[unpaidmoon]

Change and mathematical scope

Scoped identity and field ledger. No new κ. The selected conditional value stays 781451/250000000 from the selected record (PR #6030). This does not change the selected frontier.

On the published two-edge feed, every owner-indexed D-exponent-0 left map of the four final banks that keeps x0 = D1 Q^{-1} and clears y0 satisfies

m1 + m0 C1 = -Q^{-1} + Q^{-1} C1 Q C1.

The constant index writes that defect into a fresh image. The four stored endpoint banks are not overwritten. The image's x1 block remains the published three-term coefficient and is unpaid.

This is an algebra identity on the replayed banks, not a bounded search and not a claim that every physical quotient is as expensive. The field ledger is one factored circuit under inherited units: 2016 scalar ADDs, 672 monomial passes, 32 mode CLEARs, 224 COPYs, and 336 extra fields. It is not a minimum and not a tape proof.

Task and overlap

Base: 7c49fe32c55de02c2c873655c804b16e4c3fef0a. Card joint-query-controller, scope refined. The card's demand is not changed. This is the owner-indexed remainder of handoff discussion comment 19138525 after research/coded-active-feedback restored the missing coefficient.

Nearest work, and why this is distinct:

• research/coded-active-feedback (upstream) restores A only together with the y0 coupling and stops at an 8,281-policy search. It does not give this owner index or this charge.
• Fork draft PR 152, package research/active-feedback-coupling-lock, proves the declared alternating family cannot separate the witness monomials, and notes one odd-Q correction without an owner-index identity or a monomial charge. That census is not rerun. The new statement is the defect identity for every D-exponent-0 owner index, plus the charge for the constant-index image.
• The question of one feedback edge outside the 8,281-policy family is not taken.

Local overlap at the base commit searched the complete note inventory and found no note containing both "owner-indexed" and "y0 coupling". The remote overlap cache was absent. A live open-PR search for y0 returned no CrocSwap pull requests. That is not a novelty certificate.

Validation

Python 3.12, standard library only. Normal and optimized registered commands both pass:

python3 -B scripts/research_package.py --package research/owner-indexed-y0-clearance --check-only
python3 -B scripts/research_package.py --package research/owner-indexed-y0-clearance

Checks are explicit need failures. They cover the pinned replay, the finite products, the defect identity including a relocation of Q^{-1} into m0, the fresh image, dropped-monomial failures, and the ledger arithmetic. No native build, network fetch, or full multiplier replay is used. Q and Q^{-1} are charged as one monomial pass each, the predecessor's Q^2 unit; a three-factor expansion of Q^{-1} is not settled.

Credit

Cinna Davis, research/coded-active-feedback, using Dugongue's PR4948 chronology, Dillon's PR4933 code, and the passive ceiling packaged by Chris R / Clear1nsight. The uncharged one-point correction is fork PR 152. The gauge engine is the inherited research/coded-native-caller/gauge.py.

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

Open next questions

Can a fresh image clear the three-term x1 block while keeping x0, keeping y0 zero, and leaving the four final banks stored unchanged? Start with the same four-bank equation on the x1 column. This package leaves that coefficient in place.

Does one inherited monomial pass implement Q and Q^{-1}? Bind the source primitive for a single power of Q before treating 672 monomial passes as a tape cost.

Workflow feedback (optional)

The revision-8 priority note still prints κ = 0.00310045 from PR #5599, while certificates/selected-result.json has 781451/250000000. The selected record is the right orientation pin. One link to the feedback discussion is enough: #1200