s1283 — the full flat branch through o is F0; the S387 objects lie in it
  Q1_the_algebra                               {"dim s; noncompact; compact": [9, 6, 3], "ideal of Aₖ: dim; closed dim; (noncompact, compact); Killing (+, −)": [[3, 3, [2, 1], [2, 1]], [3, 3, [2, 1], [2, 1]], [3, 3, [2, 1], [2, 1]]], "max |[I_j, I_k]| (j ≠ k); rank I₁ ∪ I₂ ∪ I₃": ["<1e-12", 9], "D56 − Σ D56ₖ; ‖D56ₖ‖/‖Aₖ‖; ⟨D56ₖ, Aₖ⟩/(‖·‖‖·‖)": ["<1e-12", [2.0, 2.0, 2.0], "<1e-12"], "D_sol = 2Σ εₖ ûₖ: ε; residual": [[-1, -1, 1], "<1e-12"], "centraliser of s in e7 (dim); in the gauge algebra (dim, abelian, max |sym part|)": [28, [4, "<1e-12", "<1e-12"]], "compact part of s in the gauge algebra (min relative residual); compact gauge part in the gauge algebra (max residual)": [1.0, "<1e-10", 16], "noncompact directions fixed by that gauge torus (F0-type fixed set): dim; projector distance to p_s": [6, "<1e-10"]}
  Q2_flat_orbit_and_gravitino_law              {"8 random orbit points (|sₖ| ≤ 1.2): max |V|/scale, |∇V|/scale, gravitino law (relative)": ["<1e-11", "<1e-11", "<1e-10"], "radius torus = the û-planes x₁ = x₂ (xₖ = −2(a + εₖ b), φ = π/2): ‖tensor − pt(a, b)‖, law vs ½cosh²(4a−4b)cosh(4a+4b)": {"(0.2, 0.13)": ["<1e-10", "<1e-12"], "(-0.15, 0.31)": ["<1e-10", "<1e-12"], "(0.05, -0.22)": ["<1e-10", "<1e-12"]}, "four-form branch = the A-plane φ = 0: ‖tensor − Σ e^{+χᵢ·s}Xᵢ‖; gravitino law vs ½e^{2χᵢ·s} (×2)": ["<1e-10", "<1e-12"]}
  Q3_completeness_at_generic_points            {"A-plane (0.3, −0.2, 0.1)": {"inertia (+, −, 0)": [40, 0, 30], "gauge-orbit rank": 24, "rank(gauge ∪ p_s)": 30, "p_s ⊂ kernel (residual)": "<1e-10", "Morse–Bott (nullity = rank)": true}, "generic (0.35, −0.25, 0.4; 0.7, 2.1, 4.4)": {"inertia (+, −, 0)": [38, 2, 30], "gauge-orbit rank": 24, "rank(gauge ∪ p_s)": 30, "p_s ⊂ kernel (residual)": "<1e-10", "Morse–Bott (nullity = rank)": true}, "generic (0.6, 0.45, −0.3; 3.0, 0.2, 1.3)": {"inertia (+, −, 0)": [40, 0, 30], "gauge-orbit rank": 24, "rank(gauge ∪ p_s)": 30, "p_s ⊂ kernel (residual)": "<1e-10", "Morse–Bott (nullity = rank)": true}}
  Q4_zero_modes_at_o                           {"o: inertia (+, −, 0); gauge-orbit rank; physical zero modes (projector rank)": [[22, 0, 48], 12, 36], "p_s ⊂ kernel; rank(gauge ∪ p_s)": ["<1e-10", 18], "flat cone Ad(K)·p_s at a generic Y₀ ∈ p_s: tangent rank modulo gauge; linear span modulo gauge": [18, 36], "along p_s lines (A₁, û₁, Y₀): max |c₂…c₆|": "<1e-12", "20 projector-defined physical zero-mode lines: max |c₂|, max |c₃|; c₄ > 0 count": ["<1e-12", "<1e-12", 20], "golden point t = 0.02: tachyon count; quartic c₄ along golden ± tachyon mix (min, at β)": [2, -0.000972, -0.5], "direct V along that line at τ = 0.1, 0.2": [-9.723e-08, -1.556e-06], "direct V / (c₄τ⁴) at τ = 0.1": 1.000087}
  Q5_golden_line_in_the_gauge_saturated_orbit  {"û₁ − û₂": "<1e-09", "û₁ − û₃": "<1e-09", "û₂ − û₃": "<1e-09", "control A₁ − A₂": "best residual > 0.1", "control û₁ + û₂": "best residual > 0.1"}
  Q6_sampled_stability_map                     {"A-plane (φ = 0): negative-mode counts": [0, 0, 0, 0, 0], "û-plane (φ = π/2) on x_a = x_b [(0.3, 0.3, −0.5) is the radius torus]: negative counts": [0, 0, 0, 0], "û-plane off the planes: negative counts": [2, 2, 2], "anti-diagonals x_a = −x_b = 0.2: negative count; |λ_min − 4(1 − cosh 2s)|": {"(1, 2)": [2, "<1e-09"], "(1, 3)": [2, "<1e-09"], "(2, 3)": [2, "<1e-09"]}, "radius torus is a stability boundary: λ_min at offsets 1e-3, 2e-3 off the plane; ratio": [-0.007246, -0.014489, 1.999609], "o is a stability boundary: (0.02, −0.02, 0) negative count; |λ_min − 4(1 − cosh 0.04)|": [2, "<1e-09"], "16 random points (|sₖ| ≤ 0.8): negative counts; stable; stable and Morse–Bott": [[0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0], 10, 10]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  receipt   PASS filed_chatgpt_d1417_maps_npz
  receipt   PASS s1282_results_machinery_and_four_form_checks
  receipt   PASS s1282_kernel_machinery_source
  computed  PASS Q1_the_five_generators_close_on_sl2r_cubed_whose_gauge_centraliser_is_a_maximal_torus_fixing_exactly_p_s_so_the_orbit_is_the_F0_type_fixed_set
  computed  PASS Q2_the_whole_sl2r_cubed_orbit_is_flat_and_the_gravitino_masses_are_half_the_even_diagonal_of_P1_P2_P3
  computed  PASS Q3_at_generic_orbit_points_the_hessian_kernel_is_exactly_the_24_gauge_orbit_plus_6_orbit_directions_so_the_moduli_space_is_six_dimensional
  computed  PASS Q4_reconfirms_s1249_o_has_36_physical_zero_modes_an_18_dimensional_exactly_flat_cone_no_cubic_term_and_an_indefinite_quartic
  computed  PASS Q5_the_golden_generator_is_compact_gauge_conjugate_to_each_anti_diagonal_radius_direction_and_to_no_four_form_or_diagonal_one
  computed  PASS Q6_sampled_stability_consistent_with_A1765_the_A_plane_and_three_radius_planes_tachyon_free_anti_diagonals_one_pair_o_and_the_torus_on_the_boundary
  argument  ARG  forcing
  argument  ARG  reading
  argument  ARG  prior_record
  argument  ARG  scope
VERDICT: the flat branch through o is F0 (s1239) — the SL(2, ℝ)³ orbit fixed by a maximal gauge torus, six moduli modulo gauge, Morse–Bott at generic points; the S387 radius torus, four-form branch and golden line all lie in it; gravitino m² = ½ × the even diagonal of P₁⊗P₂⊗P₃; o is not a tree local minimum (s1249, re-confirmed).
RESULT_HASH efe1c8880e7917e5
s1283: 6 computed, 5 receipt, 4 argument, 0 failed
