Graph switching: host, event-time and exactness boundaries

Family 131; selected construction addendum, 9 October 2026 Australia/Brisbane. Source fd4aeeb2ee4fc729c18d98444fed42fd0529eeeb.

Read the complete introduction, pair-resampling setup, mixing derivation and exact sampling section, plus selected formal scope. The bound is for a precise half-hold/uniform-four-set/ordered-pair kernel on the complete host. All holding and rejected proposals count as steps. Host restrictions, directed/weighted or connected-only models need separate results. Exactness uses exponentially expensive rare residual tabulation in expectation and unbounded rejection draws; it is outside the selected formal chain estimates. The finite audit has a six-cycle-host disconnection example and an accepted-switch stationary-law example (triangle-event mass 1/5 versus uniform 1/7). These are small exact facts, not broad theorem verification. Dossier 005 is revised; literal cheap general certified sampling is deferred.

Exact sections read

• preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/build/sections/introduction.tex: full introduction/kernel.
• preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/build/sections/setup.tex: full pair-resampling setup.
• preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/build/sections/mixing.tex: full mixing section.
• preprints/Polynomial-Mixing-of-the-Switch-Chain-for-Every-Graphical-Degree-Sequence-September-25-2026/build/sections/exact-sampling.tex: full exact residual sampling section.
• lean/docs/131.md: full selected scope document.

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