Extended carrier matching on #161's complex word: conditional κ = 5.901881e-4

[DaysSky]

Built on #161 (eumemic, d14e291). #161 was closed in favour of #168 and is not on main, so this package carries the 32 files of #161 it reads (scripts, frozen arcs and physical layer, module sources and certificates) as a pinned archive, baseline-pr161.tar.gz (0.3 MB). It rebuilds them in a temporary directory, following research/coordinated-frames-and-entrance-banks. Each file's sha256 is pinned in SOURCE.json to commit d14e291; a tampered archive is rejected. No existing file changes. The compiler introduced here (compile_closure) has since been adopted into #168's scripts/paired_cube/closure.py.

Under #161's retained interfaces, this certifies

T(n) = O(n (log n)^(1 - κ)),   κ = 5901881/10^10 = 5.901881e-4

That is +0.394% over #161 (5878747/10^10). #161 is complex-bound, so a complex-side change moves κ directly.

What changes

Only the complex word's carrier arcs and its physical layer change. The graph, the gauges, the bit supplier, the phase stop, the atom exponent and the assembly are #161's.

• 48 more carrier arcs. compile_graph accepts an arc only if the donor's coordinate-padded maximal frame already lies inside the receiving frame. That pre-test is sufficient, not necessary. The construction needs less: the dependency graph with the arcs is acyclic, and every value span still lies in its full backward-intersection frame. cxlinks.compile_closure compiles with that condition. Every arc of Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161 is kept, and 48 that the pre-test rejects are added.
• The physical layer is rebuilt for the new word under Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161's own rules. The pairing is chosen by first-order saving, which on Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161's own arcs is worth +0.13% by itself.

	carrier arcs	roles R	W per vertex	complex saving	κ
#161	6,201	16,011	15,681	5885669/10^10	5878747/10^10
#161's arcs, layer rebuilt	6,201	16,011	15,681	5893384/10^10	5886444/10^10
this PR	6,249	15,963	15,633	5908857/10^10	5901881/10^10

The deficit per vertex (1,320) and the largest child (20) are unchanged. The complex side still binds; #161's bit supplier sits at 5.9308e-4.

Verify

python3 research/extended-links/verify.py      # stdlib only, about 15 seconds; do not use -O

1. Control. With Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161's arcs and the repository's operation order, compile_closure returns Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161's certified complex record exactly, and Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161's frozen physical record prices to 5885669/10^10 and 5878747/10^10.
2. Word. The repository's independent checker scripts/paired_cube/verify.py passes unchanged on the extended word: 1,742,400 signed scalar pairs, K, full backward intersections, the physical replay of every frame movement, 2,970 rank-18 gauges and the target chains. That checker has no pre-test.
3. Physical layer. Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161's scripts/paired_cube_physical.py passes unchanged on the new frames and pairs: value spans, nested spliced chains, pair chronology, target chains in read order, the telescoping deficit, and the exact aliased replay with its three controls rejected.
4. Pricing. Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161's exact_moment, finite_bridge and 47-constraint assembly give both values as the largest points of the 10^-10 grid, with the next points rejected.

One check of #161's code is relaxed in verify.py: the complex role count is not pinned to 16,011; it must equal c + q − matched and not exceed 16,011.

Run before opening:

• verify.py passes on this branch from the archive alone (Python 3.14, macOS); it also passed on 3.12 against the original Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161 tree.
• make_plan.py regenerates the three data files byte for byte.
• -O is refused.
• tests/test_recycled_bit_integration.py passes on this branch.

Not run: the complete make verify, the formal targets, and any Linux run. The new workflow runs verify.py and the plan regeneration on Python 3.11 and 3.14.

Scope and limits

PROOF.md gives the argument. Every interface #161 retains stays an assumption. Beyond that:

• No optimality is claimed. The arcs are a greedy extension of Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161's matching and the pairing is greedy.
• The operation order is a different linear extension from the repository's, so the phase-one closure differs (11,302 operations here, 10,150 in Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161). The gauges are selected by the repository's rule and checked by the repository's checker.
• Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161's bit supplier is used as certified there and is not re-run here.
• The pins refer to Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161 at d14e291. The package stays valid for that commit.
• Tried and not used, because they do not help under this pipeline: the other output merges (s, w12, and a pair-level merge of face 1 with edge 01) are cost-neutral, and two other all-but-one modules are worse.
• This has had no review other than the checks above.

Credits

• eumemic: Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161 and its lineage (Deferred bit word and a 28,705-role complex producer under stopped-product accounting: conditional κ = 1.044939e-4 #117, Physical frames and scratch reuse on Cayley covers: conditional κ = 3.32205398986e-4 #131, Late compensation and joint frame refinement: conditional κ = 4.24830828577e-4 #143, Paired cubes at p = 11 with an h = 21 bit word: conditional κ = 5.108289e-4 #152, Paired cubes at p = 11 with physical frames and a paired-cube bit word: conditional κ = 5.508074e-4 #155, Paired cubes at p = 11 with a searched pair module, physical frames and a paired-cube bit word: conditional κ = 5.555021e-4 #157): the complex DAGs, output merging, the physical layer and its checker.
• icekylinx: Paired cubes and shared completed cores for conditional kappa = 4.609169e-4 #144 and Three-stage Cayley covers for conditional kappa = 3.146011e-4 > 2^-12 #130 (paired cubes, the compiler and its independent checker, gauges, shared cores, assembly).
• an664: Completed-core sharing: conditional kappa > 2^-13 #128 completed-core sharing. jamesyc: Birth-read slot recycling: conditional kappa 1.1038332094346e-4 #124 birth-read reuse. geckods: Re-instantiated phase-stop on the p = 11 paired cubes: conditional κ = 5.108294e-4 #153 and Re-instantiated atom exponent at the toll edge on the searched pair module: conditional κ = 5.557315e-4 #158 phase stop.
• Zhihao Chen and Swapnil Jain: the bit lineage behind Merged complex outputs and an annealed bit pair module on paired cubes: conditional κ = 5.878747e-4 #161's unchanged bit supplier.

The closure-condition compile, the extended arcs and this physical layer were prepared by DaysSky, assisted with Claude. No priority over concurrent work is claimed.

[Mister-Meeseeks]

Thank you @DaysSky. This contribution is now recorded on main in the scoped reconciliation review and contributor credits.

Contribution: Expanded legal carrier relation with full backward containment.

Review and limits: Fresh full replay; acyclic relation and all 48 arcs paid.

The complete original source, proof/research notes, notices and relevant replay/CI evidence are retained through the pinned source archive. The review distinguishes fresh runs, exact-head historical CI and prior integration evidence. Closing this historical PR as reconciled; its obsolete headline does not replace the current selected bound, and draft/retracted claims retain their explicit qualifications.

Reviewed head: 279b2ff6d3f0a1abe4a61c1f2ea4944bca7cf3dd. Publication: b84ba67156a01f9c2cb34fe1e3cb1dcdeab00d9c.