s1244 — the one-loop potential on the stable region of F0: homogeneity, the common-shift law, a heat-kernel sign, no local minimum; c_c not stationary
receipts {'s1239': '5a5c62f3770072d8'}
  moments          {'monomials_degree_le_7': 330, 'nonzero_degree_le_7': 0, 'nonzero_degree_8': {'(2, 2, 2, 2)': 16}, 'max_rel_k1_k2_k3': 2.6436393428116224e-16, 'min_rel_k4': 0.020916593236743667}
  homogeneity      {'max_rel': 3.623109913880957e-16, 'unit_weight_control_min_rel': 0.12874407160003248}
  common_shift     {'closed_form_max_rel': 3.6846984253263254e-16, 'house_substrate_max_rel': 1.980455074656362e-15, 'dVdh_vs_2V_sum_tan_max_rel': 2.9964016273610123e-12, 'q_scales_max_rel': 8.298497641003242e-16}
  heat_kernel      {'max_rel': 8.182343691487404e-14, 'PSD_probes_min_Z_over_max': 0.0}
  census           {'stable': 16176, 'tachyonic': 3824, 'psd': 0, 'indefinite': 16176, 'V_nonneg': 0, 'q_vs_mass_disagree': 0, 'Z_negative_indefinite': 0, 'samples': 20000, 'max_V_on_stable': -7.722243965392224e-05, 'min_Z_over_max_indefinite': 0.0}
  no_local_minimum {'sigma_points': 200, 'strict_max_along_shift': 200, 'worst_rel_rise': -0.007538431652961251, 'control_a_flat_rises_at_o': True}
  runaway          {'from_interior_points': [{'monotone_decreasing': True, 'final_V': -3351.200423679402, 'min_q_along': 4.931631404094307, 'peak_at_index': 134}, {'monotone_decreasing': True, 'final_V': -64045.228983619396, 'min_q_along': 1.2855791255768871, 'peak_at_index': 16}, {'monotone_decreasing': True, 'final_V': -5301.060563957059, 'min_q_along': 8.863977959275418, 'peak_at_index': 64}], 'D56_vs_A1763_max_rel': 9.992007221626409e-15, 'V_o': -0.07358367, 'V_o_vs_A1763_exact': 2.7755575615628914e-16}
  c_c              {'z': [0.0, 0.0, 0.0, 0.0, 0.643501109, 0.0], 'sum_tan_delta': 0.75, 'mu_sq': [0.625, 0.625, 0.625, 0.625], 'q': [0.0, 1.0, 0.0], 'V_Lambda': -0.078383375, 'V_vs_A1764_printed': 1.7325030299275568e-13, 'dVdh_FD_vs_law_rel': 7.85160825245157e-12, 'dV1dh_FD_vs_law_rel': 4.6905964812271606e-07, 'dVdh_law': -0.117575063}
  closed_form      max_rel <1e-10 · c_c location <1e-09 · V1 vs V_Lambda <1e-07 · control True
  receipt   PASS s1239_is_the_filed_kernel_whose_head_supplies_the_branch_and_the_spin_half_B
  receipt   PASS A1765_report_is_the_source_of_the_closed_form_the_inverse_map_and_the_stable_region_NOT_imported
  receipt   PASS A1766_report_is_the_source_of_the_lattice_sum_V_Lambda_and_the_a_flat_minimum_NOT_imported
  receipt   PASS A1763_report_is_the_source_of_the_D56_closed_form_NOT_imported
  receipt   PASS A1764_report_is_the_source_of_V1_at_c_c_NOT_imported
  receipt   PASS s1225_is_the_filed_evaluator_kernel_executed_head_only
  receipt   PASS s1235_is_the_filed_kernel_whose_charge_construction_is_copied
  receipt   PASS s1238_is_the_filed_house_check_of_the_lanes_point_c_c
  receipt   PASS the_filed_A1764_lane_report_is_the_source_of_B_c_and_of_the_lattice_weights_NOT_imported
  receipt   PASS s1220_is_the_filed_kernel_whose_construction_is_copied
  receipt   PASS s121a_is_the_file_whose_potential_is_copied
  computed  PASS the_two_generator_stacks_agree
  computed  PASS golden_vacuum_is_a_Minkowski_critical_point_as_s121a_says
  computed  PASS golden_vacuum_is_2lnphi_from_the_origin
  receipt   PASS s640_lib_is_the_S220_A_layer_executed_verbatim
  receipt   PASS s646_is_the_source_of_the_SV_vector_operator_executed_verbatim
  receipt   PASS s645c_results_hold_the_P6_gradient_reproduced_here
  computed  PASS the_S220_frame_is_this_kernels_frame
  computed  PASS Z0_the_torus_T0_its_fixed_directions_p0_and_three_commuting_sl2R_planes
  computed  PASS Y1_the_lattice_weights_annihilate_every_monomial_of_degree_le_7_and_exactly_n1sq_n2sq_n3sq_n4sq_survives_at_degree_8
  computed  PASS Y2_V_is_homogeneous_of_degree_two_in_B_and_unit_weights_break_it
  computed  PASS Y3_the_closed_form_is_the_house_spin_half_B_at_eight_points_c_c_is_located_and_V_Lambda_is_the_registered_V1_where_defined
  computed  PASS Y4_the_common_shift_law_B_scales_by_prod_cos_ratio_closed_form_and_house_substrate_hence_dVdh_equals_2V_sum_tan_delta_and_S_is_shift_invariant
  computed  PASS Y5_V_equals_minus_one_over_32_pi_sq_times_the_integral_of_t_to_minus_3_Z_and_Z_is_nonnegative_at_the_PSD_probes
  argument  ARG  Y5_the_PSD_proof
  computed  PASS Y6_on_20000_seeded_points_the_stable_set_is_q_nonnegative_V_is_negative_at_every_stable_point_and_Z_is_nonnegative_at_every_indefinite_stable_point
  computed  PASS Y7_at_every_one_of_200_seeded_points_of_SIGMA_in_S_V_has_a_strict_maximum_along_the_common_shift_and_the_a_flat_control_returns_a_minimum
  argument  ARG  Y7_the_reduction
  computed  PASS Y8_V_is_unbounded_below_along_the_common_shift_from_interior_points_of_S_and_D56_is_A1763s_closed_form
  computed  PASS Y9_c_c_lies_on_two_walls_of_S_has_sum_tan_delta_3_over_4_and_dVdh_equals_3_halves_V_c_c_nonzero_by_V_Lambda_and_by_the_registered_V1_so_c_c_is_not_stationary
  argument  ARG  reading

VERDICT On S, V(s^2 B) = s^4 V(B) and B rescales along the common shift, so dV/dh = 2 V sum tan delta: stationary points with V != 0 lie on SIGMA and are strict maxima along the shift where V < 0; V < 0 proved on the PSD strata, observed at every indefinite stable sample; no local minimum of V on S; V unbounded below from every point; c_c not stationary
RESULT_HASH c60e71f7949e5d3d
s1244: 14 computed, 14 receipt, 3 argument, 0 failed
