Singlet contextual model

In plain terms

Here is the problem. Bell's theorem says no local hidden-variable model matches quantum predictions for entangled pairs. A deterministic programme must answer two questions, not one. Can you evade the no-go -- and can you actually deliver? Most discussions stop at the first. The second is where models die: it is easy to be contextual, hard to be contextual and correct.

This capstone does both, in one machine-checked statement. Existence: an explicit model, with shared context dependence, reproduces the singlet's full outcome table -- marginals and correlations -- at every measurement setting. Obstruction: no global, context-independent assignment is compatible with that same table.

Evading Bell is cheap talk until the model is on the table. Here it is on the table, with a proof assistant checking both directions.

In CSD

The model is built from the corpus's own arena -- the Kahler instance with its fibre measure -- with per-context outcome maps read through arc partitions of the fibre, weighted by the singlet kernel. Contextuality is not a bug being excused; it is the mechanism, and the companion theorems locate it precisely: the model's wings provably cannot be setting-local, and the operational no-signalling conditions are proved for it rather than assumed.

The pair of results -- existence plus obstruction -- is the citation anchor for the programme's Bell analysis.

Mathematically

c1_singlet_contextual_capstone: a measurable shared-context family reproduces the full singlet table (marginals one-half, correlations minus the dot product) at every context, and no global assignment is compatible with it. Scope, carried over from the obstruction and stated in the theorem's own docstring: the table half holds at every context, but the incompatibility half constrains only the four CHSH settings, and this capstone does not subsume the separate product-partition result. Supporting theorems prove the model's remote marginal invariance -- measurement independence named as a premise, not smuggled -- and its non-product character. The general obstruction is retained as a separate ledger row; the two are designed to be read together.