[flyingviper]

A proposed productive helper would carry entry13 + dirty_entry416 on a one-dimensional chart. This package proves that its required local encoder cannot be realized by any ascending common-chart scalar circuit at the retained boundary, even with arbitrary rational coefficients, circuit length, preparation and interleaving. No improved kappa is claimed.

The new invariant goes beyond the forward/inverse support tests, which this candidate passes. A no-return argument commutes all single-input-group scalar gates before all mixed-group gates. Nine outputs must remain within one group, forcing the other 15 outputs' hot-input rowspace to be generated by its single-group subspaces. Exact source reconstruction gives rank 7, but those subspaces span only 5 dimensions. A single column relation already supplies the contradiction.

The obstruction extends to every rational invertible basis change in the complete three-channel common-native-map class that fixes the desired productive value. After invertible complement mixing, this reduces to two rational shear parameters. An exact polynomial kernel identity proves rank 7 for every parameter choice, while the single-group subspaces span at most 6 dimensions. This is a universal symbolic certificate, not a parameter grid.

The result covers direct H=P T M on the 24-role, 150-gate source interval [9961,10111); it requires no R/E or cold-basis prefix. Independent workspace returned unchanged does not help. A changed productive output, broader boundary, internal native operation or paid nonascending transport is outside the main claim. This differs from #5361's support obstructions for the persistent output basis.

Validation at 2104af7b98c592dea295f90d047fe94eefddc1c9:

• Independent matrix reconstruction, normal-form proof review, universal-family algebra review and final package audit.
• Source-pinned registered normal and optimized isolated replays pass; seven corruption controls and two scope controls pass.
• Original source positive control: 40 single-group gates, 110 mixed gates, 72 commuting inversions; exact full 24 matrix identity; rank 8 with group dimensions 2,2,2,2.
• Metadata, committed bytes, full source ancestry and whitespace checks pass.
• Official export integrity and optimized Git-free replay with empty PATH pass. Hosted CI is reported separately by GitHub on the current head.

python3 -B scripts/research_package.py --package research/productive-helper-color-cut

One scoped package on canonical main 7c472563474e60185e6ca101a17622133d047e56. Source is #5301's integrated compression certificate; no frozen source, shared tooling or selected-result changes. Credit Cao Yifan's #4610, Cinna Davis's #4692 and #4470/controller lineage, Dugongue, zxv, Jacob Alan Sussman and retained predecessors. Prepared for flyingviper with substantial OpenAI Codex assistance and independent AI agents; no human or proof-kernel acceptance is claimed. Apache-2.0.