s1313 — the face audit
  Q1_inventory           {"kernels defining face() (serial < s1313)": ["s1284", "s1286", "s1287", "s1289", "s1290", "s1291", "s1292", "s1293", "s1296", "s1297", "s1298", "s1299", "s1300"], "distinct definitions (block hash: kernels)": {"73636affa9fb5260": ["s1284", "s1286", "s1289", "s1290", "s1291", "s1292", "s1293", "s1296", "s1297", "s1298", "s1299", "s1300"], "7c3f6a37fbc1e169": ["s1287"]}, "kernels calling face() off ±D56": ["s1284", "s1286", "s1287", "s1289", "s1300"], "their call arguments": {"s1284": ["D56", "H", "gen((0.3, -0.2, 0.1), (0, 0, 0))", "gen(*v)", "gen(s_, (0, 0, 0))", "gen(s_, ph_)"], "s1286": ["-D56", "D56", "H", "H4", "gen(s0, p0)"], "s1287": ["D56", "H", "gen(s0, p0)"], "s1289": ["-D56", "D56", "H4"], "s1300": ["-D56", "D56", "H"]}}
  Q2_exact_weight_face   {"directions": 128, "chart residual (max)": "<1e-12", "joint spectrum: |eig R − integer|, |Vᵀhₖ V − diag w|, |[hᵢ, hⱼ]| (max)": ["<1e-12", "<1e-12", "<1e-12"], "multiplicities of −1, 0, +1 of each hₖ (all directions)": ["[[12, 12, 32], [12, 12, 32], [12, 12, 32]]"], "present components: min norm / ‖X‖": 0.075326, "absent components: max norm / ‖X‖": "<1e-13", "four-form directions: face − X_i (i = argmax χᵢ·c), max": "<1e-12", "four-form directions checked": 15, "quadratic constraints of every exact-weight face (max)": "<1e-10"}
  Q3_audit               {"filed call-site directions": 121, "face() as used: the s1284 text (support 1e-12) at the 64 directions it was run on − exact, max": "<1e-10", "face() as used: the s1287 form (support 1e-9) at its 57 census directions − exact, max": "<1e-08", "the s1287 form at every filed direction − exact, max (a truncation at the 1e-9 level)": "<1e-08", "filed directions on an exact wall (several top components)": ["s1284 Q1 / s1287 R135", "s1284 Q1 / s1287 R45", "s1284 Q4 one factor, φ = 0", "s1284 Q4 one factor, φ = 0.7", "s1284 Q4 one factor, φ = π/2", "s1284 Q4 two factors, different angles", "s1284 Q4 two factors, same angle", "s1287 census ONE1", "s1287 census ONE2", "s1287 census ONE3", "s1287 census R135", "s1287 census R45", "s1287 census TWO2", "s1287 census TWO3", "s1287 census TWO4"], "directions with wall gap < 0.01": {"s1284 Q3 #10": 0.005785, "s1284 Q3 #38": 0.00352, "s1300 draft1 four-form random 2": 0.004908}, "smallest relative eigen-gap of H at a filed direction": "1.01e-04", "s1287 census E35: relative eigen-gap of H; wall gap (the s1284 text is host-fragile here — DRAFT HISTORY)": ["1.01e-04", 0.533246], "s1300 draft 1 failing direction: χ·c; relative eigen-gap of H; exact face − X_i": [[0.344195, 1.49048, -3.315486, 1.480811], "1.46e-03", "<1e-12"]}
  Q4_mechanism           {"δ = 0.1": {"top pieces i": [0], "exact − Σ X_i": "<1e-12", "relative eigen-gap of H": "4.8e-02", "face() − exact": "agrees (<1e-10)", "face() top − true top, in units of δ/2": 0.0}, "δ = 0.01": {"top pieces i": [0], "exact − Σ X_i": "<1e-12", "relative eigen-gap of H": "5.0e-03"}, "δ = 0.001": {"top pieces i": [0], "exact − Σ X_i": "<1e-12", "relative eigen-gap of H": "5.0e-04"}, "δ = 0.0001": {"top pieces i": [0], "exact − Σ X_i": "<1e-12", "relative eigen-gap of H": "5.0e-05"}, "δ = 1e-06": {"top pieces i": [0], "exact − Σ X_i": "<1e-12", "relative eigen-gap of H": "5.0e-07", "face() − exact": "WRONG (1.00)", "face() top − true top, in units of δ/2": 1.0}, "δ = 1e-07": {"top pieces i": [0], "exact − Σ X_i": "<1e-12", "relative eigen-gap of H": "5.0e-08", "face() − exact": "WRONG (1.00)", "face() top − true top, in units of δ/2": 1.0}, "δ = 0": {"top pieces i": [0, 1], "exact − Σ X_i": "<1e-12", "relative eigen-gap of H": "1.0e+00", "face() − exact": "agrees (<1e-10)", "face() top − true top, in units of δ/2": "<1e-12"}}
  receipt   PASS filed_d1414_house_frames_npz
  receipt   PASS filed_chatgpt_d1417_maps_npz
  receipt   PASS filed_kernel_s1284
  receipt   PASS filed_kernel_s1286
  receipt   PASS filed_kernel_s1287
  receipt   PASS filed_kernel_s1289
  receipt   PASS filed_kernel_s1290
  receipt   PASS filed_kernel_s1291
  receipt   PASS filed_kernel_s1292
  receipt   PASS filed_kernel_s1293
  receipt   PASS filed_kernel_s1296
  receipt   PASS filed_kernel_s1297
  receipt   PASS filed_kernel_s1298
  receipt   PASS filed_kernel_s1299
  receipt   PASS filed_kernel_s1300
  receipt   PASS A1778_census_csv_directions
  receipt   PASS s1284_results_face_definition
  receipt   PASS s1283_results_F0_construction
  computed  PASS Q1_thirteen_filed_kernels_define_face_twelve_identically_s1287_with_support_1e-9_and_five_call_it_off_the_special_rays
  computed  PASS Q2_the_exact_weight_face_reads_integer_joint_weights_from_one_s_independent_operator_separates_present_from_absent_components_by_eleven_orders_and_is_consistent
  computed  PASS Q3_every_filed_call_site_face_as_its_kernel_used_it_equals_the_exact_weight_face_two_filed_samples_lie_within_0_006_of_a_wall_and_are_right_and_the_s1300_draft1_direction_is_X_i
  computed  PASS Q4_face_fails_only_near_but_not_at_a_wall_its_spurious_top_is_one_near_degenerate_eigen_gap_above_the_true_top_and_the_exact_weight_face_is_exact_for_every_delta
  argument  ARG  forcing
  argument  ARG  reading
  argument  ARG  scope
VERDICT: face() is right at every filed call site in the form its kernel used (s1284 text < 1e-10, s1287 form < 1e-8 against the exact-weight face); its failure mode is eigh mixing of near-degenerate eigenvalues of H — near but not at a wall, or far from walls where H alone is near-degenerate (s1287 E35, host-dependent); the exact-weight face (integer joint weights from h₀ + 3h₁ + 9h₂) is exact for every direction. No filed result is affected.
RESULT_HASH 40d0e4ddcbefae90
s1313: 4 computed, 18 receipt, 3 argument, 0 failed
