nucleation

ARG-017: A constant kernel fits any one source–target pair, so one pair does not identify the procedure-level fidelity score

3 min read

Properties9
StatusProposed
Version2
Formformal-application
Tagsprobabilistic-modeling, translation
Linepragmatic-transport
Rests onCLAIM-207 — The transports of Propositions 1–2 and of D_obs act on judgement outcomes, not texts, and for any one source–target pair a constant kernel transports any overlap-consistent target, so they constrain a translation only once one kernel family is fixed across many utterances and derived from the text channel, CLAIM-011 — Intertwining with an uninformative correspondence is vacuous or lossy, so the source–target correspondence must be anchored to independently measured distinctions and evaluated on tasks other than those it was estimated on, CLAIM-381 — Over a finite class of items with finite judgement outcomes, a constant outcome kernel fits every item only when the target readers' averaged responses do not vary with the item, an exact fit is a garbling with the item as common parameter, and Le Cam's deficiency and its restriction to finitely many decision problems are finite computations
ConcludesCLAIM-228 — D_obs restated over a rendering procedure, with one kernel family fitted on some source items and scored on held-out ones and the target term the readers' response averaged over the procedure's output, separates rendering procedures that receivers' task-indexed recovery separates, so restated it measures observational fidelity informatively
SupersedesCLAIM-200 — The procedure-level fidelity thesis's title says observational fidelity is not defined for a single rendering of a single item, which is more than it shows: one source–target pair does not identify the procedure-level score, and a single rendering can still be judged, as a sample of its procedure or by another measure stated as such, as its own body says
Rendered intodocs/arguments-by-conclusion.md

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The inference

CLAIM-207: the transports of D_obs act on judgement outcomes, not texts, and for any one source–target pair a constant kernel makes the per-item term zero. CLAIM-011: a correspondence must be anchored to independently given structure, or intertwining with it is vacuous. CLAIM-381 states when a constant outcome kernel fits every item of a finite class. So the score is a property of a rendering procedure over a class of items, tested by a kernel family fitted on some items and scored on others, and one pair does not identify it (CLAIM-228).

Critical questions

  • Does the mapping premise hold? Yes. The transports act on judgement outcomes, and the kernel is fitted across items (CLAIM-207, CLAIM-381).
  • Are the model’s assumptions met in the new domain? For the conclusion as now titled, yes: a finite class of items with finite judgement outcomes. For the conclusion as first titled, no. Version 1’s title ended “for a single rendering of a single item it is not defined”, whose subject is observational fidelity, not the measure. CLAIM-200: that “is more than it shows”. A240 of the exchange: “it does not follow that an individual translated utterance has no fidelity properties. It means only that the proposed procedure-level distributional score is not identified by one isolated pair.”

Verdict

Active, as an inference to CLAIM-228’s version 2, which “changes the title only” and leaves the derivation and the defeat condition as they were. As an inference to version 1’s title it was Rejected, by CLAIM-200, granted on 2026-10-10 “because it can be checked by reading”. A single rendering can still be judged, as a sample of its procedure or by another measure stated as such (CLAIM-230’s remedy: “For single renderings, a different measure, stated as such”).

This argument spells out CLAIM-228’s own rests_on, with CLAIM-207 named. It is filed because CLAIM-200’s verdict was about this support relation.

Filed 2026-10-28 by the ADR-061 migration, from CLAIM-200.

Note of 2026-10-28: Proposed, waiting on a result

The sixth status review moved this argument from Active to Proposed. CLAIM-228 was retitled to the proposal it kept at version 3, that the restated measure is informative. These three premises carry the structural part, which CLAIM-207 and CLAIM-381 already hold, and not that one. CLAIM-381 says so itself: “It does not say the restated measure tells rendering procedures apart. That is CLAIM-228’s defeat condition”. The inference is offered, and a CASE-055 result would be its fourth premise. The verdict above is the history of version 1.

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