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19.2 Base and tangent argument obstructions

For a realized argument diagram

\[ D_{\mathrm{Arg}}:J_{\mathrm{Arg}}\longrightarrow \mathcal C, \]

the base obstruction is

\[ O_0 = \mathcal O_{\mathbb S_{\mathrm{Arg}}}(D_{\mathrm{Arg}}). \]

It represents admissible diagnostics of missing or incompatible claims, grounds, warrants, qualifiers, rebuttals, sources, graph obligations, and global promotion.

Choose a declared tangent site \(\mathcal T_{\mathrm{Arg}}\) and lift the same sketch:

\[ O_1 = \mathcal O_{\mathbb S_{\mathrm{Arg}}}(T D_{\mathrm{Arg}}). \]

The tangent obstruction asks whether warrant structure survives declared changes in wording, evidence, source, context, model, prompt, intervention regime, and preference population.

Tangent site	Example probe	Characteristic failure
Surface form	Meaning-preserving paraphrase	Parser- or wording-dependent role assignment
Evidence	Delete or substitute one ground	Unsupported claim or discontinuous warrant
Warrant	Swap the inference rule while holding roles fixed	False bridge acceptance
Qualifier	Tighten or relax scope	Silent strengthening of the claim
Rebuttal	Inject, remove, or strengthen an exception	Obstruction erasure
Source	Move evidence across provenance domains	Source pullback failure
Context	Restrict or expand the local chart	Failure of naturality under context change
Preference population	Change annotator or prompt stratum	Hidden cyclic or heterogeneous preference obstruction

Table 19.1 A tangent site declares which argument variations carry semantic meaning.