Research: isolate orthogonal remainder overlays (no new κ)

[1337isnot1337]

Result

For each port p = 0,...,111 at owner replica 0, under the pinned PR3148 fill, fixed chronology, cover identity and PR3187 exact eight-stream replay, this package proves a conditional implication for any finite bundle size. If every component is one of the source-bound admissible singleton hosted-remainder transfers, the moved axes are pairwise orthogonal over F_2, and the combined assignment satisfies the rank and within-child orthonormality checks, then at each moved axis v_i:

M_bundle(v_i) = M_singleton_i(v_i) != M_baseline(v_i).

At character v_i, every other moved axis contributes dot(v_i,v_j)=0 to every idle-sweep phase, so the bundle replay is exactly the singleton replay. The singleton census checks the inequality for every component in the stated domain. This is an exact operator obstruction relative to the pinned replay semantics, not a formal proof-kernel result.

Reproducible evidence

The verifier authenticates all 2,717,280 fill rows and independently projects owner-zero rows for all 112 ports. It examines 9,384 hosted-remainder candidates: 5,575 fail the commuting rule; all 3,809 that pass the rule and final rank/frame checks change the exact matrix at their own axis character. Forty-seven ports have no passing singleton.

A legal two-move control at port 0 transfers 2^32 from child 4 to child 0 and 2^72 from child 14 to child 0. The axes are orthogonal. Both baselines are i I_8; the singleton differences have 2 and 5 changed entries respectively. The bundled matrix equals its corresponding singleton at each moved-axis character. Exact matrices and differences are in RESULT.json.

The candidate domain relaxes PR3190's construction restrictions by allowing hosted receivers and bundles in which a child has both donor and receiver roles. It is an operator-level superset audit and does not establish native controller or hosting legality.

Verification

• PASS, registered package replay: python3.12 scripts/research_package.py --package research/pr3190-distinct-axis-basis-isolation (Python 3.12.15).
• PASS, direct replay: python3 -I -B research/pr3190-distinct-axis-basis-isolation/verify.py (Python 3.14.8).
• PASS, metadata and source pins: python3 scripts/research_package.py --package research/pr3190-distinct-axis-basis-isolation --check-only.

Relationship and limits

Open PR #3296 supplies the current all-singleton handoff; open PR #3311 independently audits a port-zero literal witness. This PR adds the all-port singleton replay and the pairwise-orthogonal arbitrary-finite-bundle implication, reusing PR3187's exact operator model and source loader unchanged.

Nonorthogonal moved-axis bundles, components outside the singleton domain, owner replicas other than zero, changed host schedules, and repaired or rescheduled exchanges remain open. The result adds no kappa and leaves the selected kappa = 836330098538459/500000000000000000 unchanged. No human or proof-kernel review is claimed.

Substantial OpenAI Codex assistance is disclosed in TASK.json.