s1265 — three twist classes on the registered 56
  twist_classes               {"provenance": {"B1 − s1026 braid generator 1": "<1e-12", "B2 − s1026 braid generator 2": "<1e-12", "W_h − s1026 hyperbolic word": "<1e-12", "G − B1·O": "<1e-12"}, "B1": {"order": null, "radius": 1.0, "homology trace": 2.0, "symplectic": true, "anti-symplectic": false, "(B−I)²": "<1e-12", "rank B−I": 12}, "B2": {"order": null, "radius": 1.0, "homology trace": 2.0, "symplectic": true, "anti-symplectic": false, "(B−I)²": "<1e-12"}, "B1B2": {"order": 6, "radius": 1.0, "homology trace": 1.0, "symplectic": true, "anti-symplectic": false, "charpoly / (t²−t+1)¹² (t−1)³² − 1": "<1e-09"}, "B1B2B1": {"order": 4, "radius": 1.0, "homology trace": 0.0, "symplectic": true, "anti-symplectic": false}, "B1B2^-1": {"order": null, "radius": 2.618034, "homology trace": 3.0, "symplectic": true, "anti-symplectic": false}, "W_h": {"order": null, "radius": 2.618034, "homology trace": 3.0, "symplectic": true, "anti-symplectic": false, "charpoly / (t²−3t+1)¹² (t−1)³² − 1": "<1e-09"}, "G": {"order": null, "radius": 1.618034, "homology trace": null, "symplectic": false, "anti-symplectic": true}, "(B1B2)³ − (I − 2P_act)": "<1e-12", "word census": {"reduced words, length ≤ 6": 1456, "enumeration lock": "f7f5c850064d3ffa", "classes on the 56": {"hyperbolic": 772, "periodic": 344, "unipotent-type": 340}, "classes by homology trace": {"hyperbolic": 772, "periodic": 344, "unipotent-type": 340}, "mismatches": 0, "least hyperbolic radius": 2.618033989}}
  minimal_stretch             {"GL(2,ℤ) entries in [−4,4], det ±1": 360, "least radius > 1, det −1": 1.618033989, "least radius > 1, det +1": 2.618033989, "least unit > 1 of ℤ[φ]": 1.618033989, "ln φ (regulator of ℚ(√5))": 0.481211825, "ln radius(W_h)": 0.96242365, "ln radius(G)": 0.481211825, "s1225 d(o, φ*) (printed precision 1e-5)": 0.96242}
  braid_sl2                   {"[h,e] − 2e": "<1e-12", "[h,f] + 2f": "<1e-12", "e in e7": "<1e-12", "f in e7": "<1e-12", "[e, D_sol]": "<1e-12", "[f, D_sol]": "<1e-12", "[e, D56]": "4.000e+00", "X-variation of e": "5.000e-01", "e7-centraliser of e (dim, inertia)": [99, [36, 30, 33]], "orbit dim 133 − dim C(e)": 34, "spec h (real)": [[-1.0, 12], [0.0, 32], [1.0, 12]], "spec r (imag)": [[-1.0, 12], [0.0, 32], [1.0, 12]], "exp(πr) − (I − 2P_act)": "<1e-12"}
  pencil                      {"θ = 0·π/16": {"k² + cos2θ·P_act": "<1e-12", "max|Re|": 0.0, "max|Im|": 1.0, "type": "elliptic"}, "θ = 1·π/16": {"k² + cos2θ·P_act": "<1e-12", "max|Re|": 0.0, "max|Im|": 0.961187, "type": "elliptic"}, "θ = 2·π/16": {"k² + cos2θ·P_act": "<1e-12", "max|Re|": 0.0, "max|Im|": 0.840896, "type": "elliptic"}, "θ = 3·π/16": {"k² + cos2θ·P_act": "<1e-12", "max|Re|": 0.0, "max|Im|": 0.618614, "type": "elliptic"}, "θ = 4·π/16": {"k² + cos2θ·P_act": "<1e-12", "max|Re|": 0.0, "max|Im|": 0.0, "type": "nilpotent"}, "θ = 5·π/16": {"k² + cos2θ·P_act": "<1e-12", "max|Re|": 0.618614, "max|Im|": 0.0, "type": "hyperbolic"}, "θ = 6·π/16": {"k² + cos2θ·P_act": "<1e-12", "max|Re|": 0.840896, "max|Im|": 0.0, "type": "hyperbolic"}, "θ = 7·π/16": {"k² + cos2θ·P_act": "<1e-12", "max|Re|": 0.961187, "max|Im|": 0.0, "type": "hyperbolic"}, "θ = 8·π/16": {"k² + cos2θ·P_act": "<1e-12", "max|Re|": 1.0, "max|Im|": 0.0, "type": "hyperbolic"}, "wall k(π/4) − √2·e": "<1e-12"}
  kk_centre_vs_braid_rotation {"spec Z (imag)": [[-1.0, 12], [0.0, 32], [1.0, 12]], "spec r (imag)": [[-1.0, 12], [0.0, 32], [1.0, 12]], "e7-centraliser of Z": [67, [36, 31, 0]], "e7-centraliser of r": [67, [36, 31, 0]], "tr Z²": -24.0, "tr r²": -24.0, "g Z g⁻¹ − r (g = exp Y, Y ∈ e7; Y not printed)": "<1e-10", "g symplectic": "<1e-09", "g exp(πZ) g⁻¹ − (I − 2P_act)": "<1e-09", "[r, Z]": "1.000e+00", "exp(πZ) − (I − 2P_act)": "2.000e+00"}
  gauge_so21                  {"NC symmetric (noncompact)": "<1e-12", "NC X-variation (max)": "<1e-12", "[P,[Z,P]] off ℝ·Z (P not printed)": "<1e-12", "[Z,[Z,P]] + P": "<1e-12", "n³": "<1e-12", "rank n": 24, "rank n²": 12, "X-variation of n": "<1e-12", "e7-centraliser of n": [67, [20, 15, 32]], "orbit dim": 66, "braid Dehn-twist orbit dim": 34}
  golden_generator_control    {"in e7": "<1e-12", "X-variation": "7.071e-01", "[Lgen, h]": "<1e-12", "[Lgen, Z]": "<1e-12", "[Lgen, e]": "5.000e-01", "[Lgen, r]": "5.000e-01", "spec Lgen (real)": [[-1.0, 2], [-0.5, 16], [0.0, 20], [0.5, 16], [1.0, 2]], "e7-centraliser of h": [67, [37, 30, 0]], "e7-centraliser of Lgen": [49, [28, 21, 0]]}
  vocabulary                  {"forbidden-token hits in this file": 0, "control (each token once)": 5}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_d1409_generators_npz
  receipt   PASS filed_s1026_LANE_D1192_LENS_ARTIFACTS_npz
  receipt   PASS s1258_result_the_braid_56_is_twelve_punctured_torus_homologies
  receipt   PASS s1260_result_the_braid_is_level_zero_for_D_KK
  receipt   PASS s1225_result_holds_the_golden_length
  computed  PASS Q1_the_registered_ladder_carries_all_three_twist_classes_parabolic_dehn_twists_elliptic_trefoil_class_hyperbolic_figure8_and_gieseking
  computed  PASS Q2_the_figure8_and_gieseking_stretches_are_the_least_in_GL2Z_phi_is_the_fundamental_unit_and_ln_phi_squared_is_s1225s_golden_length
  computed  PASS Q3_the_dehn_twists_span_an_sl2_in_e7_level_zero_for_D_sol_not_gauge_e_in_the_minimal_nilpotent_orbit_and_exp_pi_r_is_the_braid_central_element
  computed  PASS Q4_on_the_pencil_the_parabolic_dehn_twist_is_the_wall_between_the_elliptic_rotation_and_the_hyperbolic_boost
  computed  PASS Q5_app_Gs_kk_centre_Z_is_E7_conjugate_to_the_braid_rotation_r_by_an_exhibited_element_but_is_not_the_same_element
  computed  PASS Q6_the_gauge_algebra_has_an_so21_through_Z_whose_null_element_preserves_X_in_a_different_nilpotent_orbit_from_the_dehn_twist
  computed  PASS Q7_control_the_golden_generator_commutes_with_h_and_Z_but_is_not_in_the_braid_sl2
  computed  PASS V1_no_momentum_vocabulary_for_D_KK_in_this_file
  argument  ARG  knot_theory_reading
  argument  ARG  number_theory_reading
  argument  ARG  the_third_point
  argument  ARG  two_null_elements
VERDICT the registered braid ladder carries all three twist classes — parabolic Dehn twists, the elliptic trefoil class, the hyperbolic figure-8 / Gieseking classes; the Dehn twists span an sl(2) in e7 (level 0 for D_sol, not gauge) whose rotation is E7-conjugate to App G's KK centre Z and whose parabolic direction is the wall between the clock and the boost; the Dehn twist is in the minimal nilpotent orbit, the figure-8 / Gieseking stretches are the least in GL(2, ℤ) and ln φ² is s1225's golden length; the gauge algebra has its own so(2,1) through Z with an X-preserving null element in a different orbit. A reading only: no mass, vacuum or length scale.
RESULT_HASH 867eb84d34d06322
s1265: 8 computed, 6 receipt, 4 argument, 0 failed
