s1278 — how the +2 and −6 vacua balance
  Q1_closed_form               {"(8,0)": {"tr η": 8.0, "V(o) at ω = 0, 0.3, π/4, 1.1": [-6.0, -6.0, -6.0, -6.0], "2 − (tr η)²/8": -6.0, "max deviation": "<1e-12"}, "(7,1)": {"tr η": 6.0, "V(o) at ω = 0, 0.3, π/4, 1.1": [-2.5, -2.5, -2.5, -2.5], "2 − (tr η)²/8": -2.5, "max deviation": "<1e-12"}, "(6,2)": {"tr η": 4.0, "V(o) at ω = 0, 0.3, π/4, 1.1": [0.0, 0.0, 0.0, 0.0], "2 − (tr η)²/8": 0.0, "max deviation": "<1e-12"}, "(5,3)": {"tr η": 2.0, "V(o) at ω = 0, 0.3, π/4, 1.1": [1.5, 1.5, 1.5, 1.5], "2 − (tr η)²/8": 1.5, "max deviation": "<1e-12"}, "(4,4)": {"tr η": 0.0, "V(o) at ω = 0, 0.3, π/4, 1.1": [2.0, 2.0, 2.0, 2.0], "2 − (tr η)²/8": 2.0, "max deviation": "<1e-12"}}
  Q2_census_on_the_t_line      {"(6,2) odd 78 +π/4": {"(s12, s4, s78)": [1.0, 1.0, -1.0], "tr η": 4.0, "4s4 + 2s12 + 2s78": 4.0, "V(o)": 0.0}, "(6,2) odd 78 −π/4": {"(s12, s4, s78)": [1.0, 1.0, -1.0], "tr η": 4.0, "4s4 + 2s12 + 2s78": 4.0, "V(o)": 0.0}, "(6,2) odd 12 +π/4": {"(s12, s4, s78)": [-1.0, 1.0, 1.0], "tr η": 4.0, "4s4 + 2s12 + 2s78": 4.0, "V(o)": 0.0}, "(6,2) odd 12 −π/4": {"(s12, s4, s78)": [-1.0, 1.0, 1.0], "tr η": 4.0, "4s4 + 2s12 + 2s78": 4.0, "V(o)": 0.0}, "(8,0) +π/4": {"(s12, s4, s78)": [1.0, 1.0, 1.0], "tr η": 8.0, "4s4 + 2s12 + 2s78": 8.0, "V(o)": -6.0}, "(8,0) −π/4": {"(s12, s4, s78)": [1.0, 1.0, 1.0], "tr η": 8.0, "4s4 + 2s12 + 2s78": 8.0, "V(o)": -6.0}, "(4,4) +π/4": {"(s12, s4, s78)": [-1.0, 1.0, -1.0], "tr η": 0.0, "4s4 + 2s12 + 2s78": 0.0, "V(o)": 2.0}, "(4,4) −π/4": {"(s12, s4, s78)": [-1.0, 1.0, -1.0], "tr η": 0.0, "4s4 + 2s12 + 2s78": 0.0, "V(o)": 2.0}, "registered X": {"V(o)": 0.0}}
  Q3_fermion_shift_ledger      {"so(8) twin": {"gravitino term −(3/4)|Â1|²": -6.0, "spin-½ term (1/24)|Â2|²": 0.0, "V": -6.0, "sum − V": "<1e-12"}, "registered X": {"gravitino term −(3/4)|Â1|²": -1.5, "spin-½ term (1/24)|Â2|²": 1.5, "V": 0.0, "sum − V": "<1e-12"}, "so(4,4) twin": {"gravitino term −(3/4)|Â1|²": 0.0, "spin-½ term (1/24)|Â2|²": 2.0, "V": 2.0, "sum − V": "<1e-12"}}
  Q4_pointwise_on_the_torus    {"points": {"(-0.25, -0.25)": {"gravitino term": -5.643294, "spin-½ term": 5.643294}, "(-0.25, +0.00)": {"gravitino term": -5.511339, "spin-½ term": 5.511339}, "(-0.25, +0.25)": {"gravitino term": -21.231175, "spin-½ term": 21.231175}, "(+0.00, -0.25)": {"gravitino term": -5.511339, "spin-½ term": 5.511339}, "(+0.00, +0.00)": {"gravitino term": -1.5, "spin-½ term": 1.5}, "(+0.00, +0.25)": {"gravitino term": -5.511339, "spin-½ term": 5.511339}, "(+0.25, -0.25)": {"gravitino term": -21.231175, "spin-½ term": 21.231175}, "(+0.25, +0.00)": {"gravitino term": -5.511339, "spin-½ term": 5.511339}, "(+0.25, +0.25)": {"gravitino term": -5.643294, "spin-½ term": 5.643294}}, "max |gravitino + spin-½| / |gravitino|": "<1e-12", "|Â2|² / |Â1|² values": [18.0]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS s1275_results_fix_the_A1_A2_normalisations
  computed  PASS Q1_V_at_o_is_2_minus_tr_eta_squared_over_8_for_every_signature_and_every_dyonic_angle
  computed  PASS Q2_the_census_lies_on_the_t_line_so8_at_t8_minus6_so62_at_t4_zero_so44_at_t0_plus2
  computed  PASS Q3_the_ledger_is_minus6_plus0_for_so8_minus1p5_plus1p5_for_the_registered_and_0_plus2_for_so44
  computed  PASS Q4_on_the_whole_radius_torus_the_gravitino_and_spin_half_terms_cancel_pointwise_with_ratio_18
  argument  ARG  how_they_balance
  argument  ARG  scope
VERDICT: V(o) = 2 − (tr η)²/8 for every signature and dyonic angle; the twins sit at t = 8 (−6) and t = 0 (+2), the registered at their midpoint t = 4 (0), where its two planes cancel; the fermion-shift ledger reads −6 + 0, 0 + 2 and −3/2 + 3/2, and the registered cancellation holds pointwise on the radius torus. Different gaugings; algebraic.
RESULT_HASH 0bba1471b5c99dc4
s1278: 4 computed, 2 receipt, 2 argument, 0 failed
