=== Imaginary-quadratic action ===
J_d =
Matrix([[0, -d], [1, 0]])
J_d^2 =
Matrix([[-d, 0], [0, -d]])

=== Orbit determinant ===
v = Matrix([[a], [b]])
J_d v = Matrix([[-b*d], [a]])
det[v, J_d v] = a**2 + b**2*d

=== Concrete rational tests ===
d=1, v=(1,0), det=1, rank=2
d=1, v=(0,1), det=1, rank=2
d=2, v=(3,-5), det=59, rank=2
d=3, v=(2/3,5/7), det=871/441, rank=2
d=5, v=(-4,9), det=421, rank=2

=== Bridge rank accounting ===
raw bridge rank = 1
symmetry-closed rank = 2
defect dimension = 2
bridge defect = 0
amplification factor = 2

=== Module-generator interpretation ===
HW is 1-dimensional over K but 2-dimensional over Q.
Therefore mu_K(HW)=1 while dim_Q(HW)=2.
One nonzero algebraic seed is enough for K-module closure.

ALL EXACT 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.
