=== Rational quartic parametrization ===
[s:t] -> [s^4 : s*t^3 : s^3*t : t^4]
q∘nu_C = 0

=== Degree-2 ideal piece ===
dim I_C,2 = 1
unique quadric generator = x*w - y*z

=== Degree-3 ideal piece ===
dim I_C,3 = 7
dim q*R_1 = 4
q*R_1 plus 3 extra cubics spans I_C,3

=== Quartic containment and homogeneity ===
f∘nu_C = 0
quartic monomial degrees = [4]

=== Smoothness of quartic surface ===
chart x=1: unit gradient ideal = True
chart y=1: unit gradient ideal = True
chart z=1: unit gradient ideal = True
chart w=1: unit gradient ideal = True
PASS: S is smooth.

=== Segre residual factorization ===
f|_Q = (a**3*d - b**3*c)*(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)
C factor bidegree (3,1); D0 factor bidegree (1,3).

=== Residual rational quartic D0 ===
dim I_D0,2 = 1
dim I_D0,3 = 7

=== Cubic intersection dimensions ===
dim(I_C,3 + I_D0,3) = 10
dim(I_C,3 ∩ I_D0,3) = 4
intersection equals q*R_1

=== Jacobian cubic space ===
dim J_S,3 = 4

=== Total geometrically explained cubic space ===
dim(I_C,3 + I_D0,3 + J_S,3) = 14

=== Theorem-bridged purity defect ===
theorem: dim I_alpha(C),3 = 16
geometric span dimension = 14
Geometric Purity Defect PD_3 = 2

=== Failure certificate ===
unique quadric dimension       : 1
carrier cubic dimension       : 7
residual cubic dimension      : 7
common cubic dimension        : 4
Jacobian cubic dimension      : 4
geometric cubic span          : 14
Hodge annihilator cubic dim   : 16 (theorem bridge)
geometric purity defect       : 2
purity breakdown depth        : 3
safe reconstruction depth     : 2
level-2 output                : unique quadric envelope Q
level-3 output                : non-geometric signature sector

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.
