The design
CASE-055 with a third language and a second route. Its Stage 0 (measurement), its named receiver populations, its criterion (choice of act and of continuation under stated tasks) and its rule that predictors are rated by other raters than those supplying the criterion all carry over unchanged.
Items. Utterances whose pragmatic effect can be separated from their content: requests, promises against predictions, honorific and T/V choices, implicatures, and pragmatic explicitations. Neither registered corpus supplies them ready-made.
- PETra (LIT-1798) has one English→X route per item. Its additions supply background knowledge and do not change act or footing. Three quarters of its pairs were found by a classifier, and it reports no agreement between annotators.
- VakyArth’s translation items and its inference items are different material, with one overlap in its release (LIT-1817).
Items have to be written for this design, with PETra’s categories as one source of candidates.
Routes. For each source item in language A, a direct translation into C and a relay through B, by translators assigned independently and working to stated briefs.
Readouts, on the same items.
| readout | what it measures |
|---|---|
| static preservation | proposition, act, stance, politeness, as CASE-055 rates them |
| dynamic preservation | response to a later framing or continuation (CLAIM-202) |
| path discrepancy | distance between the direct and relay routes’ target response distributions |
| task loss | CLAIM-259’s directed decision term on declared tasks, per route |
| change of cover | target questions the source leaves open, asked of source readers too (CLAIM-257) |
Correspondence arm. Build each community’s response matrix R(u, q): utterances by pragmatic probes, from its own readers. Fit correspondences on training items by: orthogonal Procrustes on embedded responses; unrestricted linear maps; stochastic kernels; Gromov–Wasserstein (LIT-1818); fused GW with independently validated anchor items, varying the weight on structure (LIT-1813); and co-optimal transport, which matches utterances and probes jointly (LIT-1804). Score each on held-out items, translators and, where possible, situations. Fit each edge independently, so that the composed A→B→C map can disagree with the A→C map. Name the POT release used: the 2021 paper (LIT-1809) has neither fused GW nor co-optimal transport, which came in later releases. Two of the readings constrain this arm:
- Co-optimal transport must match every probe, so a probe one community lacks is absorbed into the coupling, not reported. CLAIM-257’s change of cover needs an unbalanced variant (THEORY-1155).
- A joint fit across three communities makes the pairwise couplings jointly realizable. They compose along routes only when the couplings are deterministic (THEORY-1132), so path discrepancy should be read from independently fitted edges.
Controls.
- A degenerate translator that renders every item as one generic expression. It should reach low path discrepancy and fail the task readouts (CLAIM-496).
- A shared-provenance pair: two routes through the same intermediate translation or translator, to estimate how much agreement between routes shared provenance alone explains.
- A flipped distinction: formal and informal address exchanged with proposition kept, to test that the readouts see a change of effect and not only of wording.
- Baselines a transport account must beat: static pragmatic similarity, xCOMET (LIT-1816), and a supervised predictor of act labels. CASE-071 shows why the metric is a baseline, not a criterion.
What would be measured, and the main threat
The main test is incremental prediction of held-out receiver choices from path discrepancy, dynamic preservation and the fitted correspondences, over the static profile and the baselines. The main threat is measurement. Single judges of pragmatic similarity agreed at a mean pairwise correlation of 0.45 in Ward and Marco’s first session, within one language and with the judges conferring (LIT-1812). A nine-judge mean at that level would have a reliability near 0.88 by Spearman–Brown. Single politeness raters in TyDiP agreed at about 0.46 (LIT-1799). So the criterion must be a panel mean, and Stage 0’s reliability targets must be met, across languages, before any transport readout is interpreted. A second threat is identification.
- GW sees each community only through its similarity matrix, so it identifies a correspondence only up to the two structures’ symmetries (THEORY-1133).
- Co-optimal transport can permute a block of utterances together with its block of probes at no cost (THEORY-1155).
- Anchors break only the symmetries that move them (THEORY-1129). So anchors must be chosen that no symmetry of the response structure leaves in place, and validated independently of the fit.
What each outcome would show
- Path discrepancy and task loss uncorrelated across routes: the independence CLAIM-496 constructs also holds of real translations.
- Dynamic preservation predicting choices the static profile does not: support for CLAIM-202’s measured structure beyond the static profile.
- Anchored fused GW or co-optimal transport beating orthogonal maps on held-out items: evidence that the right transports are lossy and not invertible, as CLAIM-098 holds, and against carrying LIT-1820’s O(d) machinery over to translation.
- No transport readout beating the baselines: the pragmatic point may stand without the transport mathematics.
Stipulated, it shows nothing yet. Run, it could not show that a fitted correspondence constitutes a communicative kind (CLAIM-135), only that it predicts.