Brill--Noether existence through genus five

The complete Atanasov--Ranganathan theorem is assembled here entirely inside the public LowGenus library. Genus four reduces to six closed cubic rows. Genus five reduces to the sixteen constructions from the source paper and four bridge rows, all handled by one checked (2,3) articulation theorem. Semantic loops in either genus are discharged uniformly after fossilization by splitting off a rigid genus-one wedge factor.

theorem AtanasovRanganathan.genusFourRankOneExistence : Utilities.GenusFourRankOneExistence

Every connected finite graph of genus four carries a degree-three rank-one divisor.

theorem AtanasovRanganathan.brillNoetherExistenceThroughFive : Utilities.BrillNoetherExistenceThroughFive

Atanasov--Ranganathan existence through genus five. Every connected finite graph of genus at most five satisfies Brill--Noether existence.