# RMO-75: input errors and local MHD diagnosis

## Result in one sentence

The two synthetic shock types remain conditionally identifiable for some finite
input bounds, although noisy central values fail the tight exact-conservation check.
These are model demonstrations, not classifications of solar observations.

## What was found

- Fast shock A63 passes the sufficient interval certificate at factors 0.01 and 0.05.
- Slow shock A17 passes at 0.01. At 0.05, entropy and the downstream slow-speed crossing are not certified.
- At 0.10 neither shock passes the initial sufficient test; this is not evidence for a second feasible solution.
- At 0.10 for A63, tightening only pressure half-widths to 1% restores the certificate. This demonstrates a useful additional constraint, not a globally optimal observing strategy.
- Exact contact and rotational-discontinuity diagnoses are retained. Their equality constraints are not certified by a free, independently varied error box.
- Missing field, front speed or pressure produces an explicit missing-measurement result. No missing value is replaced by zero or a coronal mean.

The shared speed and field correlations required by a single front are retained.
Joint covariance inference, geometry uncertainty and dynamical stability are outside
this test. The four inputs are known test fixtures with separate historical scoring
labels, not an external unseen validation set or a measured success-rate sample.

## What the percentages mean

For density and thermal pressure, half-width = f times the absolute central value.
For each velocity/field component and front speed, half-width = f times max(1,
absolute central value), in the declared normalized units. Zero vector components
therefore have nonzero uncertainty. Factors 0.01, 0.05 and 0.10 are illustrative
bounded input designs; they are **not instrument errors, standard deviations,
confidence levels or universal accuracy requirements**. Gamma and normal geometry
are fixed. Inspect every half-width in the exported request.

## Exact equalities versus measured data

Rankine-Hugoniot conservation is tested at scaled tolerance 1e-10 for an exact
supplied pair. Measurements generally have much larger errors. Failure of that
exact-pair check does not itself exclude a shock interpretation.

In two controls the downstream-pressure centre was shifted upward by 0.25%, with
the same 1% box design. The original exact point lies within the box. A bounded
least-squares search using conservation alone found a numerical witness; no type
label or saved solution was passed to the search. Every adjustment is recorded.
Independent 70-digit lab-frame arithmetic checked each witness. The witness is
**not** a unique reconstruction, maximum-likelihood estimate or posterior sample.

| Model | Noisy-centre scaled RH | Witness independent scaled RH | Certified local type |
|---|---:|---:|---|
| A17 | 0.00191 | 9.8e-13 | slow_shock |
| A63 | 0.00147 | 1.82e-12 | fast_shock |

## Full model outcomes

| Model | Factor f | Outcome | Type |
|---|---:|---|---|
| A17 | 0 | EXACT_LOCAL_CLASS | slow_shock |
| A17 | 0.01 | CONDITIONAL_ROBUST_CLASS | slow_shock |
| A17 | 0.05 | NOT_CERTIFIED | No certified type |
| A17 | 0.1 | NOT_CERTIFIED | No certified type |
| A42 | 0 | EXACT_LOCAL_CLASS | contact |
| A42 | 0.01 | NOT_CERTIFIED | No certified type |
| A42 | 0.05 | NOT_CERTIFIED | No certified type |
| A42 | 0.1 | NOT_CERTIFIED | No certified type |
| A63 | 0 | EXACT_LOCAL_CLASS | fast_shock |
| A63 | 0.01 | CONDITIONAL_ROBUST_CLASS | fast_shock |
| A63 | 0.05 | CONDITIONAL_ROBUST_CLASS | fast_shock |
| A63 | 0.1 | NOT_CERTIFIED | No certified type |
| A88 | 0 | EXACT_LOCAL_CLASS | rotational_discontinuity |
| A88 | 0.01 | NOT_CERTIFIED | No certified type |
| A88 | 0.05 | NOT_CERTIFIED | No certified type |
| A88 | 0.1 | NOT_CERTIFIED | No certified type |

Certification combines a checked numerical anchor with outward-rounded interval
bounds for compression, entropy increase, field trend and characteristic ordering.
It is conditional on a **single conservation-compatible planar ideal-MHD
discontinuity** within the supplied box. The interval tests are sufficient, not
necessary: failing a bound is NOT CERTIFIED, not proof of ambiguity between two
constructed physical solutions. No complete Riemann-fan uniqueness is inferred.

## Existing EUV example: what geometry tells us

T. Podladchikova et al. (2019), ApJ 877, 68, Tables 4-5,
[source DOI](https://doi.org/10.3847/1538-4357/ab1b3a). Event: 13 February 2009.
The same selected front patch is used, as identified in the source record by a study author.

| Point | Apparent pattern speed (km/s) | Corrected surface pattern speed (km/s) | Reduction relative to apparent |
|---|---:|---:|---:|
| 1 | 260.83 | 207.51 | 20.44% |
| 2 | 258.62 | 208.38 | 19.43% |
| 3 | 259.05 | 205.12 | 20.82% |

Thus the already published geometry changes the inferred surface pattern speed by
about 19-21%. This is a reproducibility/application check of published values, **not
a new discovery or shock-type determination**. Local normal geometry, shock-frame
plasma velocities, co-spatial thermomagnetic states and their joint errors are absent
from these extracted tables. Pattern speed and crest-height change cannot simply be
inserted as plasma normal velocity and shock-normal speed. No assumed beta or
unreported field was substituted to manufacture a solar classification.

## Verification and interface

The study passed 74 assertions, including anonymous-input scoring,
missing/invalid input controls, fixed shared Galilean offsets and normal reversal.
Independent 80-digit arithmetic checked characteristic enclosures at
384 deterministic box points. This checks the
implementation; it is not exhaustive validation or a probabilistic accuracy claim.

QuickLook offers the saved study offline, editable local-state inputs and exports.
The added Python diagnosis action uses the existing protected local service and
preserves the exact request, result, adjustments and source hashes. It is separate
from a full Riemann solve and from the preserved Brio-Wu viewer. Native Chrome,
accessibility and public hosting acceptance remain unverified.