s1261 — the transported vs the fixed A861 potential
  structure_group        {"max rel |Det∘g − Det|": "<1e-12", "rel |gᵀG(gJ)g − G(J)|": "<1e-05", "min |Δ ½TrJ²| at 4 points": 0.49347, "min |Δ Tr KJ| at 4 points": 0.947096, "g·J_n − J_{n+1}": "<1e-12"}
  fixed_branch           {"-2": {"γ_n": -2.236068, "|∇V|": "<1e-07", "sig H": [15, 12], "sig G": [15, 12], "min G⁻¹H": 1.145898, "imag": "<1e-06", "G⁻¹H blocks (mean)": {"past (1,2)": 1.381966, "present (1,3)": 2.0, "future (2,3)": 3.618034}, "G⁻¹H diag": [1.145898, 2.0, 7.854102], "max rel dev from closed form": "<2e-04"}, "-1": {"γ_n": -1.0, "|∇V|": "<1e-07", "sig H": [15, 12], "sig G": [15, 12], "min G⁻¹H": 1.381966, "imag": "<1e-06", "G⁻¹H blocks (mean)": {"past (1,2)": 1.618034, "present (1,3)": 2.0, "future (2,3)": 2.618034}, "G⁻¹H diag": [1.381966, 2.0, 3.618034], "max rel dev from closed form": "<2e-04"}, "0": {"γ_n": 0.0, "|∇V|": "<1e-07", "sig H": [15, 12], "sig G": [15, 12], "min G⁻¹H": 2.0, "imag": "<1e-06", "G⁻¹H blocks (mean)": {"past (1,2)": 2.0, "present (1,3)": 2.0, "future (2,3)": 2.0}, "G⁻¹H diag": [2.0, 2.0, 2.0], "max rel dev from closed form": "<2e-04"}, "1": {"γ_n": 1.0, "|∇V|": "<1e-07", "sig H": [15, 12], "sig G": [15, 12], "min G⁻¹H": 1.381966, "imag": "<1e-06", "G⁻¹H blocks (mean)": {"past (1,2)": 2.618034, "present (1,3)": 2.0, "future (2,3)": 1.618034}, "G⁻¹H diag": [1.381966, 2.0, 3.618034], "max rel dev from closed form": "<2e-04"}, "2": {"γ_n": 2.236068, "|∇V|": "<1e-07", "sig H": [15, 12], "sig G": [15, 12], "min G⁻¹H": 1.145898, "imag": "<1e-06", "G⁻¹H blocks (mean)": {"past (1,2)": 3.618034, "present (1,3)": 2.0, "future (2,3)": 1.381966}, "G⁻¹H diag": [1.145898, 2.0, 7.854102], "max rel dev from closed form": "<2e-04"}, "3": {"γ_n": 4.0, "|∇V|": "<1e-07", "sig H": [15, 12], "sig G": [15, 12], "min G⁻¹H": 1.055728, "imag": "<1e-06", "G⁻¹H blocks (mean)": {"past (1,2)": 5.236068, "present (1,3)": 2.0, "future (2,3)": 1.236068}, "G⁻¹H diag": [1.055728, 2.0, 18.944272], "max rel dev from closed form": "<2e-04"}}
  kinetic_metric_reading {"1": {"H = ((1+r_k)/r_k)·G per block (rel)": {"past (1,2)": "<1e-04", "present (1,3)": "<1e-04", "future (2,3)": "<1e-04"}, "negative H per block": [4, 4, 4], "min eig G·H": 0.527864, "covariant past/future (G⁻¹H)": 1.618034, "φⁿ": 1.618034, "s1257 flat future/past": 1.618034}, "2": {"H = ((1+r_k)/r_k)·G per block (rel)": {"past (1,2)": "<1e-04", "present (1,3)": "<1e-04", "future (2,3)": "<1e-04"}, "negative H per block": [4, 4, 4], "min eig G·H": 0.167184, "covariant past/future (G⁻¹H)": 2.618034, "φⁿ": 2.618034, "s1257 flat future/past": 2.618034}, "3": {"H = ((1+r_k)/r_k)·G per block (rel)": {"past (1,2)": "<1e-04", "present (1,3)": "<1e-04", "future (2,3)": "<1e-04"}, "negative H per block": [4, 4, 4], "min eig G·H": 0.058834, "covariant past/future (G⁻¹H)": 4.236068, "φⁿ": 4.236068, "s1257 flat future/past": 4.236067}}
  transported_branch     {"base 1": {"γ_b": 1.0, "spectrum G⁻¹H at base": [1.38197, 1.61803, 2.0, 2.61803, 3.61803], "rung 1": {"|∇V|": "<1e-07", "max |spec − base spec|": "<1e-04", "imag": "<1e-06"}, "rung 2": {"|∇V|": "<1e-07", "max |spec − base spec|": "<1e-04", "imag": "<1e-06"}, "rung 3": {"|∇V|": "<1e-07", "max |spec − base spec|": "<1e-04", "imag": "<1e-06"}}, "base 0": {"γ_b": 0.0, "spectrum G⁻¹H at base": [2.0], "rung 0": {"|∇V|": "<1e-07", "max |spec − base spec|": "<1e-04", "imag": "<1e-06"}, "rung 1": {"|∇V|": "<1e-07", "max |spec − base spec|": "<1e-04", "imag": "<1e-06"}, "rung 2": {"|∇V|": "<1e-07", "max |spec − base spec|": "<1e-04", "imag": "<1e-06"}, "rung 3": {"|∇V|": "<1e-07", "max |spec − base spec|": "<1e-04", "imag": "<1e-06"}}}
  inequivalence          {"V_1^(2) vs every V_γ'": {"relative residual": 0.050068, "best (γ', c)": [2.244427, 2.019756]}, "V_1^(3) vs every V_γ'": {"relative residual": 0.065522, "best (γ', c)": [3.972883, 7.396578]}, "V_0^(1) vs every V_γ'": {"relative residual": 0.107142, "best (γ', c)": [1.002769, 0.504404]}, "V_0^(2) vs every V_γ'": {"relative residual": 0.169139, "best (γ', c)": [2.30125, 2.652797]}, "V_1∘g⁻¹ vs every V_γ' (is g a symmetry of the fixed family?)": {"relative residual": 0.210227, "best (γ', c)": [2.028351, 1.531512]}}
  receipt   PASS A861_drill_is_the_filed_source_of_the_probe_statics
  receipt   PASS app_I_is_the_printed_file_of_the_kinetic_metric_and_the_saddle
  receipt   PASS s1257_results_hold_the_flat_hessian_rung_curvatures
  computed  PASS P1_g_preserves_Det_and_the_kinetic_metric_but_not_TrJ2_or_TrKJ_and_steps_the_rungs
  computed  PASS P2_fixed_potential_each_rung_needs_its_own_gamma_n_and_the_rungs_have_distinct_positive_frequency_spectra
  computed  PASS P3_in_the_kinetic_metric_the_saddle_is_oscillatory_in_all_27_directions_and_the_past_block_is_heavier_by_phi_n
  computed  PASS P4_transported_potential_one_coupling_and_every_rung_isospectral_to_the_base_rung
  computed  PASS P5_no_transported_rung_potential_equals_a_fixed_potential_and_g_is_not_a_symmetry_of_the_fixed_family
  argument  ARG  verdict_on_one_coupling
  argument  ARG  the_saddle_in_its_own_metric
  argument  ARG  kk_link
VERDICT the golden boost is in the structure group (Det and the kinetic metric invariant; Tr J², Tr KJ not). Fixed potential: running γ_n, rungs distinct. Transported potential: one coupling, rungs isometric to the base. The branches never coincide. In the kinetic metric the A861 saddle is oscillatory in all 27 directions; its 12 negative-curvature directions are G's 12 negative-norm directions, and covariantly the past block is heavier by φⁿ.
RESULT_HASH cb085f43e4fd8017
s1261: 5 computed, 3 receipt, 3 argument, 0 failed
