s1276 — the two U(1) charges and the T² Kaluza–Klein mass formula
  Q1_charge_tables             {"[Q12, Q78] on 8_s": "<1e-12", "gravitini (n12, n78)": {"(-0.5, -0.5)": 2, "(-0.5, 0.5)": 2, "(0.5, -0.5)": 2, "(0.5, 0.5)": 2}, "vectors": {"(-1.0, -1.0)": 1, "(-1.0, 0.0)": 4, "(-1.0, 1.0)": 1, "(0.0, -1.0)": 4, "(0.0, 0.0)": 8, "(0.0, 1.0)": 4, "(1.0, -1.0)": 1, "(1.0, 0.0)": 4, "(1.0, 1.0)": 1}, "scalars": {"(-2.0, 0.0)": 1, "(-1.0, -1.0)": 4, "(-1.0, 0.0)": 8, "(-1.0, 1.0)": 4, "(0.0, -2.0)": 1, "(0.0, -1.0)": 8, "(0.0, 0.0)": 18, "(0.0, 1.0)": 8, "(0.0, 2.0)": 1, "(1.0, -1.0)": 4, "(1.0, 0.0)": 8, "(1.0, 1.0)": 4, "(2.0, 0.0)": 1}, "spin-½ (|n12|, |n78|)": {"(0.5, 0.5)": 40, "(0.5, 1.5)": 8, "(1.5, 0.5)": 8}, "Q78 = Z": "<1e-12"}
  Q2_t2_mass_formula           {"grid": {"(-0.25, -0.25)": {"μ_A², μ_B²": [2.762196, 4.762196], "massive vectors": 20, "massive scalars": 32}, "(-0.25, +0.00)": {"μ_A², μ_B²": [0.0, 7.348452], "massive vectors": 12, "massive scalars": 22}, "(-0.25, +0.25)": {"μ_A², μ_B²": [10.391921, 17.916312], "massive vectors": 20, "massive scalars": 32}, "(+0.00, -0.25)": {"μ_A², μ_B²": [4.262291, 3.086161], "massive vectors": 20, "massive scalars": 32}, "(+0.00, +0.00)": {"μ_A², μ_B²": [0.0, 2.0], "massive vectors": 12, "massive scalars": 22}, "(+0.00, +0.25)": {"μ_A², μ_B²": [4.262291, 3.086161], "massive vectors": 20, "massive scalars": 32}, "(+0.25, -0.25)": {"μ_A², μ_B²": [10.391921, 17.916312], "massive vectors": 20, "massive scalars": 32}, "(+0.25, +0.00)": {"μ_A², μ_B²": [0.0, 7.348452], "massive vectors": 12, "massive scalars": 22}, "(+0.25, +0.25)": {"μ_A², μ_B²": [2.762196, 4.762196], "massive vectors": 20, "massive scalars": 32}}, "max relative deviation from m² = μ_A² n12² + μ_B² n78²": {"vectors": "<1e-09", "scalars + Goldstones": "<1e-09", "gravitini": "<1e-09"}}
  Q3_Z_charges_are_massive     {"min μ_B² over a 25 × 25 grid on [−0.6, 0.6]²": 2.0, "μ_A² on b = 0 (max)": 0.0, "lower bound for n78 ≠ 0": "m² ≥ μ_B² n78² ≥ 2 n78²", "massless charged states on b = 0 (vectors)": {"(-1.0, 0.0)": 4, "(1.0, 0.0)": 4}}
  Q4_vectorlike                {"Σn12, Σn78": [0.0, 0.0], "Σn12³, Σn78³": [0.0, 0.0], "Σn12 n78², Σn12² n78": [0.0, 0.0], "charge multiset symmetric under (n12, n78) → −(n12, n78)": true}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  computed  PASS Q1_gravitini_half_half_vectors_and_scalars_on_the_integer_t2_lattice_Q78_is_Z
  computed  PASS Q2_on_the_radius_torus_vectors_scalars_with_goldstones_and_gravitini_all_obey_m2_equals_muA2_n12_2_plus_muB2_n78_2
  computed  PASS Q3_every_Z_charged_state_is_massive_on_the_torus_while_the_n12_charged_states_go_massless_on_b0
  computed  PASS Q4_the_left_handed_8_plus_56_is_vectorlike_under_both_u1s_all_odd_traces_vanish
  argument  ARG  what_it_says
  argument  ARG  photon_typing
  argument  ARG  scope
VERDICT: under the two U(1) clocks the N = 8 fields sit on a T² charge lattice (gravitini (±½, ±½)), and the whole computed spectrum on the Minkowski radius torus is m² = μ_A² n12² + μ_B² n78², a two-torus Kaluza–Klein / Scherk–Schwarz mass formula with μ_A² = 2sinh²(4b)cosh(4a−4b), μ_B² = 2cosh²(4a)cosh(4a−4b); every Z-charged state is massive (m ≥ √2|n78|) and the fermions are vectorlike: Z is a KK-type photon, not QED's. Tree level, algebraic.
RESULT_HASH c92d7bfddb92aa8b
s1276: 4 computed, 2 receipt, 3 argument, 0 failed
