Review aid: packing ceilings of 14 open complex kappa claims (stacked on #1240; no new kappa)

[Mister-Meeseeks]

Stacked on #1240 (it reuses research/complex-local-word-ceiling/ceiling.py). Once #1240 lands, this PR retargets to main. No new κ. No claim is accepted, rejected or reviewed by this PR.

Card: complex-new-helper-inventory (complex-mechanisms, chooser seed 9fe32a6efcf929bf30bb65fb781eb095, base dadfea6e). Scope is refined to the card's "reject routes without headroom" step, applied to inventories already in the review queue. This answers #1240's first open question.

What it does

30 open PRs state κ above the selected 0.001672660197076918. For each, I searched one package for:

• a complex profile whose κ equals the title κ;
• live stock W and call count N;
• an idle histogram consistent with the coverage law mass = 72W + 64N.

14 claims qualify. They are pinned by head, path and Git blob in SNAPSHOT.json; rebind.py --fetch re-reads every blob. Each profile splits into local word plus idle, and #1240's exact relaxation caps any repacking of that word.

Result

All 14 obey the coverage law at 896/9 families per call, and every endpoint lies below its own cap. They use 9 distinct local words:

Word family	Caps on κ	Claims	Headroom left
selected-type (W1, W2 = selected, W4, W5)	0.0016872026–0.0016873148	#1124 #1129 #1130 #1131 #1152 #1157	0.77–0.86%
#1148 joint-entrance (W3, W6–W9)	0.0016836800–0.0016843188	#1148 #1178 #1193 #1195 #1196 #1204 #1225 #1239	0.47–0.52%

• No repacking of any covered word passes κ < 0.0016873148.
• The leading Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148 line sits on words whose caps are 0.17–0.21% below the selected word's. Those words move local mass from rank 1 to rank 2 (5,590 against 5,584–5,586 per call). The line leads because it packs closer to its cap. Its gain is in realizability, not in a better paid profile.
• For reviewers: claims on the same word differ only in packing. A claim on a lower-cap word can never overtake the best packing of a higher-cap word. The largest remaining packing prize is about +0.7%, for packing W1 or W2 as tightly as the Conditional κ = 0.001675560947524449: joint k8 entrances, rank-seven ends, and T16 hosting #1148 line packs its own words.

Not covered

• 16 claims (Conditional κ = 0.001672691689152441: rank-seven helper ends and T16 owner packing on the seven-slot k8 word #1104 Conditional κ = 0.001672765980186726: rank-seven helper ends and T16 owner packing on the seven-slot k8 word #1107 Conditional κ = 0.001672780159952542: reverse one entrance promotion to fill T16 gaps #1111 Conditional κ = 0.001672846995880185: rank-seven helper ends and T16 owner packing on the seven-slot k8 word #1117 Conditional κ = 0.001672965558289236: rank-seven helper ends and T16 owner packing on the seven-slot k8 word #1121 Conditional kappa 0.001672716806120974: rank-seven T16 owner exchanges #1150 Conditional kappa = 0.001673260706543984: adaptive joint kernel demotion on PR1117 #1154 Conditional κ = 0.001675568675201533: joint entrances with T37 owner packing #1169 research/gauge44-ends7-t16: cross-replica exchange extinguishing remainders 5 and 6 (kappa = 0.001672802407467250) #1172 Conditional kappa 0.001675338871723469: whole-owner map at the packin… #1175 Add files via uplConditional kappa = 0.001675224519162937: cross-call gap augmentation for three extra kernel islandsoad #1176 Conditional kappa 0.001675603180601302: mixed entrance providers on T37 owners #1183 Conditional kappa 0.001675670695307702: cross-call T37 entrance augmentation #1192 Conditional kappa 0.00167576776285696: mixed T37 source-holder fusions #1201 Conditional kappa 0.001675807682652: X54 on mixed T37 fusion providers #1207 Conditional kappa 0.001675809683500501: global mixed allocation with X54 and fusions #1218) do not record a profile matching the title κ together with an idle histogram in one package. They are listed in SNAPSHOT.json.
• research/gauge44-ends7-t16: cross-replica exchange extinguishing remainders 5 and 6 (kappa = 0.001672802407467250) #1172's head moved during the snapshot, and the fetched head was used.
• Caps are planning bounds (κ < a/(1+a)). They allow fractional counts and ignore helper widths, windows and chronology.

Reproduce

python3 -I -B research/complex-queue-ceiling-census/verify.py           # ~12 s
python3 -I -B research/complex-queue-ceiling-census/rebind.py --fetch   # re-binds all 14 blobs
python3.12 scripts/research_package.py --package research/complex-queue-ceiling-census

Credit: every construction belongs to its PR's authors; the coverage identity is PR1012's. Prepared by Douglas Colkitt with substantial Claude (Anthropic) assistance. Apache-2.0.

🤖 Generated with Claude Code