Correct the κ=0.1 complex cost screen and bound scalar-query repairs

[1337isnot1337]

Findings

This rechecks the conditional d=3 complex budget row from #3107. Under its stated private-copy coverage law, copy rank mass must be counted in both the local profile and total paid mass. Restoring that charge moves the centre-retained moment from 0.995605075916 to 1.091829820390, above one.

Payload replication by I_d does not establish additional unpaid address dimensions. Retaining the original 224 rank-seven data legs gives a separate lower bound of about 1.036807899646 even with a free decoder, under the scoped model.

General query constraint

For complex scalar fitting decoders on nondegenerate rank-k binary ports, with complete binary pairing tariffs r_j, this contribution proves

sum_j (2^r_j - 1) >= V*(2^k - 1).

The bound allows asymmetric queries, cancellations, and repeated ports. At h=8, k=3, it rules out queries capped at rank six under the stated coverage model; rank-seven/eight relaxations remain open.

This complements #3111, which audits the fixed selected bit histogram. The present work covers the complex copy-accounting correction and constraints on replacement scalar-query geometries.

Validation and limits

python3 -I -O -B research/kappa01-repair/verify.py passes 11 exact scoped replays on CPython 3.14.7. The selected result is unchanged. This contribution supplies no new bit or complex supplier, analytic extension, or multiplication theorem, so it does not establish κ=0.1.