s1274 — vacuum → null cosmological constant → photon: the Minkowski radius torus of the registered gauging
  Q1_frame_formula_normalisation   {"dim p (e7 ∩ sym), dim k (e7 ∩ antisym)": [70, 63], "p, k inside e7 (residual)": "<1e-12", "V_electric SO(8)(o)": -6.0, "exact gradient − central differences (max)": "<1e-08", "Hessian entries exact − finite difference (H_ij, H_ii)": ["<1e-04", "<1e-04"], "invariance V_X(V₀e^{2Z}V₀ᵀ) − V_{V₀⁻¹·X}(e^{2Z})": "<1e-12"}
  Q2_vacuum_energy_at_o            {"registered X": {"V(o)": 0.0, "|grad V|(o)": "<1e-08"}, "(6,2) odd 78 +π/4": {"V(o)": 0.0, "|grad V|(o)": "<1e-08"}, "(6,2) odd 78 −π/4": {"V(o)": 0.0, "|grad V|(o)": "<1e-08"}, "(6,2) odd 12 +π/4": {"V(o)": 0.0, "|grad V|(o)": "<1e-08"}, "(6,2) odd 12 −π/4": {"V(o)": 0.0, "|grad V|(o)": "<1e-08"}, "(8,0) +π/4": {"V(o)": -6.0, "|grad V|(o)": "<1e-08"}, "(8,0) −π/4": {"V(o)": -6.0, "|grad V|(o)": "<1e-08"}, "(4,4) +π/4": {"V(o)": 2.0, "|grad V|(o)": "<1e-08"}, "(4,4) −π/4": {"V(o)": 2.0, "|grad V|(o)": "<1e-08"}, "control: electric SO(6,2), ω = 0": {"V(o)": 0.0, "|grad V|(o)": 1.414214}}
  Q3_minkowski_radius_torus        {"grid": {"(-0.3, -0.3)": {"zero modes": 38, "nonzero levels (value: count)": {"0.379746": 8, "0.546412": 8, "0.926158": 12, "1.518982": 2, "2.185649": 2}}, "(-0.3, +0.0)": {"zero modes": 48, "nonzero levels (value: count)": {"0.989364": 20, "3.957458": 2}}, "(-0.3, +0.3)": {"zero modes": 38, "nonzero levels (value: count)": {"2.110226": 8, "3.036384": 8, "5.14661": 12, "8.440905": 2, "12.145536": 2}}, "(+0.0, -0.3)": {"zero modes": 38, "nonzero levels (value: count)": {"0.301776": 8, "0.687588": 8, "0.989364": 12, "1.207104": 2, "2.750354": 2}}, "(+0.0, +0.0)": {"zero modes": 48, "nonzero levels (value: count)": {"0.166667": 20, "0.666667": 2}}, "(+0.0, +0.3)": {"zero modes": 38, "nonzero levels (value: count)": {"0.301776": 8, "0.687588": 8, "0.989364": 12, "1.207104": 2, "2.750354": 2}}, "(+0.3, -0.3)": {"zero modes": 38, "nonzero levels (value: count)": {"2.110226": 8, "3.036384": 8, "5.14661": 12, "8.440905": 2, "12.145536": 2}}, "(+0.3, +0.0)": {"zero modes": 48, "nonzero levels (value: count)": {"0.989364": 20, "3.957458": 2}}, "(+0.3, +0.3)": {"zero modes": 38, "nonzero levels (value: count)": {"0.379746": 8, "0.546412": 8, "0.926158": 12, "1.518982": 2, "2.185649": 2}}}, "worst": {"|V|": "<1e-08", "|grad|": "<1e-08", "most negative Hessian eigenvalue (relative)": "≥ −1e-09", "closed-form levels (relative)": "<1e-08"}}
  Q4_unbroken_and_photon           {"Z = c·A56: c, residual": [-1.414214, "<1e-12"], "points": {"(+0.0, +0.0)": {"unbroken (dim, derived, Tr56 inertia)": [16, 15, [0, 15, 1]], "centre dim": 1, "Z, A_sol in the centre (relative residual)": ["<1e-10", "1.000e+00"], "centre ⊂ span{A56, A_sol} (max residual)": "<1e-10", "A56, A_sol unbroken (relative residual)": ["<1e-10", "<1e-10"]}, "(+0.3, +0.0)": {"unbroken (dim, derived, Tr56 inertia)": [16, 15, [0, 15, 1]], "centre dim": 1, "Z, A_sol in the centre (relative residual)": ["<1e-10", "1.000e+00"], "centre ⊂ span{A56, A_sol} (max residual)": "<1e-10", "A56, A_sol unbroken (relative residual)": ["<1e-10", "<1e-10"]}, "(+0.0, +0.3)": {"unbroken (dim, derived, Tr56 inertia)": [8, 6, [0, 6, 2]], "centre dim": 2, "Z, A_sol in the centre (relative residual)": ["<1e-10", "<1e-10"], "centre ⊂ span{A56, A_sol} (max residual)": "<1e-10", "A56, A_sol unbroken (relative residual)": ["<1e-10", "<1e-10"]}, "(-0.3, +0.3)": {"unbroken (dim, derived, Tr56 inertia)": [8, 6, [0, 6, 2]], "centre dim": 2, "Z, A_sol in the centre (relative residual)": ["<1e-10", "<1e-10"], "centre ⊂ span{A56, A_sol} (max residual)": "<1e-10", "A56, A_sol unbroken (relative residual)": ["<1e-10", "<1e-10"]}}}
  Q5_twin_hessians                 {"so(8) twin": {"-0.333333": 70}, "so(4,4) twin": {"-0.333333": 2, "0.0": 16, "0.166667": 16, "0.333333": 36}}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  computed  PASS Q1_the_frame_splits_e7_as_63_plus_70_the_potential_is_normalised_by_electric_so8_at_minus_6_and_the_exact_jet_matches_finite_differences
  computed  PASS Q2_at_o_the_so62_members_are_minkowski_the_so8_twins_ads_minus6_the_so44_twins_ds_plus2_all_stationary_and_electric_so62_is_not
  computed  PASS Q3_V_vanishes_and_is_stationary_on_the_radius_torus_the_hessian_is_psd_and_its_levels_are_the_closed_forms_mA_mB
  computed  PASS Q4_the_unbroken_algebra_is_so6_so2_on_b0_with_centre_exactly_Z_and_so4_u1_u1_off_it_with_centre_the_two_anchors_both_unbroken_everywhere
  computed  PASS Q5_the_so8_twin_has_the_standard_ads_spectrum_minus_one_third_and_the_so44_twin_two_tachyons_at_o
  argument  ARG  vacuum_null_photon
  argument  ARG  relative_sign_is_lambda
  argument  ARG  kk_angle
  argument  ARG  scope
VERDICT: the registered gauging is Minkowski and stationary at o and on the whole radius torus, tachyon-free at quadratic order, with levels m_A = (1/6)sinh²(4b)cosh(4a−4b), m_B = (1/6)cosh²(4a)cosh(4a−4b); at o the unbroken algebra is so(6) ⊕ so(2) whose centre is exactly Z (the unique massless abelian gauge field), off b = 0 the clock-2 rotation joins it; the relative sign is the sign of the vacuum energy at o (so(6,2) 0, so(8) −6, so(4,4) +2). Tree level, bosonic, algebraic.
RESULT_HASH 7a90adf0fc354d79
s1274: 5 computed, 2 receipt, 4 argument, 0 failed
