Add 87 reusable Lean theorem APIs and conditional κ = 0.00168357

[Dugongue]

This contributes a checked conditional κ = 0.00168357 application, improving the PR #2260 supplier under the documented modern-outer premises, together with a standalone Mathlib-only toolkit of 87 named theorem APIs (76 in three new modules, 11 retained from #2260) for future integer-multiplication workers. It covers phase-correct native inverses and chart changes, arbitrary dirty relays, literal family-tagged reordering, arbitrary-width stopped recurrences, common-grid reserves, finite bootstrap reachability, and reserve-aware paid-moment transfer including real-power concentration. Counts include supporting facts and extensions; they do not claim 87 novel mathematical discoveries. All 87 theorems and 19 supporting definitions pass a fresh source-bound kernel/transitive-axiom audit with only standard foundational axioms. Toolkit.lean imports Mathlib only; no personal Lean tree is needed.

The included application changes 93 literal owner/offset rows, removes eight positive children, and reduces the actual paid moment of #2260. Both independent exact rational engines accept complex saving 0.00168358 and reject the old profile at that same saving. The retained balanced-prefix outer gives conditional kappa 0.00168074; the credited #1673/#2220/#2265 modern outer gives conditional kappa 0.00168357. An explicit 31-level finite ordinary bootstrap supplies the modern ledger's near-endpoint ordinary interface. The stronger result requires the additional capped-fusion, gauge-free, radix-union and fine-prime-padding premises documented in the proof guides.

This is not the current numerical record: the final review through #2279 found #2269 claiming approximately 0.001696247139 on a different T74 borrow43 supplier, itself crediting the anticipatory borrowing in #2226. Its claim was read, not independently replayed here. The general theorem interfaces can support that newer line, but no automatic T74 transplant or better-than-#2269 claim is made.

Validation: complete relocated replay of all 5,992 native jobs, 31,392 physical roles, 7,118 literal charts, exact factor partition and invoice, two independent moment engines, 47 legacy and 54 modern strict outer rows, 17 modern rejecting controls, 19 retained outer evidence replays, and six gzip representations plus 11 corruption controls. The new wrapper checks exact decompressed payload bytes while preserving immutable checked-in byte pins. Fresh Lean audit replay also passes. The 70-file #2260 predecessor is included byte-for-byte and source-bound. See README.md, LEMMA-GUIDE.md and the reproducible audit scripts.

The all-size compiler, fixed-tape execution, ordinary/bit, recovery and analytic interfaces remain explicitly inherited conditions. The full multiplication theorem and finite Python certificates are not formalized in Lean. Local checks used Lean/Mathlib 4.33.0 and Python 3.11.9; hosted CI/Python 3.12 and independent human review are not claimed. Upstream attribution and Apache-2.0 notices are retained. Substantial OpenAI Codex assistance: one primary agent and three collaborating agents.