Prove stability under unknown comparisons, count independent families of stable outcomes, and adapt proposal invariants to unequal populations.
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Unknown comparisons must be checked at both endpoints.
No. Both participants must prefer one another to their current partners, or to being unmatched when the model permits it.
Unequal populations still need the best-seen proposal invariant.
The receiver keeps its favorite proposal so far, so its held partner never gets worse. Rejected proposers then try their next untried choice.
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Audit the quantifiers and matching assumptions
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Use reachability in consistent comparison orders to determine whether a fixed matching stays stable under every independent completion.
6 practice tasks.
Use strict preference barriers to combine local outcomes, exclude cross-block matches and prove an exact exponential family count.
6 practice tasks.
Allow exhausted proposers, prove stability and saturation with complete acceptable lists, and locate the boundary when lists become incomplete.
6 practice tasks.
