=== Del Pezzo lattice ===
root Gram =
Matrix([[-2, 1], [1, -2]])
index of <b1,b2,r1,r2> in Pic(S) = 3

=== Root descent pairing test ===
r1 dot b1 = 0 dot b2 = 0
r2 dot b1 = 0 dot b2 = 0
PASS: f_* q^*(root) pairs trivially with h1^2 and h2^2.
PASS: root-sector descent obstruction vanishes.

=== Descended root Gram ===
Matrix([[6, -3], [-3, 6]])

=== Visible block ===
Matrix([[20, 16], [16, 14]])

=== Orthogonality symbolic check ===
barp_*(h^3) = 9*v**2 + 8*v*x1 + 8*v*x2 + 4*x1**2 + 8*x1*x2 + 4*x2**2
v-linear coefficient = 8*x1 + 8*x2
barp_*(sigma11*h) = 6*v**2 + 4*v*x1 + 4*v*x2 + 2*x1**2 + 5*x1*x2 + 2*x2**2
v-linear coefficient = 4*x1 + 4*x2
PASS: root orthogonality to x1,x2 kills both cross pairings.

=== Full explicit rank-4 sublattice ===
Matrix([[20, 16, 0, 0], [16, 14, 0, 0], [0, 0, 6, -3], [0, 0, -3, 6]])
det = 648

=== Candidate index-3 saturation ===
if the Pic(S) 3-gluing survives, determinant = 72

ALL ROUND-23 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.
