[zxv]

Result

This improves the conditional κ of #4076 by 1.61385622611621004 × 10⁻⁷ (+0.0093243%).
It composes exact dirty receiver sharing with #4076's three staged helper entries
and literal T360 owner allocation, building on #3945's terminal refit.

	#4076	This contribution
Complex root lower endpoint	0.001730809033576552081734	0.001730970419199163702738
Outer loss	10⁻⁴⁶ + 10⁻⁷⁰	10⁻⁴⁶ + 10⁻⁷⁰
Binding supplier	Complex	Complex

The exact conditional claim is

κ = 0.001730970419199163702738 − 10^-46 − 10^-70.

Both claims subtract the same outer losses, so the increase in κ is exactly
the increase in the supplier endpoint. The percentage compares the displayed endpoints.

The added receiver identity replaces 672 += 544; 676 -= 544 with
672 += 676; 676 -= 544; 672 -= 676, with the required frames and regenerated
cleanup. It preserves arbitrary dirty inputs and changes the local paid profile
by {1:-1, 2:-1, 3:+1}. The complete native/owner invoice prices that change.

The submission also supplies exact operator checks that reject the faulty
phase-axis overlay used by the earlier #3955/#3959 chain. The new supplier uses
no such overlay. The historical high complex claim remains withdrawn; the
research target 0.001745 remains open.

Evidence and validation

• The new gate checks 10,416 exact phase identities across all 112 ports,
  including signed controller, final translation and global phase. Its stated
  algebraic scope covers all characters and positive tensor multiplicities
  under the retained local-endpoint interface. The old faulty overlay rejects.
• The stronger owner invoice checks all 1,321,920 hosted rows and 70,876 owner
  reassignments, recovering the original child operators from hosted and
  complementary residual factors.
• A separate exact rational calculation confirms the final complex root bracket,
  rank mass, binding supplier, outer losses and comparison arithmetic.
• Fresh portable replay passed 14 scientific stages and 29 comparisons
  in 115.20 seconds, including both complete five-stage native providers. Three
  portability rejection controls passed. Fresh receipts and logs are retained.
• All supplied archive bytes are preserved. The submission adds unpacked
  source/evidence trees rather than committing the 168 MB ZIP.

Two local portability issues were identified and documented: the native audit
requires NumPy, and native gzip OS header bytes differ between Linux and macOS.
The new review runner uses the unchanged core and native scientific scripts.
It compares gzip payloads exactly and authenticates each derived receipt's
container digests before comparing every remaining scientific field. It permits
only the documented phase-review runtime difference. The frozen submission
and expected receipts remain unchanged.

python3.12 -m venv /tmp/kappa-repair-env
/tmp/kappa-repair-env/bin/python -m pip install numpy==2.2.6
/tmp/kappa-repair-env/bin/python -B research/kappa-operator-repair-review/verify.py \
  --out /absolute/path/to/a/fresh-directory
python3.12 -B research/kappa-operator-repair-review/check_price.py
python3.12 -B research/kappa-operator-repair-review/check_import.py --git-ref HEAD

The review and fresh evidence live in research/kappa-operator-repair-review/.
The authoritative final claim is
research/kappa-operator-repair/late-staged-composition/CLAIM.json; the package's
top-level claim is an earlier, weaker checkpoint.

Scope and attribution

The portable review freshly executes core proofs and both native providers.
It authenticates the retained completed full-release evidence without rerunning
that long release. The retained BIT supplier is also source-bound rather than
freshly executed here. Uniform native/cover embeddings, physical primitives,
compiler/tape costs, precision, recurrence and outer transfer remain conditional.
There is no complete GL64 physical execution, formal-kernel acceptance,
independent human approval, or maintainer admission. The selected frontier stays
unchanged.

Canonical main was refreshed to bb4bccbf42844d2801487450727c2f63e10d1d0f.
#3945 and #4076 heads match the supplied pins; related open PRs were checked.
The direct improvement comparison is to the pinned #4076 claim.

Credit David Ganz / Dugongue (#3945), Rohan Arun (#4076), Tekalign's native
runner, Ross Richardson, dataisfire, ChaloupeMusic / Erwan Secousses,
Marius-Paul Dumitrean, Sagar Thakrar, roger-sato, the full T360/BIT/outer lineage,
and Nick Petalas, Matarener and Erwan for the earlier operator obstruction.
Original notices are retained. Substantial OpenAI Codex assistance; Apache-2.0.

Open next questions: independent review of the retained full release, admission
of uniform native/owner and precision interfaces, and further gains on the
repaired staged/receiver word with complete invoices.

[tekuuu]

CLAIM — new-kappa construction search, canonical base bb4bccb, exact PR4085 head c5854c7. I am testing ternary covector sharing and its transpose: one dirty carrier aggregates THREE stable source fields, serves a repeated coefficient triple, then restores itself. The existing pair searches aggregate two fields; this tests joint changes that need not win separately. Domain: literal A/B/restore, finite bounded windows, exact frame-domain optimization with floating nomination only; candidates must pass exact dirty semantics, regenerated cleanup, native/interface and full same-owner invoice checks. No added helper or uncharged restoration. Expected result: one fully checked improving candidate or a bounded failed-search record; no assumed stronger bound. Expected finish17:50UTC. Tekalign (tekuuu), with substantial OpenAI Codex assistance; credit Nick Petalas and the PR4085/4076/frame/native lineage.