# R137 · E02: image structure and physical discrimination

**E02 R137 RESULT: UNRESOLVED**

**Physical progress:** the retained evidence supports distinct leading and trailing image patterns with different evolution. R137 separates that result from the stronger claim that both patterns are independent propagating MHD discontinuities. It establishes why their speed ordering cannot select FAST and SLOW, tests the alternative assignments without importing a preferred label, and gives an explicit conditional measurement criterion for distinguishing ordinary compressive FAST and SLOW shocks.

This is an evidence and identifiability result. It is neither a failed MHD solution nor a numerical demonstration of several admissible E02 families. No checked E02 state pair exists in the retained record. All R136 and earlier project files remain unchanged.

## Exact event and scientific credit

E02 is **27 July 2010**, associated with **Chen and Wu (2011)**, DOI [10.1088/2041-8205/732/2/L20](https://doi.org/10.1088/2041-8205/732/2/L20), [arXiv:1103.0871](https://arxiv.org/abs/1103.0871). The frozen RMO66 and R123 entries already identify this source correctly. The earlier conversational description linking this date to Liu is not used: the retained Liu overtaking paper describes 8 April 2010. Its ridges and overtaking behaviour are not E02 inputs.

The saved E02 record had inspected the abstract and contained a graph of published summary speeds, not a recovered image sequence. R137 inspected the full same-event primary paper and all four figures. The original observations, processing, tracks and interpretation remain credited to Chen and Wu and the instrument teams. R137 contributes the falsification audit, separation of inference levels and conditional discriminator derivation. It does not replace the authors' event study or existing MHD methods.

## Compact source evidence

| Source item | Retained evidence |
| --- | --- |
| Data and processing | AIA 193 Å; 12 s cadence; rotation-corrected percentage base differences; reference 08:44:55 UTC. |
| Figure 1 | Later leading/trailing image separation; local loop interaction. |
| Figure 2, slice A | F1: initially about 560 km/s; S1: initially about 190 km/s, then deceleration and near-stationarity; F2: an additional later branch near 310 km/s. |
| Figure 2, slice B | F3: about 470 km/s; faint S2: about 170 km/s. |
| Path convention | Great-circle paths on an adopted solar surface, not measured local 3-D front normals. |
| Figure 3 | PFSS topology and a proposed relation to the stopping position; not a bounded local field vector. |
| Figure 4 | Published degradation to 150 s obscures separation; the authors report a shorter-than-70 s requirement for this example. |

All values in this table are **SOURCE_DERIVED**, not new RMO measurements. They have no supplied numerical covariance or justified independent uncertainty boxes. The source labels F1–F3 and S1–S2 identify tracks; they are not family inputs. Machine-readable records use neutral A1/A2/A3/B1/B2 identifiers with an explicit source-label mapping.

The source receipt records three inconsistencies without silently correcting the paper: the Figure 1 caption date, slightly different stopping time/distance statements, and a track identifier in the slice-B reflection discussion. None is converted into an error bar, new event, or mode-selection argument.

## What the falsification controls establish

The most useful distinction is between **separate image ridges**, **separate physical responses**, and **independent propagating MHD fronts**. These are different claims. A driver and a wave can produce different physical responses within one evolving eruption; two brightness ridges need not be two shocks.

| Alternative or control | R137 assessment | Consequence |
| --- | --- | --- |
| Different sectors or epochs of one track | Same-slice evidence contains simultaneous tracks. | A sectors-only explanation does not account for the published pattern. |
| One rigidly translating front with fixed internal ridge spacing | Incompatible with differential ridge motion and the change of phase. | This restricted hypothesis fails at source-evidence level. A deforming disturbance is a separate, surviving possibility. |
| Exactly two continuously propagating fronts throughout the interval | Not supported. The trailing phase must be treated separately once it becomes nearly stationary. | Do not extrapolate its initial pattern speed or assign a propagating shock to its whole lifetime. |
| Front plus loop/driver restructuring | Remains a physically relevant alternative. | A morphological split is not proof of two independent MHD waves. |
| Cadence or difference-image artefact | A useful source cadence control exists; arbitrary processing artefacts have not all been tested. | No claim of independent raw-data reproduction or complete artefact exclusion. |
| Projection or several ridges of one deforming disturbance | Not excluded by a surface-slice plot. | A local 3-D surface and a plasma association cannot be inferred from the plot alone. |
| Stationary brightness mistaken for motion | The moving and nearly stationary phases must be distinguished. | A stationary pattern can be meaningful without being a propagating front. |

**Structural conclusion:** distinct leading/trailing image patterns are supported at source level. Two independent propagating MHD fronts are **not established**. Conversely, the evidence does **not prove** that there is only one physical front. Therefore `NOT TWO INDEPENDENT FRONTS` would overstate the available exclusion.

The original calibrated AIA arrays, movie and quantitative coordinate tracks were not recovered or reprocessed in R137. This limits an independent test of ridge choice, background/reference choice, registration, projection and time-dependent uncertainty. It is not a claim that such observations do not exist in an archive. No broader solar-data download was undertaken because the retained evidence already lacks the co-spatial plasma-state constraints required for a family decision; image processing alone would not supply them.

## Provenance and linked inputs

| Label | R137 treatment |
| --- | --- |
| MEASURED | No new calibrated image or plasma measurement is produced. A missing local state measurement remains missing, never zero. |
| SOURCE_DERIVED | Published track quantities and descriptions retain their source, phase, slice, processing dependencies and limitations. Published magnetic-model output is marked as model-dependent within this category. |
| ASSUMED | Surface-slice geometry belongs to the source construction. Ridge-to-discontinuity association, upstream rest, radial normal, invariant shape and a shared intervening plasma state are not adopted as observations. The magnetic-jump criterion below explicitly assumes a regular compressive ideal-MHD shock. |
| MODEL_DERIVED | Local normal speed, plasma-frame speed, characteristic speeds, compression and a completed MHD state would require additional inputs; no finite E02 interval is manufactured. The algebraic discriminator is model-derived. |

The two track estimates share image calibration, timing, the reference image and geometric choices. Those dependencies prevent treating every speed, ridge position and phase as an independent adjustable box. There is no supported joint E02 domain for the local upstream/downstream density, pressure, velocity and magnetic field. An unrestricted mathematical parameter range would not be an observational uncertainty domain.

No E05 or E11 speed, density, compression, field, geometry, threshold or checked root is transferred into E02. Similar instrument names or similar patterns do not justify such a transfer.

## Why image ordering cannot select a family

A measured image pattern first needs a physically supported local front normal and front association. If the local normal front speed is `Vn` and the upstream plasma velocity is `u1`, the incoming plasma-frame normal speed has magnitude

`w1 = |Vn - u1 · n|`.

A slope measured along an adopted surface path is not automatically `Vn`; it can also depend on front orientation, projection and the motion of the intersection between the front and the path. Even a known `Vn` does not determine `w1` when upstream plasma motion is unknown.

FAST and SLOW refer to characteristic ordering relative to the local plasma, not to which image ridge is ahead or has the larger speed in km/s. Their characteristic speeds depend on pressure, density, field and field-to-normal geometry. Different locations can have different states. Assuming a common uniform upstream state for both ridges would itself require evidence.

The source's wave/restructuring interpretation is retained as an attributed scientific interpretation. It is not a numerical family label supplied to an RMO solver, and a restructuring pattern is not automatically an `OTHER` discontinuity solution.

## Reversal control and full-physics gate

The logical comparison includes leading FAST/trailing SLOW, the reverse assignment, both FAST, both SLOW, and combinations involving OTHER. None is selected or rejected merely by positional or speed ordering.

**No one of these assignments has a checked E02 state in the retained material.** Accordingly, the machine-readable table says `NOT_RUN_INPUT_GATE` for the full state test and `NOT_DEMONSTRATED_FOR_E02` for admissibility. It does not say that all assignments are physically admissible. `MULTIPLE FAMILIES REMAIN` would require checked family members or a valid family-domain certificate; neither is available here.

The requested conservation, entropy, characteristic, evolutionary, positivity and residual checks require a consistently associated state pair or a sufficiently bounded inverse problem. Running a solver after inventing upstream motion, density, temperature, magnetic field and geometry would test those assumptions, not classify the observed E02 structures. The structural gate therefore stops numerical mode assignment.

The root record is deliberately empty and explicitly scoped: no event-specific equation system was posed. It is **not** a zero-root result, a root-completeness proof, or a numerical conditioning failure. Numerical tolerances and an angular grid are left null rather than fabricated for a calculation that was not run. Any future calculation must predefine its physical domain and numerical guard bands before execution.

## A conditional discriminator with an exact precision criterion

The first observation needed is a **time-resolved local plasma response associated with each ridge**, before and after passage, with registration and geometry bounded independently. This connects an intensity pattern to physical states and can test whether a local compressive jump is present. A Doppler shift along the line of sight alone is not the complete normal plasma velocity.

Once a regular compressive shock has been established, the **sign of the co-spatial magnetic-strength change across it** is a useful FAST/SLOW discriminator. It does not rely on which image pattern moves faster.

Choose a shock frame with positive mass flux `m = rho1*w1 = rho2*w2`. Let `r = rho2/rho1 > 1`, `Bn` be the continuous normal field and `Bt` a signed coplanar tangential component. For nonzero `Bn` and `Bt1`, tangential momentum and induction give

`m*(vt2-vt1) = Bn*(Bt2-Bt1)/mu0`,

`w2*Bt2 - Bn*vt2 = w1*Bt1 - Bn*vt1`,

and therefore

`A = mu0*rho1*w1^2/Bn^2`,

`q = Bt2/Bt1 = r*(A-1)/(A-r)`.

An ordinary fast shock has the necessary ordering `A > r`, giving `q > r > 1`. An ordinary slow shock has `0 < A < 1`, giving `0 < q < 1`. The exact identities

`q-1 = A*(r-1)/(A-r)` and `q-r = r*(r-1)/(A-r)`

make these sign statements explicit. R137 verifies their polynomial numerators using exact integer arithmetic. This is an algebra certificate, not an E02 shock reconstruction; the identities alone do not check total energy, entropy or evolutionary admissibility.

Define `D = |Bt2|^2 - |Bt1|^2`. With normal-field continuity this is also `|B2|^2 - |B1|^2`, so a properly associated total-field-strength measurement can supply the sign. Over the **entire supported joint uncertainty domain**, including state association and any shared geometric errors:

- `D_min > 0` excludes an ordinary compressive SLOW shock.
- `D_max < 0` excludes an ordinary compressive FAST shock.
- An interval touching or spanning zero does not select the ordinary families.

If an observationally justified symmetric bound `Dhat ± epsilon_D` is available, a sufficient sign-resolution condition is **`epsilon_D < |Dhat|`**. This is a quantitative criterion in field-squared units, not an invented E02 precision. E02 supplies neither a matched measured field jump nor checked competing states from which a finite required accuracy in gauss or percent could be calculated.

The criterion is conditional on compression and proper shock association. It does not classify a brightness restructuring, contact or rotational discontinuity; it does not exclude all OTHER families by itself. Parallel, switch-on/off, no-jump and characteristic-degenerate limits require separate treatment. The rational pole `A=r` is not evaluated or assigned a family. The exactly perpendicular case uses its separate limiting relations, not division by `Bn=0`.

**Minimum path to classification:** associate a local plasma transition with each ridge; then establish a joint state domain that resolves the relevant characteristic and conservation tests. A signed field jump can distinguish ordinary FAST/SLOW within that domain. No single image-speed precision can replace the missing plasma and field information.

## Final physical result

**E02 R137 RESULT:** UNRESOLVED.

**Are there observationally distinct leading and trailing fronts?** Distinct image ridges are supported in the primary study. Their independence as two propagating MHD fronts is not established, and the later stationary trailing phase must be distinguished.

**Leading-front admissible families:** No RMO-checked E02 family assignment. The published fast-wave interpretation remains attributed to its authors.

**Trailing-front admissible families:** No RMO-checked E02 family assignment. A slower image track does not establish SLOW; restructuring remains a relevant physical alternative.

**Reversal/alternative control:** Completed as an evidence and identifiability audit. Reverse and same-family assignments are not excluded by speed ordering, but no uncomputed candidate is called admissible.

**What observation actually selects or fails to select the families:** Image morphology and motion distinguish patterns. They do not supply the locally associated plasma/field states needed for characteristic classification. The conditional signed magnetic-jump test is explicit but not measured for these E02 tracks.

**Remaining bottleneck:** An independently associated local plasma-state transition for each ridge, with the normal, flow and field information required to test it as a physical front.

**Classification level:** source-supported structural evidence and an exact conditional discriminator; observational MHD family selection remains unresolved. This stage assigns no observed FAST or SLOW shock.

## Reproducibility and scope

The update contains immutable source identity, neutral track records, provenance, seven falsification controls, seven assignment controls, the null parameter-domain and root records, an exact algebra certificate, code, logs, scientific-lock and file-integrity checks. Source figures were visually inspected; no raw image fit, difference-image experiment, solar-data reconstruction or event-specific MHD survey is claimed.