[Matarener]

Requested by Mark

Change and mathematical scope

Side result (ideal budget screen); no new κ. The selected κ is unchanged.

Priority revision 7 says its allocation predates #4359 and has not been reassessed. The #1240 lever table (levers.py) was computed on the old #1094 word. This package recomputes the same one-at-a-time ideal budgets on the current complete invoices: #4470's complex RESULT.json and the retained query-thinned BIT bit_invoice. It uses #4470's fixed-profile root Σ T_r r^(1−C) = Σ P_r r^(1−C) with certified brackets of width 1e-10.

• Where the paid moment goes. Whole-idle stages take 59% (complex) and 56% (BIT). The 18 calls' small local jobs take 40% and 43%. The 15 query-only shears take 0.7% and 0.8%. The owned centre takes 0.5% (complex only). Surplus mass is 752 = 48·18 − 112 and 753.
• Lever ceilings (complex / BIT raw roots). Baseline 0.0030202 / 0.0034642. Centre free 0.00765 (2.53×; old 2.80×). Centre shared 0.00533. Rank-16 local children 0.0174 / 0.0332. Two unpaid coordinates per idle family 0.0282 / 0.0319. Query shears free 0.0099 / 0.0113. Pairing every rank-one local job 0.003404 / 0.003751. Free idle stages give > 1/6.
• Readings. κ ≤ min(complex, BIT), so a complex-only lever stops at the admitted BIT 0.0034 (+12.6%), and a BIT-only lever changes nothing. Applied symmetrically, complex still binds in every row. The margin is thin: about 94 units of paid moment separate complex from BIT. That surplus is fixed by the controller, and repacking at fixed mass is weak. Most of the bill (idle stages and query shears) is controller work, not local-word work.

Remaining scope: every lever is a hypothetical relaxation with no new charge, and outer rows, strictification and BIT ordinary conversion are not recomputed. "Two unpaid coordinates" has no literal counterpart in the new invoice, so the table gives one reading. Root uniqueness is not certified.

Task and overlap

• Card. complex-new-helper-inventory, priority revision 7; its first step asks for levers.py budgets. Scope changed: it updates that planning screen and builds no interface (TASK.json).
• Base. f626db5c3a3d781d8f7695038776c621651f75e1. Inputs pinned in SOURCES.json.
• Overlap. Research note: packing ceiling (+0.87%) and 1/99 budget for the selected complex local word (no new kappa) #1240 (old table). Certify zero four-shear headroom in twelve PR4470 receiver windows (no new kappa) #4546/Close local improvements on #4470: shear rewrites (128 windows, 88 nonadjacent, len 6, |c|<=3) and 1- and 2-contact retiming - all 0 (no new κ) #4567/Independently certify all-length receiver-window floors by exact rank dominance #4581/Prove receiver-window floors with mandatory contacts and bridges (no new kappa) #4585/Independently cross-check all-length receiver floors and two pinned certificates #4587 close local window rewrites of Conditional kappa = 0.00302015 (+0.6304% over #4447): joint helper boundaries #4470, consistent with the controller-level reading here. A search found no lever re-pricing after Conditional κ = 0.0023 (+5.690e-4, +32.87% over #4181): productive helper jobs compiled into a uniform supplier #4359. A companion PR examines the query shears.

Validation

python3.12 -B scripts/research_package.py --package research/productive-lever-reprice
python3.12 -B scripts/check_research_commit.py --package research/productive-lever-reprice

Both pass (CPython 3.12, Windows, standard library only, about 12 s). Controls: the profiles are rebuilt from their physical parts (18 local calls, 15×112 / 15×111 queries, idle, centre); the complex bracket meets #4470's root bracket; an empty lever reproduces the baseline; one extra paid rank-one job lowers the root. The interval engine is mixed_target_probe's log/exp series, rounded outward to 2^-128.

Credit

Invoices and model from 1337isnot1337 / Cinna Davis (#4440, #4470), zxv (#4359) and the retained BIT lineage; lever table from #1240. Prepared by Matarener (Mark) with substantial Claude Code assistance; no independent human review.

Open next questions

Can a controller reduce whole-idle mass or the query shears on both suppliers at once? Screen candidates with assemble/root on both invoices first. No changed topology is known.

🤖 Generated with Claude Code