Realize the coupled-carrier T740 packing cap: κ ≈ 0.001729777494678597

[jeremydiviney]

This adds a new 145-row allocation exchange for PR3133's changed helper inventory, attaining its fixed-word packing cap at T740:

κ = 0.001729777494678597011886 − 10⁻⁴⁶ − 10⁻⁷⁰, about 1.4052734766776475 × 10⁻⁹ above PR3143's precision-40 T74 claim.

Ten interleaved copies of the literal T74 fill contain twenty 48:[4,8,9,9,9,9] and ten 48:[9] non-tight bins. A deterministic exchange using twenty-five 32:[9,9,9] donors replaces these with tight patterns. The 145-row preimage-bound journal changes 55 bins; the unchanged owner engine checks all 2,717,280 roles. The exact idle delta is {1:+20,3:+21,5:-25,39:-10,48:+9}. Both local words and their ordered width arrays remain byte-identical to PR3133.

The contribution uses Nick Petalas's existing PR3024 lift/dual proof and PR3030 integration mechanism. The new exchange is specific to dcharb78's PR3133 inventory; the previous cap exchange cannot simply be reused. The exact cap proof checks all 2,551 patterns and derives 20*N_(48:[9,9,9,9,9]) = 1323*T. The resulting profile equals the fractional cap profile exactly.

This answers the new-journal alternative in handoff #3145, following Kumazaki's stopped attempt to transport the old journals. The pre-submission refresh found that earlier work after this journal was constructed. No priority claim for the T740 objective is made; the old-journal preimage failure remains valid.

Validation: all 11 complete source/native/admission/outer stages pass; the public finite and semantic checks pass. The recorded run rebuilds both current native providers and explicitly reuses an authenticated retained parent plus two retained native providers. A fresh retained bootstrap is the public reproducer's default but was not rerun in this session. The complete physical stock is 663,549, including 91 private zero buffers, versus 66,813 at T74; this small exponent gain costs roughly ten times the fixed stock. The strict physical invoice needs 1,479 prefix bits within the paid 2,048-bit allowance. Exact source/receipt/log bindings, the generator, all-role finite check, all-pattern cap proof, semantic rejection controls and full reproduction commands are in research/coupled-carrier-cap740/.

This is a conditional finite construction and outer certificate. Inherited all-size, compiler, physical/native and analytic obligations remain; no selected record is changed and no independent human or proof-kernel review is claimed. Further packing rearrangements in this fixed-word model cannot improve κ because the cap is attained.

Credit dcharb78/PR3133 and PR3042; Marius-Paul Dumitrean/PR2979 and the relaxation lineage; Nick Petalas/PR3024 and PR3030; Jeremy Kothe, Mason Hale, Yiyang Lu, Dugongue, Tekalign, icekylinx, Jeremy Diviney and the full retained supplier lineage. Gonzalo Mier's PR3143 provides the precise comparison, and Arham Tahir's code-disjoint PR3136 audit was replayed before expansion. New exchange and integration by Jeremy Diviney with substantial OpenAI Codex assistance. Full notices and source pins are retained.