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QUESTION-240: Does a transport whose local kernels commute with restriction preserve overlap consistency, and does a transport induced by one global stochastic kernel preserve global extendability?

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Properties5
StatusAnswered
Tagscontextuality, mathematics
Linepragmatic-transport
RefinesQUESTION-022 — Beyond restriction-compatible kernels and kernels induced by one global kernel, which stochastic transports carry compatible empirical models to compatible ones and preserve global extendability: which conditions are necessary, and what does a transport that changes the cover do?
Answered byCLAIM-070 — Transport induced by one global stochastic kernel carries a global extension of the source model to a global extension of the target model, CLAIM-121 — A transport whose local kernels commute with restriction maps overlap-consistent source models to overlap-consistent target models

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Answer

Yes to both, for finite scenarios. This is the part of QUESTION-022 that A110 §IX called “a starting result”, split off on 2026-10-21 (ADR-049).

  • Overlap consistency. CLAIM-121, the manuscript’s Proposition 1. If the local kernels commute with restriction, an overlap-consistent source model is carried to an overlap-consistent target model. The proof exchanges pushforward and restriction, then uses the source’s overlap consistency.
  • Global extendability. CLAIM-070, the manuscript’s Proposition 2. If each local kernel is the restriction of one global kernel K_X, the pushforward of a global extension p of the source is a global extension of the target, (K_X)#p.

Both CLAIMs are Active with a demonstrated warrant. Each answers the question as posed here, which asks whether these two classes preserve, not which classes do.

What it leaves to QUESTION-022

Both results are sufficient conditions. Neither says that a transport outside these classes fails to preserve, and neither covers transports that change the measurement cover. CLAIM-121 also concerns marginal consistency only, “not global noncontextuality”.

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