nucleation

CLAIM-256: D_obs sums over source contexts only, so a target context outside the image of τ appears in no term: a rendering that adds a relation pays nothing, and a change of cover registers only as loss

2 min read

Properties8
StatusActive
Rolegranted
Warrantdemonstrated
Tagsmathematics, philosophy-of-language
Linepragmatic-transport
Objects toCLAIM-005 — Pragmatic fidelity is the match between distributions of context-indexed communicative judgements across a correspondence of source and target contexts, not the similarity of one canonical meaning vector; the match constrains a translation only once one outcome correspondence is fixed across many items, and summed over source contexts alone it charges for loss and not for addition
ComplementsCLAIM-087 — Cross-modal reconstruction often improves a receiver's access to an implicit communicative relation beyond the text-only baseline, as when posture or expression conveys solidarity better than the source text's literal content, though a rendering made without the situation is a garbling and cannot improve what an ideal receiver could do, CLAIM-076 — Cross-modal chains expose reconstruction because media differ in expressive affordances, and each interpreter, such as a captioner, may add motives and relations that were not present
UsesTERM-021 — fidelity, as context-indexed distribution matching, TERM-043 — fidelity, as a profile of directed distortions compared component by component

Graph View

The objection

CLAIM-005 gives the manuscript’s L_obs(T) = Σ_C w_C d_C[(K_C)#e_C^o, e_τ(C)^t]. TERM-043 gives the profile’s D_obs(T) = Σ_C w_C d_C(T_C# e_C^o, e_τ(C)^t). Both sums run over source contexts C. A target context that is not τ(C) for any source context C appears in no term.

A worked case. Let the source cover have one context C, in which readers judge the speaker’s stance. Let the target cover have two: τ(C), with the same judgement, and a new context C′, in which readers judge a relation the source does not carry, such as whether the speaker is mocking a third party. Then D_obs = w_C d_C(K_C# e_C^o, e_τ(C)^t). Two renderings that agree on τ(C) and differ in any way on C′ have the same D_obs.

So a relation that a rendering adds costs nothing. A change of cover registers only as loss: a source context with no good image pays its term, and a target context with no preimage is free.

The line says additions happen. CLAIM-076: “each interpreter, such as a captioner, may add motives and relations that were not present”. CLAIM-087 is “a transport that adds a distinction”. And D_obs is the one component of the profile that can be computed. CLAIM-128: “Only D_obs has a formula”. So the one computable component is blind to additions.

What it does not say

  • It does not say no other component can catch an addition. D_struct, “Failures to preserve restriction maps and specified relational constraints” (TERM-043), could, if the added relation is specified.
  • It does not say additions are distortions. CLAIM-087’s improved access, and the deliberate adaptation of CLAIM-034, may be wanted. The point is that D_obs cannot see them either way.
  • It does not say directedness is wrong. A directed measure may weigh losses and additions differently. This one does not weigh additions at all.

Note of 2026-10-27: the edge says what the claim uses

The status review of this date (ADR-057, ADR-058) changed rests_on CLAIM-076 and CLAIM-087 to complements. The result is read off TERM-043’s definition. The two claims say only that additions happen, which motivates the result and is not a premise of it.

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