=== Build geometric signature on Q ===
dim A_geom = 10

=== Multiplication-generated carrier sectors ===
dim U_C = 3
dim U_D = 3
dim(U_C + U_D) = 6
dim J_Q = 4
dim(U_C + U_D + J_Q) = 10
PASS: A_geom = U_C + U_D + J_Q

=== Factorization-incidence kernels on A_geom ===
(3, 1): kernel dimension = 1
(1, 3): kernel dimension = 1
(2, 2): kernel dimension = 0
(3, 0): kernel dimension = 0
(0, 3): kernel dimension = 0
(2, 1): kernel dimension = 0
(1, 2): kernel dimension = 0
kernel (3,1) factor = -a**3*d + b**3*c
kernel (1,3) factor = a*c**3 + a*c*d**2 - a*d**3 - b*c**3 - b*c**2*d - 2*b*c*d**2 + b*d**3
PASS: unique kernels recover F_C and F_D

=== One explicit 12-dimensional extension ===
extension directions correspond to:
   a**3*c**3
   a**3*c**2*d
A_star (3, 1): kernel dimension = 1
A_star (1, 3): kernel dimension = 1
A_star (2, 2): kernel dimension = 0
A_star (3, 0): kernel dimension = 0
A_star (0, 3): kernel dimension = 0
A_star (2, 1): kernel dimension = 0
A_star (1, 2): kernel dimension = 0
PASS: explicit 12D extension preserves unique carrier factors

=== Dimension budget for actual Hodge signature ===
literature theorem: dim I_alpha,3 = 16
kernel of restriction R_3 -> H^0(Q,O(3,3)) is q*R_1, dimension 4
therefore predicted/derived dim A_alpha|_Q = 12
known geometric factor + Jacobian sector dimension = 10
purity-defect budget on Q = 2

ALL SYMBOLIC 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.
