bounds: correct transpose() docstring — Replicate is NOT exact for Lame/bending

[balbasty]

Workstream: claude-jitfields-to-fastfields

Context

Independent correctness audit of the recent self-adjointness fixes to the JRLS regularisers (matvec_lame_jrls#31, bending RLS/JRLS #38). Both fixes are verified genuinely correct — see verification below — but auditing them surfaced a separate, pre-existing documentation bug in bounds.h's transpose() comment (added in f39ee7b), which this PR corrects. No functional/code change — comment only.

The bug

f39ee7b documented transpose() as yielding an exactly self-adjoint Lamé/bending operator "for DFT / Zero / Replicate / NoCheck" (alongside DCT2↔DST2). That claim is wrong for Replicate.

Verification

Built the explicit operator matrix column-by-column (L eⱼ for every basis vector eⱼ, i.e. a strictly stronger check than the existing <Lx,y> == <x,Ly> bilinear-form oracle) for matvec_lame/matvec_all (flow) and matvec_bending (field), 2D and 3D, with and without JRLS weighting, across all 8 bound::type values:

• Zero, DCT2, DST2, DFT, NoCheck: max|L - L^T| / max|L| is exactly 0 (or at float64 rounding noise, ~1e-16) in every configuration tested, including the 3D lame_jrls path that the CPU test suite doesn't cover at all. The two audited self-adjointness fixes are genuinely correct here.
• DCT1, DST1: asymmetric, as already correctly documented (excluded from the CPU suite's symmetry assertions with a clear rationale).
• Replicate: also asymmetric (max|L-L^T|/max|L| ≈ 0.03–0.5 depending on configuration) — but undocumented, and silently absent from the RLS/JRLS symmetry tests (which only cover Zero/DCT2/DST2/DFT). The same asymmetry reproduces bit-for-bit with no weight map at all (the plain, non-JRLS operator), proving this is a structural property of transpose(Replicate) == Replicate predating both audited commits, not something the JRLS fixes introduced or missed. Only the cross-channel Lamé and 2nd-order bending stencils are affected — absolute/membrane stay exactly self-adjoint under Replicate.

Fix

Update the comment to move Replicate into the same documented-limitation bucket as DCT1/DST1, with the numeric evidence and rationale (clamp has no parity to flip, but clamping is not its own adjoint for a difference operator — same structural gap). Also confirmed (separately, via git ls-tree/git blame) that:

• The kernels submodule pins in fastfields-cpu-impl/fastfields-cuda-impl correctly point at commits including both fixes, gitlinks are still mode 160000 in both.
• fastfields-cuda-lib's post-rewrite (PR regularisers/flow: fix channel strides typed as reduce_t in kernel_all #28) reg_field.cpp/reg_flow.cpp still contain correct field_precond/field_forward/flow_precond/flow_forward logic mirroring the CPU dispatch, with the try { sym_solve(...) } catch(...) { freeDevice(...); throw; } pattern intact on every exit path, no duplicate definitions across the reg_field.cpp/reg_field_rls.cpp split, and no dead files. CI timeout-minutes: 120 / -O1 / -j2 / BOUNDFLAGS are internally consistent with the current Makefile.

Not done here (flagging for human judgement, not fixing)

Whether Replicate should be excluded from the regularisers (like a hard-rejected bound), given a test-suite note like the DCT1/DST1 one, or left as an accepted "documented but not solver-safe" option is a design call, not a bug fix — left to human review rather than acting on it unilaterally.

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Generated by Claude Code

[balbasty]

Agreed -> implement.

Symmetry-breakoung boundaries should not be part of the statically compiled suite (only runtime, in case they are ever useful).

[balbasty]

Let's keep it, documented as "not safe". For now.