=== 1. Ambient lattice parity ===
signature = (24, 2)
difference = 22
PASS: a unimodular lattice of this signature cannot be even.
Therefore the middle lattice is odd unimodular.

=== 2. Inherited lattice A1 + A3 ===
A =
Matrix([[2, 0, 0, 0], [0, 2, -1, 0], [0, -1, 2, -1], [0, 0, -1, 2]])
det(A) = 8
SNF(A) =
Matrix([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 2, 0], [0, 0, 0, 4]])
discriminant group = Z/2 + Z/4
q_A generators = 1/2 and 3/4

=== 3. Hard complement coarse data ===
rank T = 22
sig(T) = (20, 2)
sig(-T) = (2, 20)

=== 4. Exact finite quadratic refinements ===
(0, 0) Gauss = -1
(0, 1) Gauss = 1
(1, 0) Gauss = I
(1, 1) Gauss = -I
Brown invariants = {(0, 0): 4, (0, 1): 0, (1, 0): 2, (1, 1): 6}

=== 5. Milgram selection ===
Br(q_-T) required = 6
selected refinement = [(1, 1)]
q(a) = 3/2 == -1/2 mod 2
q(b) = 7/4 == -1/4 mod 2

=== 6. K3^[2] degree-4 div-1 primitive lattice ===
rank = 22
signature = (2, 20)
|det| = 8
q_K generators = -1/4 and -1/2
PASS: q_K == q_-T.

=== 7. Nikulin uniqueness condition ===
rank = 22
discriminant length = 2
rank >= length+2: True
PASS: indefinite even lattice is unique in its genus in this range.
Conclusion: -T is integrally isometric to the degree-4 div-1 K3^[2] primitive lattice.

ALL ROUND-25 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.
