The six closed cubic genus-four rows

This is the small concrete ledger consumed by the public genus-four pseudocore reduction. Rows 095, 097, and 098 have readable structural closed-face proofs. Rows 096, 099, and 100 use kernel-checked generated certificates for the boundary faces; row 096 additionally has a readable symbolic proof on the positive orthant.

theorem AtanasovRanganathan.GenusFourRowsClosed.rowClosedCoverage : GenusFourCubicCoverage.RowClosedCoverage

All six public cubic genus-four rows carry degree-three pencils throughout their genus-preserving closed orthants.

theorem AtanasovRanganathan.GenusFourRowsClosed.cubicClosedCoverage : GenusFourPseudocoreCoverage.CubicClosedCoverage

The public classifier and the six-row ledger cover every connected loopless cubic genus-four core.

theorem AtanasovRanganathan.GenusFourRowsClosed.genusFourRankOneExistence : Utilities.GenusFourRankOneExistence

Every connected finite graph of genus four carries a degree-three rank-one divisor, using only public modules.