The claim
A34 §4: “the degree to which interpretive perspectives interfere with each other could itself be part of what a faithful translation preserves.” Manuscript §9: “If ΦA≈A’Φ and ΦB≈B’Φ, compare Φ[A,B] with [A’,B’]Φ … This identity bounds commutator distortion by local intertwining defects and operator norms.”
Its argument is ARG-006.
What it does not say
That the commutator structure is preserved: only its image under Φ (CLAIM-011).
Note of 2026-10-10: the replies
After CLAIM-253: the intertwining defects are not identified from data, since two models with the same observations can carry defects 0 and
- CLAIM-231 bounds the observed order effect by observational distortions alone: if each order’s response distribution is within ε of the source’s under one outcome correspondence, the observed order effect is within 2ε. The identity explains that bound under a state model, and ARG-006’s algebra stands. The defeat condition above, stated on “measured order effects”, is to be read against that bound. The manuscript’s text quoted above is unchanged.
Note of 2026-10-19: split under ADR-043
The identity Φ[A,B] − [A′,B′]Φ = A′E_B + E_A B − B′E_A − E_B A, with its norm bound, is now CLAIM-373. It is proved there and Active, and it is the approximate case that ARG-006 names. This claim keeps the thesis that the identity is used for: that interference between perspectives can be part of what a translation preserves. That thesis is tested by measured order effects. Given CLAIM-253, the identified bound to test against is CLAIM-231’s observational 2ε, not the defects. No study has been run, so the claim is interpretive.
Note of 2026-10-28: what holds it back
The fourth status review (ADR-057) took this claim because ARG-006, which concludes it, is a sound argument: its inference is Active and its one premise, CLAIM-373, is Active. The claim stays Proposed, because the inference carries less than the claim says, and the record already says where:
- CLAIM-011 (Active) limits the result to Φ’s image. Preserving Φ’s image of a commutator does not establish preservation of the whole commutator structure unless Φ is informative enough.
- CLAIM-253 (Active) is a live objection, and it undercuts ARG-006. The intertwining defects are defined on interpretive-state spaces and are not identified from judgement data. The identity reaches observed order effects only with a readout-intertwining defect, O′Φ − O, which the claim does not state.
What would clear it is a version that states the readout defect and bounds observed order effects by the intertwining defects together with it, and that names an identified choice of Φ, so that the defects are fixed by the data. Until then, how far interpretive perspectives interfere is part of what a translation preserves only in an unidentified sense.
Note of 2026-10-29: CLAIM-253 written in
The identity is CLAIM-373’s and holds on interpretive states. A study observes responses. There the identity bounds the order effect only with the readout defect added, ‖O′[A′,B′]Φμ − K O[A,B]μ‖ ≤ ‖E_O[A,B]μ‖ + 2(‖E_A‖ + ‖E_B‖), and the data do not fix its defects. The bound identified from data is CLAIM-231’s 2ε, under one outcome correspondence fixed across items, and the defeat condition now tests the thesis on that footing. The note of 2026-10-28 called CLAIM-253 live; it is now written in. The identification result its second answer asks for, a minimal-realization theorem, is still open.
Note of 2026-10-29: what holds it back
No study has measured the order effects of different renderings of the same sources under one outcome correspondence fixed across items. CASE-065’s two administrations change language and readership together, and report correlations rather than response distributions, so no ε can be computed from them.