AR row 08, assembled

Atanasov--Ranganathan's seventh genus-five family. The paper draws three of the four sign patterns of (|e4| - |e3|, |e7| - |e2|); the fourth is the image of the third under the core automorphism sigma = (0 6)(1 7)(4 5), so the row needs three chamber proofs and one orbit transport.

• chamber 1 (|e4| ≤ |e3|, |e7| ≤ |e2|) -- GenusFiveRow08ChamberOne, a ConfigurationThree pair on the stem plus two equal-arm banana pairs;
• chamber 2 (|e3| ≤ |e4|, |e2| ≤ |e7|) -- GenusFiveRow08ChamberTwo, the chipped triangle plus two equal-arm banana pairs;
• chamber 3 (|e3| ≤ |e4|, |e7| ≤ |e2|) -- GenusFiveRow08ChamberThree, the divisor with a double chip, a ConfigurationThree pair and the lopsided banana pair of ConfigurationBananaDoubleChip.

GenusFiveRow08Symmetry.chamber_covers moves every length vector into that three-way disjunction, and ClosedOrbit.closedConstruction_of_chamber turns one chamber proof per disjunct into the statement on the whole closed orthant.

theorem AtanasovRanganathan.GenusFiveRow08.chamber_pencil (length : Fin 12 → ℕ) (forest : Utilities.Certificate.ContractionForestCensusGeneral.IsForest GenusFiveCoreAtlas.row08Core (Configurations.zeroSlots length)) (notLoopy : ¬Utilities.Certificate.ContractionForestCensusGeneral.IsLoopy GenusFiveCoreAtlas.row08Core (Configurations.zeroSlots length)) (hP : GenusFiveRow08Symmetry.Chamber length) : Nonempty (Configurations.DegreeFourDharPencil (Configurations.faceSpec GenusFiveCoreAtlas.row08Core chamber_pencil._proof_1 length forest notLoopy).graph)

The three drawn scopes, each discharged by its own chamber file.

theorem AtanasovRanganathan.GenusFiveRow08.row08_closedConstruction : Configurations.ClosedSubdivisionDharConstruction GenusFiveCoreAtlas.row08Core chamber_pencil._proof_1

AR's seventh family on row 08. The paper's own divisors -- one per scope, including the one with two chips on a single vertex -- have rank at least one on every nonloopy forest face, all four sign patterns at once.