# R139 canonical scientific record: E09

This canonical record integrates the completed E09 analysis onto verified R138.
All 3,804 inherited R138 files are preserved. The scientific review below is
retained from the completed E09 reproduction; only image links are adapted to
their canonical location. Its original text and all numerical outputs remain
unchanged under `completed_analysis/`.

The correct scientific source is `E09_Ye2026_Reproduction.zip` (22 June 2015).
The separately completed `R139_IRIS_Event_Analysis.zip` concerns 5 April 2017;
it remains preserved separately and is not relabelled as E09.

No new observations, fits, model calculations or MHD searches were performed
during canonical integration. The current physics core does not claim exhaustive
enumeration of every MHD configuration unless that completeness was explicitly
established. Checked results retain their stated scope.

---

# E09: reproduction of the published IRIS slow-shock example

**Result: the published spectral decomposition is reproducible, and the supplied model cut supports slow ordering in an isothermal limiting test. A complete independent verification of the conductive MHD shock is not established by this reduced dataset.**

This is a bounded reproduction of the flare-loop example of **Ye et al. (2026)**, not a new discovery or a global EUV-front classification. The observation, simulation and original interpretation belong to the authors. RMO contributes the independent numerical checks described below. No frozen checkpoint or physics-core file was changed.

Source: [Ye et al., *Propagating slow-mode shocks discovered in dynamical solar flare loops*, Nature Communications 17, 8150](https://doi.org/10.1038/s41467-026-75039-z). The accompanying Source Data workbook supplies the numerical profiles used here. The additional [author dataset](https://doi.org/10.6084/m9.figshare.30371113) was identified, but its API returned HTTP 403 in this session. This is an access limitation, not evidence of absent data.

## What was reproduced

The selected event is **22 June 2015**, E09 in the saved RMO catalogue. It concerns hot flare-loop plasma. The supplementary figure identifies the observed S2/S3 profiles as slit 9 at **17:55:41 UTC**. This is a source-labelled time; a new FITS-header/exposure audit was not performed.

The calculation reads 12 Figure 7 profiles, including three processed IRIS profiles with 78 bins each, and the 320-point model cut in Supplementary Figure 4. It also checks the supplied blend subtraction. It does not recalibrate raw IRIS data, rerun the three-dimensional simulation, or generate new MHD shock roots.

### 1. Spectral reproduction

For S2 and S3, subtracting the authors' supplied blend curves from their supplied original profiles reproduces their cleaned profiles to better than **1.1 × 10⁻¹⁴ DN**. Those cleaned profiles are identical to the Figure 7 intensity columns. This verifies the recorded subtraction, not its astrophysical uniqueness.

The published component curves recover these Doppler centres:

| Profile | Published decomposition recovered from curve samples (km/s) | Independent refit to processed intensity (km/s) |
|---|---:|---:|
| S1 | single component, approximately +8.0 | +8.012 |
| S2 | −92.834, −2.275 | −94.984, −4.018 |
| S3 | −78.503, −7.206 | −78.503, −7.207 |

The independent column uses a constant background and a thermal-width-floor scenario. S3 reproduces the published decomposition closely. S2 is close but not identical; its narrower component reaches the imposed width floor. This is not claimed as exact replication of an undocumented weighting procedure. The table does not report measurement uncertainties.

The independent profile model is

\[
 I(v)=b+\sum_j A_j\exp[-(v-\mu_j)^2/w_j^2],
 \qquad \mathrm{FWHM}_j=2\sqrt{\ln 2}\,w_j.
\]

The source figure's displayed widths agree with FWHM values recovered from its component curves. We keep FWHM and the exponential width parameter `w` distinct.

The thermal scenario assumes a minimum Fe XXI FWHM of 0.43 Å, giving `w >= 57.174 km/s` with the conversion used here. This is an **ASSUMED** line-formation constraint, not an independent temperature measurement for each component. An exploratory fit allowing widths down to two spectral pixels is retained separately. Its narrow components are not promoted to physically identified hot-plasma components.

All **360 numerical starts converged**, across ten profile/mask/width scenarios and one- or two-Gaussian fits. Convergence does not establish unique spectral components or exhaustive physical-model coverage. The script retains every start and active bound.

With the thermal floor and all supplied bins, the descriptive AICc difference `single − double` is **−6.29 for S1, +4.49 for S2 and +0.80 for S3**. Thus the fit comparison supports a simple S1 profile, while the extra S3 component has weak preference under this particular complexity penalty. Excluding neighbourhoods of the fitted blends gives +6.22 for S2 and +1.21 for S3. These are not calibrated detection significances: the source table does not supply a noise covariance or the full error model used by the authors. The two-component interpretation remains sensitive to the fitting assumptions, especially for S3.

![Independent spectral reproduction](completed_analysis/results/E09_spectral_reproduction.png)

### 2. Conductive-model audit

The source simulation includes thermal conduction. The existing RMO core inspected here uses an ideal, adiabatic energy flux and requires `gamma > 1`. It must not be presented as having verified the source's non-adiabatic balance. In particular, **setting gamma to 1 in that energy equation is not a valid implementation of conduction**.

We used the source cut at **1.06 t0**, keeping it separate from the synthetic Figure 7 samples at **1.08 t0**. The cut contains density, pressure, temperature and absolute normal/tangential quantities, rather than a complete signed vector-state pair.

For the representative endpoints `0.018 L0` and `0.038 L0`, the recomputed diagnostics are:

| Diagnostic | Value |
|---|---:|
| Density ratio, downstream/upstream | 1.3558 |
| Pressure ratio | 1.3957 |
| Temperature ratio | 1.0295 |
| Conditional shock-frame speed, upstream/downstream | 456.18 / 342.84 km/s |
| Shock-frame speed ratio | 1.3306 |
| Mass-flux ratio, downstream/upstream | 1.0189 |
| Normal-field magnitude ratio | 0.9576 |
| Tangential-field magnitude ratio | 0.8457 |

The speed transformation assumes the source's approximately **258 km/s** shock motion is opposite to the positive evaporation speed: `|u_n| = |V_n| + 258 km/s`. The signed transformation cannot be deduced from the magnitude columns alone. No uncertainty on that reported shock speed was supplied here.

For each endpoint we evaluate the limiting magnetosonic speeds,

\[
c_{f,s}^2=\frac12\left[a^2+v_A^2\pm
\sqrt{(a^2+v_A^2)^2-4a^2v_{A,n}^2}\right],
\]

using `a² = p/rho` for an isothermal limit and `a² = (5/3)p/rho` for the adiabatic principal part. Magnetic speeds use consistent Gaussian-cgs units with `4π`.

The representative isothermal slow speeds are **366.79 and 381.34 km/s**. The transformed flow is above the upstream slow speed, below the upstream normal Alfvén speed, and below the downstream slow speed. This is the ordinary slow ordering in this limiting diagnostic. The same check holds for all **nine** retained endpoint alternatives.

The adiabatic slow speeds are **472.30 and 490.56 km/s**: the upstream flow is already sub-slow at the representative cut boundary. None of the nine endpoint alternatives passes that adiabatic ordering at the nominal 258 km/s transformation. This difference demonstrates why the closure matters; it does **not** refute the authors' conductive simulation.

The nine alternatives span upstream positions `0.017–0.019 L0` and downstream positions `0.037–0.039 L0`. Density ratios span **1.341–1.363** and temperature increases **2.61–3.33%**. These are analysis-window alternatives around the plotted interface, not an observational confidence interval or a complete geometry/speed uncertainty study.

![Thermal closure audit](completed_analysis/results/E09_thermal_closure_audit.png)

### 3. Why this is not yet full conductive-MHD verification

The representative mass flux differs by about **1.89%**, and the normal magnetic magnitude by about **4.24%**, between these finite-cut endpoints. Background variation, surface geometry and time dependence cannot be separated from a local jump using this worksheet alone. We retain these discrepancies explicitly. A nonuniform background does not remove the local magnetic-divergence constraint on a properly defined discontinuity.

For a stationary, planar control volume, the relevant energy balance would contain

\[
[F_{\mathrm{ideal},n}+q_n+F_{\eta,n}]
=\int \rho\,\mathbf g\cdot\mathbf u\,dn,
\]

where `q_n` is the normal conductive heat flux and `F_eta,n` is the resistive contribution. Time-dependent and lateral flux terms must also be included when those reductions are not justified. Signed tangential velocities, full magnetic vectors, heat fluxes and these spatial/time terms are not supplied by the one-dimensional worksheet.

The temperature derivative along the sampled line is not enough to recover anisotropic conduction: the magnetic-field direction and transverse temperature gradients can contribute to the normal heat flux. We therefore do not invent a heat flux to make energy close.

The computed gas-entropy proxy `ln(p2/p1) − (5/3) ln(rho2/rho1)` is approximately **−0.174** for the representative endpoints. This must not be used alone to reject a conductive shock. In a suitable steady control volume, the entropy balance includes both advected entropy and `q_n/T`, with non-negative total entropy production. That full balance is not evaluated here.

**Minimum model input for the next verification:** a compact, signed state/flux export across the same simulated patch and adjacent times, specifying the local normal, shock motion, density, pressure, velocity vector, magnetic vector and conductive/resistive fluxes. It should permit a finite-volume conservation and entropy audit, including relevant lateral/time terms. A full multi-gigabyte simulation download is not intrinsically required.

## Provenance and limits

| Category | Meaning in this reproduction |
|---|---|
| `MEASURED` | Underlying IRIS detector spectra, observed by IRIS and analysed by the source authors; not independently recalibrated here. |
| `SOURCE_DERIVED` | Downloaded processed profiles, blend removal, calibrated wavelength/velocity coordinates and source-labelled sampling time. |
| `ASSUMED` | Independent fit family, residual weighting, thermal-width floor, endpoint choices and conditional signed speed transformation. |
| `MODEL_DERIVED` | The authors' simulation cut and synthetic spectra; separately, RMO's refits, characteristic diagnostics and numerical comparisons. |

No two line components are automatically assigned as upstream and downstream. No observational magnetic, density or shock-normal state pair is manufactured. No FAST or other competing MHD family has been exhaustively searched or excluded in this reproduction. The published slow-shock interpretation and its authorship remain explicit.

## Reproducibility and exceptions

`reproduce_e09.py` reads the unmodified Source Data workbook. It saves the extracted numeric data, all fit starts, deblending checks, nine model-cut alternatives, figures and runtime versions. The design records bounds and numerical tolerances before fitting.

The observed S2/S3 published Gaussian curves pass the preset relative reconstruction threshold `1e-5` at approximately machine precision. **Two ancillary P2 synthetic component curves do not pass that threshold**: maximum relative reconstruction errors are approximately **0.068% and 0.415%**. Those source columns contain rounded values. The original failed numerical check is preserved; no threshold was relaxed. This is distinct from file corruption or a hash failure.

The supplied velocity axis is consistent with `c = 300000 km/s` and a reference wavelength of approximately `1354.079956 Å`. Recomputing with `299792.458 km/s` and `1354.08 Å` differs by up to **0.1554 km/s**. Profile fits retain the source velocity axis unchanged; this small convention difference is not an inferred plasma motion. Blend-mask boundaries use the independently stated conversion in the script.

The 17 available frozen physics-core Python files match their saved originals byte for byte. The saved R138 QuickLook matches its known hash. This is not a claim that the entire historical canonical tree was reconstructed in this task.

**Final interpretation:** the reproduction provides a concrete published slow-shock comparison with recoverable spectra and a physically informative conductive-model test. It does not turn a spectral fit into an independently measured shock state, and it does not claim that the present adiabatic RMO core has gained or fully verified a conductive solver.