Marks kernel attempt
v178_marks_kernel_attempt.py · registry
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an honest ATTEMPT at the two open obligations QGEO.MARKS.01 + QGEO.KERNEL.01 — NOT a closure (they are genuine constructive-geometry/AQFT statements, not finite computations), but a deeper reduction: each finite/algebraic CORE is closed [E] and each obligation reduced to ONE sharper irreducible [O] premise. MARKS finite core [E]: a genus-0 double with an order-4 clock ρ (~z↦iz, fixed points {0,∞}) and sheet reflection τ forces the marks to be a generic ρ-orbit {1,i,−1,−i}=μ₄ (NOT the fixed points), distinct iff b₁=4−1=3=N_fam (collision drops b₁, excluded), τρτ=ρ⁻¹ ⇒ faithful D4 order 8 — so MARKS reduces to the single topological/clock premise. KERNEL finite core [E]: on the 3-dim multiplicity-free H¹ the μ₄ characters (1,2,3) are distinct, so by Schur a μ₄-equivariant operator is forced DIAGONAL and completely determined by its eigenvalue per character — two such with the same forced transfer spectrum {1,(2/3)⁶,(1/3)⁶} (v162) and the unique residue-normalised basis (v177) are EQUAL as operators (the 'spectrum vs operator' worry vanishes on the finite block); so KERNEL reduces to the single full-operator-reduction premise (principal symbol |k| Lee-Uhlmann v156, no drift v158). NET: neither obligation closed; both sharpened to milder premises.
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