=== Equivariant localization ===
weights = [1, 2, 3, 4, 5, 6, 7]
matrix = [[Fraction(20, 1), Fraction(16, 1)], [Fraction(16, 1), Fraction(14, 1)]]
weights = [-3, -2, -1, 0, 1, 2, 3]
matrix = [[Fraction(20, 1), Fraction(16, 1)], [Fraction(16, 1), Fraction(14, 1)]]
weights = [2, 5, 11, 17, 23, 31, 41]
matrix = [[Fraction(20, 1), Fraction(16, 1)], [Fraction(16, 1), Fraction(14, 1)]]

=== Ambient plane ===
M_amb = [[Fraction(20, 1), Fraction(16, 1)], [Fraction(16, 1), Fraction(14, 1)]]
det(M_amb) = 24
signature(M_amb) = (2,0)
PASS: sigma_2 and sigma_11 are independent.

=== c5 middle signature ===
b4 = 26
signature value = 22
(b+,b-) = (24, 2)
hard rank = 24
hard Hodge = (1, 22, 1)
hard cup signature = (22, 2)
sign-reversed K3-type signature = (2, 22)

=== OG10 lattice ===
rank = 24
BB signature = (3, 21)
|disc| = 3

=== Quadratic gate ===
c5 possible global-sign signatures = {(22, 2), (2, 22)}
OG10 possible global-sign signatures = {(21, 3), (3, 21)}
overlap = set()
FAIL candidate: direct natural-form c5-hard == OG10 H2.
PASS regression: rank/Hodge match is rejected by quadratic gate.

=== Kuga-Satake fallback ===
rank = 24
KS abelian dimension = 4194304

ALL ROUND-20 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.
