Finite complex construction: defer historical swaps for 560 further primitives after clear elision (no new kappa)

[ToikY]

This finite scalar construction defers literal swaps across intervening macros within maximal common-frame runs of the frozen PR626 CK and JP8 programs. It remaps every source and target, then pays for scratch-copy permutation cycles at each boundary. Both forward and chronological inverse-transpose orientations save 560 real primitives after identical known-zero work-clear removal on both versions; the raw PR696 comparison saves 1,316. No new kappa is claimed.

Each orientation replaces 126 swaps in 42 changed runs with 56 paid cycles, 182 COPYs and 42 CLEARs per real component. Existing work registers begin arbitrarily dirty; all persistent helpers restore and private work clears. The compiler crosses neither frame changes nor non-scalar events. Only research/complex-swap-runs-seed37/ is added.

Reproduce with Python 3.10+ and the standard library:

python3 -I -B research/complex-swap-runs-seed37/verify.py
python3 -I -O -B research/complex-swap-runs-seed37/test_package.py

Expected: the verifier passes its full typed EXPECTED receipt; all six package test groups pass. Exact bills after the fair clear-elided comparison are CK 157184 -> 156624 and JP8 187950 -> 187390, in each orientation.

Validation: 16 full scalar projections on all 725 arbitrary input columns; independent dense replay of all 168 changed blocks and 840 local columns; independent census of all 504 swaps; 728 deleted actual materialization COPYs rejected, 13 mathematical mutations rejected, and two boundary checks. Exact row-L1 peaks and denominator guards are unchanged. Normal and optimized runs produce byte-identical receipts. Optimized isolated offline relocation, source-corruption and output-preservation checks pass. Selected-record verification and whitespace checks pass on CPython 3.12.14/macOS arm64.

Scope: exact historical scalar endpoints and paid primitive bills. Native array/frame/phase/wrapper admission, global owner invoices and outer assembly are not established. Exact row-L1 containment is not a cancellation-free envelope or approximate-rounding proof. No global optimum, runtime improvement, full-repository suite, Linux or hosted CI pass is claimed. Inherited realization, hosting, precision/tape, all-size and analytic obligations remain.

Base: 007664306fff84fbb1c9a1b4053b69f439764034. All 11 consumed source inputs have SHA-256 and Git-blob pins. Upstream advanced during the sprint to bbc600db2fc15007b7c914f4f2b2ed55fa909c87; this contribution remains tied to its immutable historical inputs. OS-random seed 37, complex-supplier track. No pinned coordination issue existed; the claim and result are local. Overlap metadata refreshed through #968; recent frame-pair decoder and bit helper-star work addresses distinct objects.

Credit: PR622/626 historical supplier lineage, Sagar Thakrar's PR696 lowering and PR839's known-zero clear removal; full predecessor attribution is in NOTICE.md. Contributed by ToikY with substantial OpenAI Codex assistance in mathematics, implementation, independent checking and writing. Apache-2.0; no independent human review yet.