Qplus cohomology
v137_qplus_cohomology.py · registry
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THE Q₊ GRADING IS COHOMOLOGY (the R5/GATE.QGEO dictionary at the spectrum level): BASIS + CHARACTERS [I]: b₁(ℙ¹∖μ₄) = 3 = N_fam with holomorphic basis ω_k = z^(k−1)dz/(z⁴−1), k = 1,2,3 (regular at infinity; the trivial character is absent); the μ₄ character of ω_k is i^k, so H¹ = χ₁⊕χ₂⊕χ₃ with each nontrivial character exactly once, and the residue vector over the punctures is the character vector ζ^k/4 exactly; THE GRADING IS Spec(Q₊) [I]: the character degrees (1,2,3) are exactly Spec(Q₊) (Q₊ = 3·cusp + 1, v69/v72), and NEW: the cusp weights {0, 1/3, 2/3} are spec(A₀*) (v115) — Mehta–Seshadri weights, cusp classes, cohomology characters and the flavor operator Q₊ are ONE spectrum in four readouts; A₃ EXPONENTS [I]: (1,2,3) are the exponents of A₃ (W(A₃) = S₄, v117) with Coxeter number h(A₃) = 4 = |μ₄| — the Q₊ generation grading IS the A₃ exponent grading, realised on the seam curve's cohomology; RESIDUE [P]: what remains of GATE.QGEO is the NATURALITY of the identification — the canonical map from the H¹ character basis to the V-axis generation basis (rowsum(V) = (1,2,3) verbatim, v135); spectrum equality is [I], the canonical map is the residue
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