual/threshold

cpu-release-native-standard-none-fused0

70/73/1

100.8635

100.83195

0.0281545

99.720549

n/a

0.87176155

cpu-release-native-standard-none-fused1

70/73/1

103.91455

103.88041

0.026821

99.790351

n/a

0.87176155

cpu-release-native-standard-jacobi-fused0

3/5/0

6.1359045

6.133435

0.002723

99.655595

n/a

0.83641225

cpu-release-native-standard-jacobi-fused1

3/5/0

5.8770945

5.875022

0.0021835

99.728347

n/a

0.83641225

cpu-release-native-explicit-none-fused0

68/137/0

158.36342

158.27195

0.083896

99.752594

n/a

0.98130942

cpu-release-native-explicit-none-fused1

68/137/0

159.26138

159.21603

0.046001

99.72865

n/a

0.98130942

cpu-openmp-native-standard-none-fused0

70/73/1

48.546378

48.520315

0.0257545

99.248994

n/a

0.87176155

cpu-openmp-native-standard-none-fused1

70/73/1

52.606431

52.584942

0.02666

99.224025

n/a

0.87176155

cpu-openmp-native-standard-jacobi-fused0

3/5/0

3.450463

3.448252

0.002453

99.151357

n/a

0.83641225

cpu-openmp-native-standard-jacobi-fused1

3/5/0

3.456848

3.454399

0.002546

99.104059

n/a

0.83641225

cpu-openmp-native-explicit-none-fused0

68/137/0

101.59005

101.48882

0.046475

99.519448

n/a

0.98130942

cpu-openmp-native-explicit-none-fused1

68/137/0

93.244557

93.199611

0.0442705

99.289699

n/a

0.98130942

cpu-blas-native-standard-none-fused0

70/73/1

90.747881

90.725233

0.023825

99.697779

n/a

0.87176155

cpu-blas-native-standard-none-fused1

70/73/1

90.203702

90.170068

0.028774

99.783773

n/a

0.87176155

cpu-blas-native-standard-jacobi-fused0

3/5/0

6.6076875

6.6001355

0.0017715

99.715629

n/a

0.83641225

cpu-blas-native-standard-jacobi-fused1

3/5/0

6.198311

6.1967285

0.0015495

99.640093

n/a

0.83641225

cpu-blas-native-explicit-none-fused0

68/137/0

171.74281

171.68967

0.053137

99.801063

n/a

0.98130942

cpu-blas-native-explicit-none-fused1

68/137/0

192.42125

192.38192

0.045734

99.794583

n/a

0.98130942

cpu-blas-blas-standard-none-fused0

70/73/1

84.548345

84.516131

0.0312445

99.656482

n/a

0.87176155

cpu-blas-blas-standard-none-fused1

70/73/1

79.859586

79.823885

0.0326855

99.726432

n/a

0.87176155

cpu-blas-blas-standard-jacobi-fused0

3/5/0

5.456052

5.453814

0.0020045

99.623192

n/a

0.83641225

cpu-blas-blas-standard-jacobi-fused1

3/5/0

5.3576465

5.356163

0.002013

99.718472

n/a

0.83641225

cpu-blas-blas-explicit-none-fused0

68/137/0

150.38634

150.36122

0.0264545

99.759554

n/a

0.98130942

cpu-blas-blas-explicit-none-fused1

68/137/0

141.27486

141.24558

0.025433

99.734617

n/a

0.98130942

provider-standard-none-fused0

70/73/1

76.042181

76.010869

0.02529

99.664691

99.514132

0.87176155

provider-standard-none-fused1

70/73/1

73.564548

73.541472

0.033333

99.741645

99.587221

0.87176155

provider-standard-jacobi-fused0

3/5/0

5.433049

5.4304385

0.0025535

99.543501

99.32157

0.83641225

provider-standard-jacobi-fused1

3/5/0

5.3692645

5.366724

0.002565

99.692583

99.522189

0.83641225

provider-explicit-none-fused0

68/137/0

136.8543

136.6764

0.0458755

99.735184

99.521313

0.98130942

provider-explicit-none-fused1

68/137/0

135.29772

135.25119

0.053275

99.732051

99.572332

0.98130942

Across the six provider-wrapped captures, the median fraction of an engine interval spent inside the actual private GEMV entry ranges from 99.322% to 99.587%. This supports investigating actual GEMV/provider/storage behavior before optimizing unrelated vector operations. It does not determine the cause of an earlier full-solver NumPy gap. Oracle matrix reads between calls and instrumentation overhead limit generalization to uninstrumented solves.

Actual private provider identity after a checked GEMV:

{
  "blasint_bytes": 4,
  "config": "OpenBLAS 0.3.30 NO_LAPACK NO_LAPACKE DYNAMIC_ARCH NO_AFFINITY USE_LOCKING Haswell SINGLE_THREADED",
  "environment_OPENBLAS_CORETYPE": null,
  "framework_score": false,
  "identity_dgemv_check_passes": true,
  "metric": "private_openblas_identity",
  "parallel_kind": 0,
  "reported_num_threads": 1,
  "schema_version": 1,
  "selected_core_after_dgemv": "Haswell"
}

All per-entry call/time medians are retained in the structured audit. Their separate medians are descriptive and need not sum to the median engine time.

Same-buffer provider and storage probe

A separate component diagnostic crosses two providers with two storage owners: actual baseline private BLAS through CpuBackend::apply and NumPy dot(out=); the exact fixture’s NumPy allocation and an actual owning cg::DenseMatrix snapshot made with std::vector<double>. Both providers use the same matrix, vector and output addresses for a given storage choice. The fixture’s rhs b is the fixed GEMV vector; these are not CG search directions. Native snapshot construction and all identity/oracle checks are outside timing. The NumPy borrowed allocation is not a claim about the full NumPy prepared adapter’s separate copied matrix.

For each size, all four fresh processes are retained in A/B/B/A label order. A and B reverse treatment enumeration before the same Williams scheduler; they use the same source and bridge, not different optimization builds. Each process uses CPU 0 and one thread in all providers, three warmups per treatment and 36 complete four-treatment Williams rounds with one call per treatment. No global THP setting or NumPy environment variable is changed.

Every fresh-process component median in milliseconds

Process

Size

Private / NumPy A

NumPy / NumPy A

Private / C++ A

NumPy / C++ A

dense2048-p1-A

2048

1.22442

1.2408155

1.268276

1.2350245

dense2048-p2-B

2048

1.372966

1.439262

1.415382

1.42037

dense2048-p3-B

2048

1.0745405

1.100359

0.979196

1.025904

dense2048-p4-A

2048

1.1087915

1.0762205

1.182623

1.165265

dense1024-p1-A

1024

0.1485445

0.1442195

0.1485685

0.1483445

dense1024-p2-B

1024

0.146474

0.1546845

0.1486875

0.151545

dense1024-p3-B

1024

0.155286

0.1519175

0.1584395

0.15542

dense1024-p4-A

1024

0.146485

0.148404

0.1498585

0.15461

Within-process ratios; values above one mean the numerator is slower

Process

Private/NumPy on NumPy A

Private/NumPy on C++ A

C++/NumPy A private

C++/NumPy A NumPy

dense2048-p1-A

0.98678651

1.0269238

1.0358178

0.99533291

dense2048-p2-B

0.9539375

0.99648824

1.0308937

0.98687383

dense2048-p3-B

0.97653629

0.95447137

0.91126951

0.93233572

dense2048-p4-A

1.0302642

1.0148962

1.0665874

1.0827382

dense1024-p1-A

1.029989

1.00151

1.0001616

1.0286022

dense1024-p2-B

0.94692099

0.98114421

1.0151119

0.97970385

dense1024-p3-B

1.0221732

1.019428

1.0203077

1.0230553

dense1024-p4-A

0.98706908

0.96926784

1.0230297

1.0418183

The observed 2048 workers do not show a consistent large provider or ownership penalty. These component medians are not a full-solver score, a 5% adoption result, or a calibrated confidence interval. Between-process variation and treatment-dependent cache state remain visible. No aggregate winner is selected. The probe does not reproduce all prepared-adapter allocations, CG operands, or real solver memory-access sequences. Provider calls include their different Python/ctypes dispatch boundaries; this is not exclusive kernel timing.

Product correctness and ownership evidence

Each worker performs four prechecks, twelve warmup checks and 144 timed-call checks, all outside timing. The oracle uses wider-long-double row products and sums, with a double forward-error bound plus a long-double oracle bound. All 160 checks per process pass. The maximum observed error and maximum rowwise bound below summarize different rows/calls; their ratio is not the per-row gate. Input and both matrix byte hashes remain unchanged.

Every worker’s independent product checks

Process

Precision bits

Passing checks

Maximum absolute error

Maximum row bound

Canonical fixture SHA256

dense2048-p1-A

64

160

6.0822458e-12

2.2138527e-08

8bda02fed9ccafa8c12f857ad51962b02d8c860ee96a006078aed872c40cae6c

dense2048-p2-B

64

160

6.0822458e-12

2.2138527e-08

8bda02fed9ccafa8c12f857ad51962b02d8c860ee96a006078aed872c40cae6c

dense2048-p3-B

64

160

6.0822458e-12

2.2138527e-08

8bda02fed9ccafa8c12f857ad51962b02d8c860ee96a006078aed872c40cae6c

dense2048-p4-A

64

160

6.0822458e-12

2.2138527e-08

8bda02fed9ccafa8c12f857ad51962b02d8c860ee96a006078aed872c40cae6c

dense1024-p1-A

64

160

4.5670134e-12

8.2972642e-09

204aa61929e5e8d34102ac2d0bda5714b6f0d17f8bf4796a7f71b535a21053bb

dense1024-p2-B

64

160

4.5670134e-12

8.2972642e-09

204aa61929e5e8d34102ac2d0bda5714b6f0d17f8bf4796a7f71b535a21053bb

dense1024-p3-B

64

160

4.5670134e-12

8.2972642e-09

204aa61929e5e8d34102ac2d0bda5714b6f0d17f8bf4796a7f71b535a21053bb

dense1024-p4-A

64

160

4.5670134e-12

8.2972642e-09

204aa61929e5e8d34102ac2d0bda5714b6f0d17f8bf4796a7f71b535a21053bb

THP observations and limits

The allocator policy was a source-grounded hypothesis: NumPy 2.2.6 can request MADV_HUGEPAGE for sufficiently large allocations, whereas the native owning snapshot uses ordinary vector storage. See the NumPy global-state documentation and versioned allocator source. The following records describe actual overlapping VMAs, not a guessed allocator policy. AnonHugePages is VMA residency; THPeligible and hg are eligibility/advice observations. A VMA may include unrelated allocations, so its huge-page bytes cannot be assigned wholly to a matrix. KernelPageSize alone is not a huge-page-residency test.

At 2048, the distinct VMA-wide AnonHugePages values are 0 kB, 30720 kB for the NumPy matrix and 0 kB for the C++ matrix. The table retains every overlapping matrix mapping in both phases. These residency/advice/eligibility fields remain unchanged across the probe. The component timings do not establish that this policy difference caused the historical prepared-solver gap. No allocator change follows from this evidence. All exact VMA records, including matrix/vector/output mappings before and after every worker, are retained below and in the structured audit.

Every overlapping matrix VMA; AnonHugePages applies to the entire mapping

Process

Phase

Buffer

VMA address range

AnonHugePages

THPeligible

VmFlags

VMA exceeds buffer

dense2048-p1-A

before

borrowed-numpy

7d56eaa1c000-7d56eaa1d000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p1-A

before

borrowed-numpy

7d56eaa1d000-7d56eca1d000

30720 kB

1

rd wr mr mw me ac sd hg

True

dense2048-p1-A

before

owned-cpp

7d56e6a1b000-7d56e8a1c000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p1-A

after

borrowed-numpy

7d56eaa1c000-7d56eaa1d000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p1-A

after

borrowed-numpy

7d56eaa1d000-7d56eca1d000

30720 kB

1

rd wr mr mw me ac sd hg

True

dense2048-p1-A

after

owned-cpp

7d56e6a1b000-7d56e8a1c000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p2-B

before

borrowed-numpy

7b9f36d1c000-7b9f36d1d000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p2-B

before

borrowed-numpy

7b9f36d1d000-7b9f38d1d000

30720 kB

1

rd wr mr mw me ac sd hg

True

dense2048-p2-B

before

owned-cpp

7b9f32d1b000-7b9f34d1c000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p2-B

after

borrowed-numpy

7b9f36d1c000-7b9f36d1d000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p2-B

after

borrowed-numpy

7b9f36d1d000-7b9f38d1d000

30720 kB

1

rd wr mr mw me ac sd hg

True

dense2048-p2-B

after

owned-cpp

7b9f32d1b000-7b9f34d1c000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p3-B

before

borrowed-numpy

76ae53a1c000-76ae53a1d000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p3-B

before

borrowed-numpy

76ae53a1d000-76ae55a1d000

30720 kB

1

rd wr mr mw me ac sd hg

True

dense2048-p3-B

before

owned-cpp

76ae4fa1b000-76ae51a1c000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p3-B

after

borrowed-numpy

76ae53a1c000-76ae53a1d000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p3-B

after

borrowed-numpy

76ae53a1d000-76ae55a1d000

30720 kB

1

rd wr mr mw me ac sd hg

True

dense2048-p3-B

after

owned-cpp

76ae4fa1b000-76ae51a1c000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p4-A

before

borrowed-numpy

717aabc1c000-717aabc1d000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p4-A

before

borrowed-numpy

717aabc1d000-717aadc1d000

30720 kB

1

rd wr mr mw me ac sd hg

True

dense2048-p4-A

before

owned-cpp

717aa7c1b000-717aa9c1c000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p4-A

after

borrowed-numpy

717aabc1c000-717aabc1d000

0 kB

0

rd wr mr mw me ac sd

True

dense2048-p4-A

after

borrowed-numpy

717aabc1d000-717aadc1d000

30720 kB

1

rd wr mr mw me ac sd hg

True

dense2048-p4-A

after

owned-cpp

717aa7c1b000-717aa9c1c000

0 kB

0

rd wr mr mw me ac sd

True

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dense2048-p3-B: observed buffers, policies and every overlapping VMA

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dense2048-p4-A: observed buffers, policies and every overlapping VMA

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dense1024-p1-A: observed buffers, policies and every overlapping VMA

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dense1024-p2-B: observed buffers, policies and every overlapping VMA

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dense1024-p3-B: observed buffers, policies and every overlapping VMA

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dense1024-p4-A: observed buffers, policies and every overlapping VMA

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Decision and remaining CPU work

Retain baseline production arithmetic and explicit native/BLAS and fusion choices. The eight-accumulator candidate is ineligible under the fixed-work gate. Preserve meaningful independent tests and these negative/diagnostic results instead of adopting a size exception, changing tolerances, or retrying arithmetic variants against observed results.

The next justified CPU investigation is attribution inside actual prepared adapter calls: observe the actual matrix pointer/owner, GEMV operand sequence and provider calls before proposing another implementation. This probe shows that a large private-provider or native-ownership penalty is not universal for the shared rhs GEMV; it does not explain the complete solver gap. Such a new diagnostic must preserve numerical work and allocation/provider policies and be declared before measurement. No further production variant is justified by the present component evidence.

The full A/A calibration is separate evidence: inconclusive controls must remain inconclusive, and a finite set of controls neither proves future host stability nor estimates a universal false-positive rate. No control or started campaign is replaced, pooled across scopes, or omitted from an adoption decision. No CPU speedup or new win over NumPy/PyTorch is claimed by this report.

Artifact identity and regeneration

The structured audit records all source JSON hashes, exact per-process argv, baseline/core/provider/bridge identities, full work and numerical gates, per-entry engine medians, all worker medians and all VMA observations. The renderer verifies each CPU diagnostic stdout hash against its execution manifest and each storage worker against completion.json. It checks frozen identity equality and complete sampling, but does not rehash binaries or rerun benchmarks. The archive/binary hashes below are the already verified worker identity records, not new hashing performed during report rendering.

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  "fixture_hashes": {
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}

Regenerate only from the preserved local evidence after quiet measurements finish. This is artifact rendering, not a command that reconstructs missing baseline binaries or reruns performance samples:

python3 build/reliable-performance-20261018/render_cpu_decision.py \
  --output build/reliable-performance-20261018/cpu-decision-report.rst \
  --analysis build/reliable-performance-20261018/cpu-decision-audit.json

All source-artifact SHA256 values read by this rendering:

Small source/JSON artifacts only

Relative artifact

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cpu-codegen-halves-note.rst

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cpu-profiles/compile-manifest.json

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