=== Blind input ===
dim U = 3 quadrics
q1 = -4*w**2 + 8*w*x - 4*w*y - 8*w*z + 10*x*y + 6*x*z + y**2 - 7*y*z - 6*z**2
q2 = 2*w*y + 6*w*z - 8*x**2 + 4*x*z + 4*y**2 + 4*z**2
q3 = 4*w**2 - 2*w*y + 6*w*z - 8*x**2 - 2*x*y - 2*x*z - 6*y**2 - 7*y*z + z**2

=== Gate 1: common-factor test ===
gcd(q1,q2,q3) = 1
PASS: no nontrivial common factor; factor-envelope branch not triggered.

=== Gate 2: linear syzygies ===
dim Syz_1(U) = 2
Hilbert-Burch candidate matrix:
\left[\begin{matrix}- x - y - \frac{z}{2} & - w + x - \frac{y}{2} - z & - x - \frac{y}{2} + z\\w + 2 x + z & w + \frac{3 y}{2} + \frac{3 z}{2} & w + y\end{matrix}\right]
Matrix([[-x - y - z/2, -w + x - y/2 - z, -x - y/2 + z], [w + 2*x + z, w + 3*y/2 + 3*z/2, w + y]])

=== Gate 3: maximal minors ===
minor deleting column 1 = -w**2 + 2*w*x - w*y - 2*w*z + 5*x*y/2 + 3*x*z/2 + y**2/4 - 7*y*z/4 - 3*z**2/2
minor deleting column 2 = -w*y/2 - 3*w*z/2 + 2*x**2 - x*z - y**2 - z**2
minor deleting column 3 = w**2 - w*y/2 + 3*w*z/2 - 2*x**2 - x*y/2 - x*z/2 - 3*y**2/2 - 7*y*z/4 + z**2/4
PASS: maximal minors regenerate the signature ideal.

=== Gate 4: Groebner / Hilbert certificate ===
leading monomial exponents = [(2, 0, 0, 0), (1, 1, 0, 0), (0, 2, 0, 0)]
H(0) = 1; 3n+1 = 1
H(1) = 4; 3n+1 = 4
H(2) = 7; 3n+1 = 7
H(3) = 10; 3n+1 = 10
H(4) = 13; 3n+1 = 13
H(5) = 16; 3n+1 = 16
H(6) = 19; 3n+1 = 19
H(7) = 22; 3n+1 = 22
H(8) = 25; 3n+1 = 25
PASS: Hilbert polynomial/function is 3*n+1.
degree = 3, arithmetic genus = 0.

=== Gate 5: nondegeneracy ===
No degree-1 generators are present; I_1 = 0.
PASS: carrier is nondegenerate in P^3.

=== Gate 6: smoothness ===
chart x=1: singular ideal unit = True
chart y=1: singular ideal unit = True
chart z=1: singular ideal unit = True
chart w=1: singular ideal unit = True
PASS: projective carrier is smooth.

=== Gate 7: carrier architecture decision ===
smooth + nondegenerate + degree 3 + genus 0 => twisted cubic
architecture_type = syzygetic_single
carrier_type = twisted_cubic

=== Gate 8: ambient containment ===
remainder of ambient quartic modulo signature ideal = 0
PASS: reconstructed carrier lies in ambient quartic.

=== Gate 9: ambient quartic smoothness ===
quartic chart x=1: gradient ideal unit = True
quartic chart y=1: gradient ideal unit = True
quartic chart z=1: gradient ideal unit = True
quartic chart w=1: gradient ideal unit = True
PASS: ambient quartic is smooth.

ALL BLIND RECONSTRUCTION CHECKS PASSED.
Spreadsheet runtime warmup failed during python startup
Traceback (most recent call last):
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/patches/warm_spreadsheet_runtime_on_startup.py", line 26, in warm_spreadsheet_runtime_on_startup
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/spreadsheet_warmup.py", line 785, in warm_spreadsheet_runtime
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/spreadsheet_warmup.py", line 720, in _warm_feature_flows
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/spreadsheet_warmup.py", line 704, in _warm_collaboration_flows
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/generated/interface/models.py", line 32317, in hydrate_crdt_from_proto
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/rpc/remote.py", line 749, in __call__
  File "/tmp/tmp.L2TH2Y5coc/artifact_tool_v2-2.8.22/artifact_tool/rpc/client.py", line 150, in call
artifact_tool.rpc.client.RemoteError: hydrateCrdtFromProto requires an empty collaborative document.
