s1257 — the golden saddle up the ladder
  rung -3 {"γ_n": -4.0, "Det": 1.0, "|∇V|": "<1e-07", "signature": [15, 12], "tachyonic curvature (mean of 4)": {"past (1,2)": -10.472133, "present (1,3)": -4.0, "future (2,3)": -2.472136}, "stable partner (mean of 4)": {"past (1,2)": 10.472139, "present (1,3)": 4.0, "future (2,3)": 2.472136}, "future / past": 0.236068, "φⁿ": 0.236068}
  rung -2 {"γ_n": -2.236067977, "Det": 1.0, "|∇V|": "<1e-07", "signature": [15, 12], "tachyonic curvature (mean of 4)": {"past (1,2)": -7.236067, "present (1,3)": -4.0, "future (2,3)": -2.763932}, "stable partner (mean of 4)": {"past (1,2)": 7.236069, "present (1,3)": 4.0, "future (2,3)": 2.763932}, "future / past": 0.381966, "φⁿ": 0.381966}
  rung -1 {"γ_n": -1.0, "Det": 1.0, "|∇V|": "<1e-07", "signature": [15, 12], "tachyonic curvature (mean of 4)": {"past (1,2)": -5.236068, "present (1,3)": -4.0, "future (2,3)": -3.236068}, "stable partner (mean of 4)": {"past (1,2)": 5.236068, "present (1,3)": 4.0, "future (2,3)": 3.236068}, "future / past": 0.618034, "φⁿ": 0.618034}
  rung +0 {"γ_n": 0.0, "Det": 1.0, "|∇V|": "<1e-07", "signature": [15, 12], "tachyonic curvature (mean of 4)": {"past (1,2)": -4.0, "present (1,3)": -4.0, "future (2,3)": -4.0}, "stable partner (mean of 4)": {"past (1,2)": 4.0, "present (1,3)": 4.0, "future (2,3)": 4.0}, "future / past": 1.0, "φⁿ": 1.0}
  rung +1 {"γ_n": 1.0, "Det": 1.0, "|∇V|": "<1e-07", "signature": [15, 12], "tachyonic curvature (mean of 4)": {"past (1,2)": -3.236068, "present (1,3)": -4.0, "future (2,3)": -5.236068}, "stable partner (mean of 4)": {"past (1,2)": 3.236068, "present (1,3)": 4.0, "future (2,3)": 5.236068}, "future / past": 1.618034, "φⁿ": 1.618034}
  rung +2 {"γ_n": 2.236067977, "Det": 1.0, "|∇V|": "<1e-07", "signature": [15, 12], "tachyonic curvature (mean of 4)": {"past (1,2)": -2.763932, "present (1,3)": -4.0, "future (2,3)": -7.236067}, "stable partner (mean of 4)": {"past (1,2)": 2.763932, "present (1,3)": 4.0, "future (2,3)": 7.236069}, "future / past": 2.618034, "φⁿ": 2.618034}
  rung +3 {"γ_n": 4.0, "Det": 1.0, "|∇V|": "<1e-07", "signature": [15, 12], "tachyonic curvature (mean of 4)": {"past (1,2)": -2.472136, "present (1,3)": -4.0, "future (2,3)": -10.472133}, "stable partner (mean of 4)": {"past (1,2)": 2.472136, "present (1,3)": 4.0, "future (2,3)": 10.472139}, "future / past": 4.236067, "φⁿ": 4.236068}
  rung +4 {"γ_n": 6.708203932, "Det": 1.0, "|∇V|": "<1e-07", "signature": [15, 12], "tachyonic curvature (mean of 4)": {"past (1,2)": -2.291796, "present (1,3)": -4.0, "future (2,3)": -15.708196}, "stable partner (mean of 4)": {"past (1,2)": 2.291796, "present (1,3)": 4.0, "future (2,3)": 15.708211}, "future / past": 6.854099, "φⁿ": 6.854102}
  curvature_checks {"max |FD − closed form|": "<2e-05", "max |future/past − φⁿ|": "<1e-04", "rung −n swaps past and future (max)": "<2e-05"}
  couplings        {"-3": [-4.0, -4], "-2": [-2.236067977, -2.236067977], "-1": [-1.0, -1], "0": [0.0, 0.0], "1": [1.0, 1], "2": [2.236067977, 2.236067977], "3": [4.0, 4], "4": [6.708203932, 6.708203932]}
  boost_orbit      {"1": "<1e-10", "2": "<1e-10", "3": "<1e-10", "-1": "<1e-10", "-2": "<1e-10"}
  receipt   PASS filed_d1412_house_frames_npz
  receipt   PASS filed_chatgpt_d1410_maps_npz
  receipt   PASS filed_d1410_solder_npz
  receipt   PASS A861_drill_is_the_filed_source_of_the_probe_statics
  receipt   PASS app_I_is_the_printed_file_of_the_golden_saddle_statics
  computed  PASS R1_A861_is_reproduced_at_the_first_rung_past_minus_2phi_present_minus_4_future_minus_2phi_squared
  computed  PASS R2_the_rung_point_diag_phi_n_1_phi_minus_n_is_stationary_for_gamma_n_and_the_signature_is_15_12_at_every_rung
  computed  PASS R3_the_block_curvatures_are_minus2_1_plus_phi_minus_n_minus4_minus2_1_plus_phi_n_and_future_over_past_is_phi_to_the_n
  symbolic  PASS R3s_future_over_past_curvature_is_x_for_x_equal_phi_to_the_n
  argument  ARG  closed_form
  computed  PASS R4_gamma_n_is_the_Lucas_number_for_odd_n_and_root5_times_the_Fibonacci_number_for_even_n
  computed  PASS R5_the_n_th_power_of_the_shell_golden_boost_carries_the_pointing_to_the_rung_n_point_sum_lambda_k_to_the_n_f_k
  argument  ARG  what_the_ladder_says
  argument  ARG  scope
VERDICT at rung n the golden saddle (stationary for γ_n = φⁿ − φ⁻ⁿ) keeps signature (15,12); its past / present / future tachyonic curvatures are −2(1+φ⁻ⁿ), −4, −2(1+φⁿ): future/past = φⁿ exactly, the present (vector) block is rung-independent; rung n is the n-th power of the shell golden boost applied to the pointing. Probe statics only; no arrow is selected.
RESULT_HASH 3f332f68b1a40ad0
s1257: 5 computed, 1 symbolic, 5 receipt, 3 argument, 0 failed
