# Projected explosion: isolated spatial-interpolation experiment

Historical baseline: `9805383f9c50d867e8555471baf5dbda8333a652`. This candidate does not replace or relabel its results. The TG runner records the actual candidate revision, dirty state, source hash and harness hashes, plus the historical baseline revision and selected explosion scheme.

Default remains `constant`. Explicit `explosion="projected_linear"` supports only a periodic, body-free, two-level, fully blocked single rectangle (window or singleton union representation). Dense, multilevel, multi-rectangle and body/Jet cases are rejected. Constructor guards have been statically reviewed; GPU construction is not yet exercised.

For each population, form a centered gradient only where both axis neighbors are original explosion donors, owned and uncovered. Otherwise set that axis derivative to zero. Project the gradient perpendicular to the population lattice direction (rest population retains its gradient), then evaluate at child offsets ±1/4 coarse cell. Read owner cores, never stale block halos. Repeating the donor for a missing axis avoids invalid reads. All neighbor reads remain within the original coarse transfer footprint.

Timing, two ghost-only streaming hops, four-child coalescence, relaxation, shifted-storage convention, bulk collision and legacy constant kernel are unchanged. There is no NEQ rescaling, limiter, time interpolation or new framework. Projection commutes with subtracting the constant lattice weights.

Method attribution: Schornbaum and Rüde, [arXiv:1508.07982](https://arxiv.org/pdf/1508.07982), Algorithm 2; Chen et al., Physica A 362 (2006) 158–167, [DOI 10.1016/j.physa.2005.09.036](https://doi.org/10.1016/j.physa.2005.09.036). Independently implemented mathematical stencil, with no GPL implementation copied. The Chen full text was not directly audited in this experiment.

## CPU checks

Run `PYTHONPATH=src python -m unittest discover -s tests/unit -p test_projected_explosion.py -v`.

- Constant populations, affine available-axis gradients, characteristic constancy, quartet means and shift invariance.
- Original donor footprint only; poison covered cells and check finite reconstruction.
- Both window and singleton-union layouts, centered/off-axis/minimal near-edge rectangles.
- Eight complete intervals, identity and SRT collision: actual fine pulls and coarse restriction tables, all eight grazing corner paths included; composite mass and both momentum components conserved within 2e-12 FP64 absolute tolerance.
- Actual CUDA kernel body compiled with a CPU C++ shim: blocked address mapping, FP32 shifted/unshifted inputs, poisoned halo/covered storage, independent NumPy parity. This checks arithmetic and indexing, not CUDA compilation or execution.
- Unprojected reconstruction is distinguished by failure of characteristic constancy. It need not fail global mass conservation in this geometry.

## Next diagnostic, only on authorized Horsea GPU

Use the same candidate checkout for paired Re100 N64 depth2 runs, differing only in `--explosion constant` versus `--explosion projected_linear`:

`python tests/validation/taylor_green/run_case.py --repo "$PWD" --re 100 --n 64 --depth 2 --explosion projected_linear --output <new-result-path>`

Select the physical CUDA device explicitly. Never overwrite historical reports. Compare frozen TG error gates and full trajectories, including mass, energy, pressure and velocity. Amplitude/nonmodal shape decomposition can inform mechanism but cannot substitute for the gates. First establish CUDA compilation and CPU/device parity, then paired end-to-end budgets. No accuracy improvement, production suitability or GPU pass is claimed by these CPU results.

## Local verification limits

Focused candidate/refinement/block-layout/build-contract checks pass (62 unittest tests). Full unittest discovery is not green: the attempted 200-test run reports 18 missing-dependency/import errors and three historical source-pin refusals (jet-circle and LES guards), plus one skipped test. Those pin refusals correctly reject the changed `blocks.cu`; their immutable fixtures were not weakened or rewritten. Python syntax checks and `git diff --check` pass. No CUDA build, device execution, GPU performance or TG improvement has been established.