Vignesh Gopakumar
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Flux preservation before smoothing is insufficient

measured
Published

November 2, 2026

measurement Entry 100 · milestone M5

The first constrained particle-flux shadow does not justify trajectory windows. The validated baseline and guard limits stay unchanged. The primer explains the guarded transport model.

The trial changes the representation of admitted particle transport while preserving its local finite-volume flux before radial smoothing. Rejected faces keep their fallback coefficients. The alternative diffusion and velocity stay within the existing limits and receive the same complete native processing. The reference includes deliberate clipping, patches and fallback; it never restores an inadmissible raw surrogate just to improve agreement.

That algebraic preservation survives the checks, but it does not make the postprocessed operator uniformly closer. the selected particle-face difference falls from 5.76626% to 4.92144%, but complete-grid total rate L1 difference rises from 15.86765% to 16.23066% and divergence difference from 47.64620% to 49.04301%C-316. A selected-face gain hides worse complete-grid flux and divergence differences.

The cap context exposes another problem. Although the original served flux remains continuous across the sampled boundary, the trial switches its coefficient representation as soon as the binary guard admits the face. Velocity compensates locally before smoothing. Mixing that compensating pair into neighboring profiles exposes a persistent paired difference: the shadow paired total-rate difference stays near 5.10177% across a hundredfold reduction in cap offset, while the baseline difference shrinks by approximately the same hundredfold factorC-317. This belongs to the trial construction, not a relaxed guard or a change to the validated baseline.

The derivative checks succeed within the tested branches: 174 observations pass bounds, algebra and baseline parity; all 48 new shadow derivative components pass strict corroboration; 368 of 372 combined components pass, with four inherited cap controls unresolvedC-318. That success does not establish continuity between branches. The failed software-test setup attempts remain in the evidence history; both scientific context runs complete under their fixed limits.

The next local design must make the remapping itself continuous and assess feasibility against the fully postprocessed face-rate and divergence operator. Only a useful admissible candidate should advance to windows starting from valid current-baseline state and auxiliary checkpoints.

These are historical fixed-state operator comparisons, not density errors, five-second fusion-power uncertainties or experimental validation. No matched window, batch job, production deployment or physics sign-off follows.

Technical details → construction and expansion screen. Milestone → M5.

Technical details → Uncertainty propagation and validation › constrained flux shadow
Decisions → OQ-47

© Copyright 2026 Vignesh Gopakumar

 
 
Code and first draft by Claude (Anthropic) and Codex, working to a brief by Vignesh Gopakumar, who reviewed and approved this page. How this is built · Tokamak Toolkit home