s1314 — light twist-charged fermions on the edges of F0
  P1_half_angle_law        {"face(r, φ) − face(1, φ)": "<1e-10", "‖F‖² / (84(1 + Π cos φ)) − 1": "<1e-10", "A1 sv − (7/8)|m| (each twice)": "<1e-10", "twist charges / max − |m| / max": "<1e-10", "selected components (joint h-weights)": ["[(1, 1, 1)]"], "twists per face": [1]}
  P2_light_census          {"generic": [{"light (8, 56)": [0, 0], "face dim": 25, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [0, 0]}, {"light (8, 56)": [0, 0], "face dim": 25, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [0, 0]}, {"light (8, 56)": [0, 0], "face dim": 25, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [0, 0]}], "spin-½ wall": [{"light (8, 56)": [0, 2], "face dim": 25, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [0, 2]}, {"light (8, 56)": [0, 2], "face dim": 25, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [0, 2]}, {"light (8, 56)": [0, 2], "face dim": 25, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [0, 2]}], "one angle on a four-form axis": [{"light (8, 56)": [4, 12], "face dim": 21, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [4, 12]}, {"light (8, 56)": [4, 12], "face dim": 21, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [4, 12]}, {"light (8, 56)": [4, 12], "face dim": 21, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [4, 12]}], "two angles on four-form axes": [{"light (8, 56)": [6, 26], "face dim": 13, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [6, 26]}, {"light (8, 56)": [6, 26], "face dim": 13, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [6, 26]}, {"light (8, 56)": [6, 26], "face dim": 13, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [6, 26]}], "four-form chamber": [{"light (8, 56)": [6, 26], "face dim": 13, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [6, 26]}, {"light (8, 56)": [6, 26], "face dim": 13, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [6, 26]}, {"light (8, 56)": [6, 26], "face dim": 13, "one twist": true, "light spin-½ ∩ goldstino span": "<1e-10", "twist-neutral (8, 56)": [6, 26]}], "four-form two-way wall": [{"light (8, 56)": [4, 20], "face dim": 22, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}, {"light (8, 56)": [4, 20], "face dim": 22, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}, {"light (8, 56)": [4, 20], "face dim": 22, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}], "four-form triple point": [{"light (8, 56)": [2, 18], "face dim": 27, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}, {"light (8, 56)": [2, 18], "face dim": 27, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}], "two-factor, generic angles": [{"light (8, 56)": [0, 0], "face dim": 26, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}, {"light (8, 56)": [0, 0], "face dim": 26, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}], "two-factor, one axis angle": [{"light (8, 56)": [4, 12], "face dim": 22, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}, {"light (8, 56)": [4, 12], "face dim": 22, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}], "one-factor, off the axis": [{"light (8, 56)": [0, 0], "face dim": 28, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}, {"light (8, 56)": [0, 0], "face dim": 28, "one twist": false, "light spin-½ ∩ goldstino span": "<1e-10"}]}
  P3_gauge_action          {"generic": [{"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}], "spin-½ wall": [{"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}], "one angle on a four-form axis": [{"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}], "two angles on four-form axes": [{"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}], "four-form chamber": [{"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 1, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}], "four-form two-way wall": [{"compact dim": 4, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "1.414e+00"], "centre dim": 1, "derived dim": 3, "derived Killing negative definite": true, "centre on light": "<1e-10", "Killing-normalised Casimir on light 56": {"0.0": 8, "1.0": 12}}, {"compact dim": 4, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "1.414e+00"], "centre dim": 1, "derived dim": 3, "derived Killing negative definite": true, "centre on light": "<1e-10", "Killing-normalised Casimir on light 56": {"0.0": 8, "1.0": 12}}, {"compact dim": 4, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "1.414e+00"], "centre dim": 1, "derived dim": 3, "derived Killing negative definite": true, "centre on light": "<1e-10", "Killing-normalised Casimir on light 56": {"0.0": 8, "1.0": 12}}], "four-form triple point": [{"compact dim": 9, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "2.000e+00"], "centre dim": 1, "derived dim": 8, "derived Killing negative definite": true, "centre on light": "<1e-10", "Killing-normalised Casimir on light 56": {"0.0": 2, "1.0": 16}}, {"compact dim": 9, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "2.000e+00"], "centre dim": 1, "derived dim": 8, "derived Killing negative definite": true, "centre on light": "<1e-10", "Killing-normalised Casimir on light 56": {"0.0": 2, "1.0": 16}}], "two-factor, generic angles": [{"compact dim": 2, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 2, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}], "two-factor, one axis angle": [{"compact dim": 2, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 2, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}], "one-factor, off the axis": [{"compact dim": 8, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}, {"compact dim": 8, "leak (8, 56)": ["<1e-10", "<1e-10"], "action, root-sum-square over an orthonormal basis (8, 56)": ["<1e-10", "<1e-10"]}]}
  P4_vectorlike            {"generic": [{"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}], "spin-½ wall": [{"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}], "one angle on a four-form axis": [{"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}], "two angles on four-form axes": [{"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}], "four-form chamber": [{"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"], "T0 leak (8, 56)": ["<1e-10", "<1e-10"], "T0 weights symmetric (8, 56)": [true, true]}], "four-form two-way wall": [{"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}], "four-form triple point": [{"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}], "two-factor, generic angles": [{"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}], "two-factor, one axis angle": [{"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}], "one-factor, off the axis": [{"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}, {"spectrum asymmetry (8, 56)": ["<1e-10", "<1e-10"]}]}
  P5_rates_and_interior    {"ray φ = (0, 1.1, 2.0), r = (1.0, 1.0, 1.0): d ln(light/heavy)/dλ over λ ∈ [2, 4]; −2r₁": [-2.0, -2.0], "ray φ = (0, 1.1, 2.0), r = (0.6, 1.0, 1.0): d ln(light/heavy)/dλ over λ ∈ [2, 4]; −2r₁": [-1.2, -1.2], "24 interior points of F0: smallest gravitino and physical spin-½ mass ratios": ["4.02e-02", "2.62e-02"]}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1414_maps_npz
  receipt   PASS filed_chatgpt_d1417_maps_npz
  receipt   PASS filed_chatgpt_d1419_maps_npz
  receipt   PASS s1300_results_machinery
  receipt   PASS s1281_results_raw_a3_and_goldstino_projection
  receipt   PASS s1313_results_exact_weight_face
  receipt   PASS s1309_results_eps2_exclusion_proved
  computed  PASS P1_on_the_generic_edge_stratum_the_face_ignores_the_radii_its_norm_is_84_times_1_plus_prod_cos_and_the_gravitino_masses_are_the_half_angle_amplitudes
  computed  PASS P2_twist_charged_fermions_become_light_on_codimension_one_loci_4_plus_12_on_a_four_form_axis_0_plus_2_on_spin_half_walls_and_the_light_counts_are_constant_on_each_stratum
  computed  PASS P3_light_fermions_are_gauge_neutral_except_on_four_form_walls_where_they_are_adjoints_four_su2_triplets_or_two_su3_octets_with_a_trivial_centre_and_neutral_gravitini
  computed  PASS P4_every_light_set_is_vectorlike_t0_weights_symmetric_on_every_one_twist_face_and_every_spectrum_symmetric
  computed  PASS P5_light_masses_fall_as_exp_minus_2_lambda_r1_toward_the_locus_and_no_sampled_interior_point_of_F0_has_a_massless_fermion
  argument  ARG  forcing
  argument  ARG  reading
  argument  ARG  the_5d_parent_route
  argument  ARG  scope
VERDICT: twist-charged fermions become light on codimension-one loci of F0's edge sphere (4 + 12 where an angle meets a four-form axis; 2 on spin-½ walls) and are gauge-neutral there; charged light fermions occur only on four-form chamber walls, as adjoints of an emergent su(2) or su(3) — real. Every light set is vectorlike; with s1309 the routes to chirality inside the registered data are closed.
RESULT_HASH 482d7e695657df1d
s1314: 5 computed, 8 receipt, 4 argument, 0 failed
