s1328 — the SL(8) frame census of X typed by the M-theory GL(7) dictionary (GGN 1312.1061)
  A machinery       {"rho_hom": "<1e-12", "rho_in_sp56": "<1e-12", "rho_g_exp_vs_exp_rho": "<1e-12", "eta62_negative_axes": [[6, 7]], "T2_vs_T_at_pi_over_4": "<1e-12"}
  B slot levels     {"theta_88": [-14], "xi_88": [14], "theta_a8": [-6], "xi_a8": [6], "theta_ab": [2], "xi_ab": [-2], "theta_aa": [2], "xi_aa": [-2]}
  C 912 levels      {"-14": 1, "-10": 35, "-6": 147, "-2": 273, "2": 273, "6": 147, "10": 35, "14": 1}  GGN parsed {"-7": 1, "-5": 35, "-3": 147, "-1": 273, "1": 273, "3": 147, "5": 35, "7": 1}  56 {"-6": 7, "-2": 21, "2": 21, "6": 7}
  D0 transform rule {"errors": {"gT_theta_g__ginv_xi_ginvT": "4.0e+01", "ginv_theta_ginvT__gT_xi_g": "<1e-09", "g_theta_gT__ginvT_xi_ginv": "3.7e+01", "ginvT_theta_ginv__g_xi_gT": "3.4e+01"}, "holds": ["ginv_theta_ginvT__gT_xi_g"]}
  D X                 axis              levels [-14, -2, 2, 14]         θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": true, "a8": false}
  D X                 null-axis g       levels [-14, -6, -2, 2, 6]      θ′ row8 {"88": true, "a8": true}     ξ′ row8 {"88": false, "a8": true}
  D X                 null-axis g^-T    levels [-6, -2, 2, 6, 14]       θ′ row8 {"88": false, "a8": true}    ξ′ row8 {"88": true, "a8": true}
  D X                 double-null g     levels [-6, -2, 2, 6]           θ′ row8 {"88": false, "a8": true}    ξ′ row8 {"88": false, "a8": true}
  D X                 double-null g^-T  levels [-6, -2, 2, 6]           θ′ row8 {"88": false, "a8": true}    ξ′ row8 {"88": false, "a8": true}
  D electric so(8)    axis              levels [-14, 2]                 θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": false, "a8": false}
  D electric so(8)    null-axis g       levels [-14, -6, 2]             θ′ row8 {"88": true, "a8": true}     ξ′ row8 {"88": false, "a8": false}
  D electric so(8)    null-axis g^-T    levels [-14, -6, 2]             θ′ row8 {"88": true, "a8": true}     ξ′ row8 {"88": false, "a8": false}
  D electric so(8)    double-null g     levels [-14, 2]                 θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": false, "a8": false}
  D electric so(8)    double-null g^-T  levels [-14, 2]                 θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": false, "a8": false}
  D dyonic so(8) π/4  axis              levels [-14, -2, 2, 14]         θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": true, "a8": false}
  D dyonic so(8) π/4  null-axis g       levels [-14, -6, -2, 2, 6, 14]  θ′ row8 {"88": true, "a8": true}     ξ′ row8 {"88": true, "a8": true}
  D dyonic so(8) π/4  null-axis g^-T    levels [-14, -6, -2, 2, 6, 14]  θ′ row8 {"88": true, "a8": true}     ξ′ row8 {"88": true, "a8": true}
  D dyonic so(8) π/4  double-null g     levels [-14, -2, 2, 14]         θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": true, "a8": false}
  D dyonic so(8) π/4  double-null g^-T  levels [-14, -2, 2, 14]         θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": true, "a8": false}
  D dyonic ISO(7)     axis              levels [2, 14]                  θ′ row8 {"88": false, "a8": false}   ξ′ row8 {"88": true, "a8": false}
  D dyonic ISO(7)     null-axis g       levels [-14, -6, -2, 2]         θ′ row8 {"88": true, "a8": true}     ξ′ row8 {"88": false, "a8": false}
  D dyonic ISO(7)     null-axis g^-T    levels [-14, -6, -2, 2]         θ′ row8 {"88": true, "a8": true}     ξ′ row8 {"88": false, "a8": false}
  D dyonic ISO(7)     double-null g     levels [-14, -2, 2]             θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": false, "a8": false}
  D dyonic ISO(7)     double-null g^-T  levels [-14, -2, 2]             θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": false, "a8": false}
  D electric ISO(7)   axis              levels [2]                      θ′ row8 {"88": false, "a8": false}   ξ′ row8 {"88": false, "a8": false}
  D electric ISO(7)   null-axis g       levels [-14, -6, 2]             θ′ row8 {"88": true, "a8": true}     ξ′ row8 {"88": false, "a8": false}
  D electric ISO(7)   null-axis g^-T    levels [-14, -6, 2]             θ′ row8 {"88": true, "a8": true}     ξ′ row8 {"88": false, "a8": false}
  D electric ISO(7)   double-null g     levels [-14, 2]                 θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": false, "a8": false}
  D electric ISO(7)   double-null g^-T  levels [-14, 2]                 θ′ row8 {"88": true, "a8": false}    ξ′ row8 {"88": false, "a8": false}
  D random frames   {"X": {"top_bottom": [[14, -14]], "X_both_rows8_nonzero": true}, "dyonic so(8) π/4": {"top_bottom": [[14, -14]], "X_both_rows8_nonzero": null}, "electric so(8)": {"top_bottom": [[2, -14]], "X_both_rows8_nonzero": null}}
  D qc              {"X": ["<1e-12", "<1e-12"], "dyonic ISO(7)": ["<1e-12", "<1e-12"], "theta=diag(1^7,0), xi=I (control)": ["1.0e+00", "1.0e+00"]}  O·electric so(8) [-2, 14]
  E X axis              electric section: Freund–Rubin slot 1₊₇ (GGN f̄r) | magnetic section: Freund–Rubin slot 1₊₇ (GGN f̄r)
  E X null-axis g       electric section: Freund–Rubin slot 1₊₇ (GGN f̄r); metric-flux-trace slot 7₊₃ (GGN f^p_pm) | magnetic section: metric-flux-trace slot 7₊₃ (GGN f^p_pm)
  E X null-axis g^-T    electric section: metric-flux-trace slot 7₊₃ (GGN f^p_pm) | magnetic section: Freund–Rubin slot 1₊₇ (GGN f̄r); metric-flux-trace slot 7₊₃ (GGN f^p_pm)
  E X double-null g     electric section: metric-flux-trace slot 7₊₃ (GGN f^p_pm) | magnetic section: metric-flux-trace slot 7₊₃ (GGN f^p_pm)
  E X double-null g^-T  electric section: metric-flux-trace slot 7₊₃ (GGN f^p_pm) | magnetic section: metric-flux-trace slot 7₊₃ (GGN f^p_pm)
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS source_GGN_1312_1061_excerpt_branching_and_identifications
  receipt   PASS s1300_results_machinery_origin
  computed  PASS A1_rho_is_a_homomorphism
  computed  PASS A2_rho_preserves_Omega
  computed  PASS A3_rho_g_integrates_rho
  computed  PASS A4_X_is_minus_T_eta62_pi_over_4_for_exactly_one_eta
  computed  PASS A5_T2_reproduces_T
  computed  PASS B1_every_slot_occupies_exactly_one_level
  computed  PASS B2_theta_slots_minus14_minus6_plus2
  computed  PASS B3_xi_slots_are_the_negatives
  computed  PASS C1_house_56_levels_are_pm2x21_pm6x7
  computed  PASS C2_house_912_by_index_counting_totals_912
  computed  PASS C3_GGN_text_parses_to_912_symmetric
  computed  PASS C4_house_levels_equal_GGN_charges_under_l_equals_minus_2q
  computed  PASS C5_and_under_l_equals_plus_2q_the_sign_is_not_fixed_by_C
  computed  PASS D0_exactly_one_transform_rule_holds
  computed  PASS D1_X_equals_T2_thetaX_xiX
  computed  PASS D2_direct_census_agrees_with_the_transform_rule_everywhere
  computed  PASS D3_X_axis_frame_minus14_minus2_2_14
  computed  PASS D4_X_null_axis_frames
  computed  PASS D5_X_double_null_minus6_to_6
  computed  PASS D6_X_random_frames_top14_bottom_minus14
  computed  PASS D7_dyonic_iso7_2_14_and_qc_zero_control_qc_fires
  computed  PASS D8_electric_iso7_level2_only
  computed  PASS D9_O_sends_electric_so8_to_minus2_14
  computed  PASS D10_dyonic_so8_top14_electric_so8_top2_in_random_frames
  computed  PASS E1_X_carries_an_eighth_row_slot_against_both_polarities_in_every_frame
  computed  PASS E2_double_null_has_no_freund_rubin_slot_either_polarity
  computed  PASS E3_electric_so8_axis_frame_is_freund_rubin_against_the_electric_section_and_empty_against_the_magnetic
  argument  ARG  eighth_row
  argument  ARG  polarity
  argument  ARG  scope
VERDICT: under GGN's GL(7) dictionary the house levels name slots: ∓14 the Freund–Rubin slot, ∓6 the metric-flux-trace slot (electric / magnetic section). X occupies an eighth-row slot of both polarities in every frame; a double-null frame removes both Freund–Rubin slots and leaves only the trace slots. None of this names X "R-type".
RESULT_HASH 55df323b6ac386c2
s1328: 27 computed, 0 symbolic, 3 receipt, 3 argument, 0 failed
