s1294 — house checks of A1780 (Grok) / A1781 (Gemini), the D1420 Wyler returns
  R_receipts           {"house 1/α_W (12 significant digits)": "137.036082448", "sentinel(s) in the AS-SENT text": ["D1420-END-415813c693bc"], "A1780_GROK_return": {"echoes AS-SENT v3": true, "echoes v4 (never sent)": false, "longest echoed token length": 16, "1/α_W printed": ["137.036082448"], "matches house to 12 s.f.": true, "sentinel count": 2, "ends with \"D1420 COMPLETE\" then the sentinel": true}, "A1781_GEMINI_return": {"echoes AS-SENT v3": true, "echoes v4 (never sent)": false, "longest echoed token length": 64, "1/α_W printed": ["137.036082448"], "matches house to 12 s.f.": true, "sentinel count": 2, "ends with \"D1420 COMPLETE\" then the sentinel": true}}
  P_prefactor          {"Vol(S⁴) / (8π²/3)": "1.000000000000000", "|9/(8π⁴) − 8/Vol(S⁴)²| relative": "<1e-14", "Hua V(Q⁵) / (8π³/3)": "1.000000000000000", "|8πV(D₅)^¼/(Vol(S⁴)V(Q⁵)) − α_W| relative": "<1e-14"}
  S_shilov_volume      {"max_n=3..8 |Hua(n) − Vol(Sⁿ⁻¹)Vol(S¹)/2| relative": "<1e-14", "CONTROL (Gemini Q1(a), S⁴ × S¹ un-quotiented): reconstruction / α_W": "0.500000000000"}
  L_so62_involutions   {"so(6,2): dim, tr(XY) inertia (+, −)": [28, [12, 16]], "diagonal involutions: fixed dims (a positive, b negative axes reflected)": {"0,1": 21, "0,2": 16, "1,0": 21, "1,1": 16, "1,2": 13, "2,0": 16, "2,1": 13, "2,2": 12, "3,0": 13, "3,1": 12, "3,2": 13, "4,0": 12, "4,1": 13, "4,2": 16, "5,0": 13, "5,1": 16, "5,2": 21, "6,0": 16, "6,1": 21}, "largest fixed dim and where (a,b; (a,b) ~ (6−a,2−b) give the same r up to sign)": [21, ["0,1", "1,0", "5,2", "6,1"]], "any fixed dim 22": false, "one positive axis: dim, centre, derived dim, inertia (+, −)": [21, 0, 21, [10, 11]], "one positive axis: ‖r Z r − Z‖": "<1e-15", "one NEGATIVE axis: dim, centre, inertia (+, −)": [21, 0, [6, 15]], "one NEGATIVE axis: ‖r Z r + Z‖ (reverses Z)": "<1e-15", "two positive axes: dim, centre, derived dim, derived inertia (+, −)": [16, 1, 15, [8, 7]]}
  Q3b_line             {"zeros of 1 − λ²": [-1.0, 1.0], "fixed points of λ ↦ 1/λ": [-1.0, 1.0], "V at each": [-6.0, 0.0]}
  receipt   PASS filed_A1780_GROK_return
  receipt   PASS filed_A1781_GEMINI_return
  receipt   PASS filed_D1420_AS_SENT_v3
  receipt   PASS filed_D1420_v4_NEVER_SENT
  computed  PASS R_both_returns_echo_the_AS_SENT_v3_sha_not_v4_print_1_over_alphaW_to_12_sf_and_carry_the_sentinel_twice
  computed  PASS P_the_prefactor_is_8_over_VolS4_squared_and_the_Grok_reconstruction_reduces_to_R5
  computed  PASS S_Hua_characteristic_volume_is_the_Z2_quotient_of_S1_x_Sn_minus_1_and_dropping_the_Z2_halves_the_reconstruction
  computed  PASS L1_the_dim5_cut_is_an_involution_of_so62_whose_fixed_algebra_is_so52_alone_dim21_centre0_noncompact10_and_commutes_with_Z_the_other_dim21_branch_is_so61_and_reverses_Z
  computed  PASS L2_so42_occurs_as_the_derived_fixed_algebra_of_reflecting_two_positive_axes_an_inclusion_only
  computed  PASS Q3b_the_critical_set_equals_the_mirror_fixed_set_and_V_is_0_and_minus6_there
  argument  ARG  general_involutions
  argument  ARG  scope
VERDICT: both receipts are of the AS-SENT v3 text; 9/(8π⁴) = 8/Vol(S⁴)²; the boundary volume 8π³/3 is the ℤ₂ quotient of S¹ × S⁴ (dropping it halves the reconstruction); the dim-5 cut of R1 is an involution of so(6,2) with fixed algebra so(5,2) alone (dim 21, centre 0, keeps Z) — the other 21-dim branch is so(6,1) and reverses Z; no involution fixes so(5,2) ⊕ so(2); so(4,2) occurs only as an inclusion.
RESULT_HASH 99aeb8f316d399fa
s1294: 6 computed, 4 receipt, 2 argument, 0 failed
