# First campaign results

Recorded 2026-10-01T15:47:38.680Z. Overall numerical and new-case negative-control outcome: **PASS**.

Three official MathWorks problem families were solved with Lemonergy. The
comparison uses published mathematical solutions and disclosed parameters;
**MATLAB was not run, and independent physical validation is not established.**
All thresholds are internal predeclared gates, not vendor specifications.

## Battery HPPC parameter identification

Source: [Estimate Battery Model Parameters from HPPC Data](https://www.mathworks.com/help/simscape-battery/ug/estimate-battery-model-parameters-from-hppc-data.html).
Scope: one BAK cell operating point, 25 °C, 0.4 SOC, 1s1p; authored pulse
traces from the published 2-RC row. This reruns existing CT-01.

| Parameter | Published | Lemonergy | Relative error | Gate |
|---|---:|---:|---:|---:|
| R0 | 40.839 | 40.84131 | 0.005655674% | 5% |
| R1 | 2.0343 | 2.031906 | 0.1176928% | 10% |
| tau1 | 1.1318 | 1.132872 | 0.09468024% | 10% |

R0/R1 use mΩ; tau1 uses seconds. OCV, R2 and tau2 are fixed; C1 is derived,
not independently fitted. On the synthetic 5 A holdout, voltage RMSE is
**0.000841162 mV/cell**, with maximum absolute
error **0.01018148 mV/cell** across
2100 samples (gates
2 and
5 mV/cell).
The direct forward check at the published parameters passes
4/4 gates.
Optimizer termination: ohmic: max-evaluations; fast-rc: max-evaluations; joint-refinement: max-evaluations.
The reported budget-exhausted stages do not establish convergence.
The measured source trace was not imported. This is parameter recovery and
equation consistency on synthetic data.

## RLC circuit

Source: [RLC solution using Laplace transforms](https://www.mathworks.com/help/symbolic/solve-differential-equations-using-laplace-transform.html).
Lemonergy solves the published circuit equations numerically, and an independent
reference evaluates the published exact current and charge expressions.
All 994 native output points over 0–25 s are retained.
The sinusoidal input is itself produced by native oscillator blocks and checked.

| Observable | Maximum absolute error | RMSE | Gate | Outcome |
|---|---:|---:|---:|---|
| current | 1.258182e-11 A | 4.11595e-12 A | 1e-7 A | PASS |
| charge | 2.354578e-11 C | 9.031566e-12 C | 1e-7 C | PASS |
| input | 1.292054e-10 V | 5.174138e-11 V | 1e-7 V | PASS |

R1 perturbation from 4 to
4.4 Ω against unchanged
current/charge reference gates: expected rejection
**PASS**.
This checks the numerical engine, not symbolic transformation capability.

## Heat transfer

Source: [Heat Conduction Through Iron Rod](https://www.mathworks.com/help/simscape/ug/heat-conduction-through-iron-rod.html).
The first three scalar targets are printed answers in the official example;
their gates allow half the final printed decimal. Additional transient checks
use independently evaluated analytical responses with the disclosed inputs.

| Observable | Reference | Lemonergy | Maximum/absolute error | Gate | Outcome |
|---|---:|---:|---:|---:|---|
| conduction-tip | 8.5554 | 8.555364 | 0.00003563185 | 0.00005 °C | PASS |
| cylindrical-convection | 17.6479 | 17.6479 | 0.000003268459 | 0.00005 W | PASS |
| insulated-heating-slope | 0.0526 | 0.05258604 | 0.00001395788 | 0.00005 K/s | PASS |
| insulated-temperature-trace | — | — | 3.907985e-13 | 1e-7 K | PASS |
| lumped-temperature-trace | — | — | 1.698197e-12 | 1e-7 K | PASS |

Where the reference and actual columns are blank, the comparison covers a full
trace rather than a single scalar. Negative-control expected rejection:
**PASS**. The combined
transient is a lumped model; it is not compared to a spatial fin midpoint.

## Traces and replay

![RLC and synthetic HPPC responses and residuals](evidence/comparison.svg)

The [CSV](evidence/comparison.csv) lists mandatory scalar and waveform gates.
The [JSON](evidence/result.json) contains every native point and oracle value,
including perturbed runs. [RLC](evidence/rlc/rlc.graph.json) and
[thermal model exports](evidence/thermal/) can be loaded into Studio.
The [README](README.md) gives exact commands and the five-case battery backlog.
Browser interaction was not tested in this batch.

## Repeatability and review status

All ten serial fresh-process runs after two warmups produced one scientific
digest: `3fbdc001f2c3678c3d0dc1037197fc3a8ab841d3a3d48e41597acb11bd58a7fc`. Parent process wall time, including
Node startup, imports, all cases, negative controls and hashing, was
2093.457 ms median; minimum 1701.81 ms;
P95/maximum 3112.995 ms; mean 2356.767 ms;
population standard deviation 511.3469 ms.
Nearest-rank percentiles are used, so P95 is the maximum of ten runs.

Environment: v22.23.2, linux
7.0.0-34-generic, x64,
AMD Ryzen 7 5700U with Radeon Graphics, 4 logical CPUs.
Background load and power management were not controlled. No MATLAB runtime
was measured; these numbers support local repeatability only.

This is working-tree evidence. The [manifest](evidence/run-manifest.json)
hashes the actual inputs and binary; a clean immutable rerun remains needed
before external release. [Review notes](REVIEW.md) retain test results and
limitations. No publication or external claim approval is recorded.