[unpaidmoon]

Change and mathematical scope

Scoped negative result, no new κ. In the published two-edge active feed, every rational sum of alternating C1/C3 words, with or without a right Q^2, preserves one monomial of the second-input coupling whenever it keeps the restored coefficient D1 Q^{-1}.

The predecessor search showed that 8,281 bounded policies attain only one of four jobs. This note is exact for the whole infinite decoder family and uses all 39 saved banks. The witness is two basis coefficients on the D1 line: α = Q^{-1} and β = Q^{-1} C1 Q. Keeping α coefficient 1 forces β coefficient 1, so the y0 block is not zero.

An explicit two-term correction from final bank 1 does clear that y0 block, but both of its words have an odd power of Q. It is outside the declared family and is not offered as a free repair. The x1 block is untouched. No selected-frontier change.

Task and overlap

Base: 7c49fe32c55de02c2c873655c804b16e4c3fef0a, priority revision 8. Card: joint-query-controller, scope refined. This does not change the QQ16 demand. It answers the open coupling question in research/coded-active-feedback after that package had already restored the missing coefficient. That question is the live remainder of handoff discussion comment 19138525, the 10th structured HANDOFF still open on #1166 in comment order.

Live inputs: research/coded-active-feedback/search.py and research/coded-native-caller/gauge.py. Nearest work is that package and the passive ceiling research/passive-saved-query-ceiling (PR #4978). No open PR title states this two-point lock. Unpaidmoon’s earlier active-width and G20 notes do not treat this row.

Validation

python3 -B scripts/research_package.py --package research/active-feedback-coupling-lock

Python 3.12, standard library only. Normal and optimized registered commands both print PASS_ACTIVE_FEEDBACK_COUPLING_LOCK. The optimized run still executes the checks. Controls: omitted second edge does not restore A; the odd-Q companion correction clears y0 and is rejected as a member of the declared family; short-control preimages miss the seven-word support.

Not run: a port-dependent map, a new feedback edge, native tape, precision, compiler, outer admission, and any selected replay. The algebra is the predecessor’s sufficient identity model.

Credit

Trace, algebra and decoder family: Cinna Davis, research/coded-active-feedback, using Dugongue’s PR4948 chronology, Dillon’s PR4933 code, and the passive ceiling packaged by Chris R / Clear1nsight. Gauge engine: inherited research/coded-native-caller/gauge.py.

Prepared by unpaidmoon with substantial Cursor Grok assistance. Apache-2.0.

Open next questions

Can a port-dependent map remove the y0 term while every required final bank stays intact? First step: one owner-indexed map with the x0 block fixed, the y0 block zero, and the other endpoint banks unchanged, then charge every new monomial. The restored bank’s x1 term is a separate unpaid obstruction.

Does one feedback edge outside the 8,281-policy family make the whole four-input row autonomous? Name the edge and test the row before adding calls. No such edge is constructed here.

Workflow feedback (optional)

The handoff’s first next sentence had already been carried out on main by research/coded-active-feedback. The useful remainder was the package’s own open question, not another replay of the passive ceiling.