[JoyboyBrian]

The physical inverse-block boundary consumer required batch-major RHS input, while the actual Gaussian Core produces separate scalar component streams. This package executes the unchanged Core.gather/Core.first_cell pair, physically packs real and imaginary RHSs, invokes the unchanged BoundaryPages consumer and recovers the original component/row order. Padding, scans, rewinds, protected output consumption, parked input and retained backing are charged.

The source-relative proof covers all positive n/B/w for this actual R=2 layout. The P16/w32 five-row fixture executes both interior first passes and distinguishes skipping the consumer. B1 and B4 cases cover separate batches and incomplete rows/columns. Exact LU(round_P(S)) is the supplied reference; old scalar BandedSolve has different rounding. Second-cell reconstruction, normalized Core installation, production coefficient preparation and the fast seven-product kernel remain open. No new κ or selected-frontier change.

Validation:

• Registered normal and optimized scientific replays pass three actual compositions and nine physical rejection/discrimination controls.
• Four real optimized CLI source/receipt corruption controls pass in a Git-free relocation.
• Final committed-byte/source-history preflight, 31-file export with explicit base input ref, offline archive check and final Git-free optimized replay pass.
• Separate Codex peer review found no blockers after entry-head and partial-acquisition cleanup fixes; reviewed proof/code hashes are unchanged at the final head. No independent human or proof-kernel verification is claimed.

Canonical claim: #4182 (comment)

Prepared by JoyboyBrian with substantial OpenAI Codex assistance. Credit Jose Manuel/jmbarrancoml's Core/runtime/fixture and block handoff, the physical-boundary-pages predecessor, Vlado Vojdanovski, Cinna Davis, Chafik Boukhalfa and the retained Gaussian/FFT/tape lineage. Apache-2.0; frozen sources and notices unchanged.