[Gonzalo-Mier]

Result

The retained transfer κ = a/(1+a) requires a > 1/9 for κ > 0.1. Exact integer-root checks at a = 1/9 show that both selected local words already exceed unit moment before idle, hosting or centre work: the complex profile is >1.155558328185663 and the bit profile is >1.195679601524970. The bit bound also omits its positive surcharge. Packing and coverage changes alone cannot take either selected word to the target.

The selected coverage laws fail separate ideal rank-cap relaxations even when local work is free: complex >1.035561535760803 at rank 51; bit >1.034037852870777 at rank 45.

More broadly, the separate format-limits result scopes the current S2 B_K/star/slot format to κ ≤ 0.0051595. Reaching 0.1 therefore also requires leaving that format or its proved transfer. That is a scoped prior result, not a universal impossibility theorem, and this PR does not replay it.

Necessary zero-cost budgets

The exact reblocking screens identify only budget targets, with all physical overhead waived:

• Complex: unpaid=3, centre=0, rank-50 blocks (111×50 + 36), bill 0.999840174348039 and no extra rank-one charge; or unpaid=4, centre=64, rank-48 blocks (116×48 + 18), bill 0.998499914030822 with at most 6 extra rank-one charges.
• Bit: unpaid=3, centre=0, rank-42 blocks (122×42 + 5), bill 0.997886898348711 with at most 8 extra rank-one charges; or unpaid=4, centre=63, rank-39 blocks (131×39 + 20), bill 0.999087171501363 with at most 3 extra rank-one charges.

These are independent relaxations, not decoders, feasible schedules, a joint coverage contract, or a κ improvement. Both local suppliers and their outer accounting still need new constructions. The selected frontier is unchanged; open PRs #3051 and #3054 are not independently reviewed here.

Reproduction

Package: research/kappa01-target-screen

python3.12 scripts/research_package.py --package research/kappa01-target-screen --check-only
python3.12 scripts/research_package.py --package research/kappa01-target-screen
python3 scripts/check_research_commit.py --package research/kappa01-target-screen --ref c9c6b59ce5f526a0082d06b24470b7ac946e62da

All checks pass. The package pins the selected record and source profiles to canonical base d8e0f83f00191df62174b641e9fff055c357f641; refreshed canonical main is still at that commit.