# Original fixed-geometry drainage energy cost attribution

Registered2026-11-13before measurement. Actual uniform5 startup passed native
and independent saved-step gates, but native loop~103s/step;10us budget~6/12h.
Full original C1/time/space/physical-flux/experiment scope unchanged. Current
20->10space49.56%dh/76.12%motion fails at10us. No long job launched here.

FIRST measure ORIGINAL CurvedEdgeEnergy, original geometry, no candidate dispatch.
Snapshots:N144initial,N544initial from cost_profile;N2112initial and ORIGINAL
mechanical endpoint(stage1) of global_five guard_dt.0625. Copy exact CSV numeric
strings, retain source hashes. Same SDS6mM/insoluble/SI scales,bath data and
gravity/DLVO-off. Require geometry/energy import error<=1e-9. No time step.

Time Value,Pressure,Fields(false),Fields(true) separately: warm1,3samples each.
Fields(true) includes value/pressure plus Hessian assembly, so times overlap,
not additive percentages of the actual coupled step. Time ONE cold cached
Hess_Apply(build+apply),10cached Hess_Apply samples and3cached all-diagonal scans.
Record Windows process CPU+wall samples; small CPU values can quantize to zero.
Process/cache/host load limits interpretation. Existing binary76e49... unchanged.

Require Fields true/false energy,node energy,area,pressure,tension exactly equal;
cached Hess action vs explicit dense H*w relativeLinf<=1e-12;
matrix symmetry max<=1e-12*max|H|;finite sinks/timings. Export ALL exact nonzero
Hessian entries(row,col,H_code) as raw CSV, nonzero count,density and original
native input. No drop tolerance, approximation or modification of energy.
This is observed nonzero support, not a physical validation or speedup claim.

Conditional followup can be registered ONLY after inspecting measurements:
if true-field assembly dominates other field calls and exact matrix has local
support, implement a separate DRIFT-owned local nonzero assembly candidate,
preserving ALL energy curvature/cross-face/bath terms. No generic solver/core
change. New candidate must be checked against full native H/diagonal/actions,
energy/pressure and actual coupled outputs with preregistered numeric gates.
Physical2%TIME/10%SPACE/force/energy/inventory thresholds never loosened.
Default solver remains unchanged until evidence warrants adoption.

Classical sparse-assembly prior art, not method novelty:
https://eigen.tuxfamily.org/dox/group__TutorialSparse.html
https://eigen.tuxfamily.org/dox/classEigen_1_1SparseMatrix.html
No implementation choice or bottleneck share is assumed from these references.

4sequential cases,240s percase,600s total native cap,no>2h task. Preserve ALL
raw inputs,potential failures,all logs/hashes,white Nature red/bluePNG+vectorPDF,
bounded byte-exact raw ZIPs and all4research result entry points/public report.
Any later>2h actual trajectory requires half-hour monitoring BEFORE launch.