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Adds Sahni's multiplier-flow gadget: each Partition element becomes an item vertex whose multiplier amplifies a binary source choice into either 0 or a_i units entering a relay. A single bottleneck arc of capacity S/2 converts the target's "net inflow at least R" condition into the exact equality needed by Partition. Odd-S inputs reduce to a fixed infeasible 3-vertex instance. - src/rules/partition_integralflowwithmultipliers.rs: reduction impl with odd-S/even-S branches and witness extraction from source arcs - src/unit_tests/rules/partition_integralflowwithmultipliers.rs: 5 tests (closed-loop, structure on even-total YES instance, even-total NO exercises bottleneck, odd-total fixed NO target, witness extraction, canonical example spec) - src/rules/mod.rs: register module and example specs - docs/paper/reductions.typ: full theorem with construction, correctness proof, and worked example using the canonical fixture Closes #363. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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## main #1068 +/- ##
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Coverage 97.93% 97.93%
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Files 966 968 +2
Lines 100154 100294 +140
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+ Hits 98083 98222 +139
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Summary
Add the implementation plan for the
Partition -> IntegralFlowWithMultipliersreduction and then execute it in follow-up commits.Fixes #363