# R136 E11: outer-front upstream-flow closure

A checked conditional FAST interpretation has a clear physical basis, and the observation required to make it unique among the regular families is quantitatively specified by frozen R135. R136 establishes how the retained evidence relates to that test: the published small-wind and radio-nose statements are model assumptions, while the imaging and radio spectra provide complementary pattern and spectral constraints.

The practical result is a precise two-part observational target: a bounded local upstream normal flow below 277.5 km/s and an independent association of the radio compression with the same EUV patch. These conditions remain to be established; the physical solutions and the quantitative test are preserved.

**E11 R136 RESULT: UPSTREAM FLOW NOT SUFFICIENTLY CONSTRAINED — FAMILY SELECTION UNRESOLVED.**

The retained E11 observations do not supply an independent bounded upstream normal-flow interval for the selected outer front. They also do not establish that the radio compression belongs to that same local EUV patch. Consequently the two required observational conditions are not met, and the R135 conditional SLOW family is not excluded. The checked FAST family remains intact. This is an observational limitation, not a new numerical failure or a rejection of the published shock interpretation.

## Target and frozen comparison

The event is 13 June 2010. The selected outer AIA patch is near PA 116 degrees, X = 1137.700 arcsec, Y = -554.893 arcsec in the retained R109 convention. Its fitted projected normal is PA 120.277 degrees. The primary interval is 05:38:32.06–05:40:08.06 UTC. The radio frequencies are reported near 05:40 UTC. The interval mean and the endpoint patch must not be presented as simultaneous, spatially resolved plasma-state measurements.

R135 is frozen. At its fixed G0 effective normal speed Vn = 705.535341 km/s, the full retained radio/temperature domain has the exact conditional upper-flow boundary 277.513560 km/s. The requested **u1n < 277.5 km/s**, including observational uncertainty, is a slightly conservative rounded sufficient requirement. The central tuple has a different threshold, 396.920575 km/s; it is not substituted for the whole-domain requirement.

The domain retains the linked radio frequencies fL = 127–137 MHz and fU = 150–180 MHz, with r = (fU/fL)^2 and T = 1.4–2.2 MK under the existing pressure/composition closure. It is a declared source-scenario enclosure, not a measured joint confidence region. No bounds, roots, tolerances or R135 certificates are changed.

## What the retained sources actually constrain

| Evidence | Provenance and credit | Consequence for this test |
| --- | --- | --- |
| Saved AIA positions, projected tangent and motion | MEASURED image-derived diagnostics, R106/R107 | Constrain a brightness ridge and pattern motion. They do not identify or measure the upstream material velocity. |
| Radio lanes and timing near 05:40 | SOURCE_DERIVED, Ma et al. and the retained radio analyses | Supply frequencies and event timing. Compression and density share the harmonic and state-pair interpretation. |
| Radio height and speed | MODEL_DERIVED in the published density-model reductions | Frequency-to-height conversion traces the emitting front through a chosen density profile. It is not the upstream flow. |
| Negligible solar wind in the standoff analysis | ASSUMED, Gopalswamy et al. | A premise in converting image speed and Mach number to Alfven speed; no local measured velocity interval is provided. |
| RMO FLOW0 and earlier flow scans | ASSUMED model scenarios | Zero or scanned flow was assigned. Successful conservation checks do not turn it into a measurement. |
| Regional DEM and emission-history fits | SOURCE_DERIVED, Kozarev et al. and Lee et al., with explicit model dependencies | Constrain thermal/emission interpretations. They do not recover the needed pre-front velocity component. |
| PFSS overlay | MODEL_DERIVED published geometry context | Motivates a possible quasi-perpendicular configuration, without a numerical local velocity bound or measured field-to-normal angle. |

The full provenance table is R136_PROVENANCE.csv. The labels distinguish the nature of a quantity from who contributed it: a published model output remains a model output and is not an RMO measurement.

### The decisive upstream-flow check

Gopalswamy et al. explicitly use negligible solar-wind speed in the coronal region when setting VA = Vsh/M (Section 2.3). The retained text supplies no same-patch velocity estimate, detection limit or uncertainty for that premise. The resulting magnetic field and Alfven speed cannot be used as independent evidence to recover the very flow assumption used to derive them.

Ma et al. use AIA ridge motion and radio-frequency drift converted through a coronal density model (Section 3.2 and Figure 7). Both concern front propagation. Subtracting one of those front-speed estimates from another would mix diagnostic, geometry and density-model differences; it would not measure upstream plasma motion.

Kozarev et al. report that the upstream DEM comparison region R4 did not give a statistically significant result. Even a successful DEM would be a thermal/emission diagnostic, not a velocity measurement. Lee et al. fit post-passage AIA emission histories in a fixed box under ionization and background assumptions. Their fitted density, temperature, timescale and line-of-sight depth do not provide an independent upstream vector flow.

No retained E11 result independently identifies a pre-front material tracer whose displacement can be assigned to the plasma along this normal. A stationary brightness pattern need not imply stationary plasma. “No reported flow” therefore remains missing information; it is not FLOW0 and it supplies no finite error bar.

This is a finite audit of the saved material, not a claim that every possible solar archive has been searched or that such a measurement is impossible in principle.

## Projection and uncertainty

In the frozen G0 geometry, the local axes are X toward solar west, Y toward solar north and Z toward the observer. The normal is

    n = (0.8636020941, -0.5041740007, 0).
    u1n = u1 · n = 0.8636020941 uX - 0.5041740007 uY.

These coefficients are copied from R109; they are not a new geometric measurement. A line-of-sight Doppler velocity constrains uZ and cannot alone bound this G0 normal component. A justified material-motion measurement in the image plane, or sufficiently constrained vector-flow geometry, would be required.

No velocity vector or bounded set of compatible vectors is established in the retained evidence. There is therefore no observational interval to project and no legitimate finite uncertainty to propagate. The machine-readable interval is **null**, meaning unavailable, rather than zero, infinity, a statistical distribution or a solver error.

The earlier 113–126 degree normal-estimator spread is not a complete observational bound. It must not be combined with an assumed velocity to manufacture a flow confidence interval. If the normal or Vn is independently revised later, the fixed-G0 277.5 km/s number cannot be applied unchanged.

## Radio/EUV association: three distinct levels

| Association level | Strongest retained support | Status |
| --- | --- | --- |
| Same eruption | Temporal coincidence, morphology and the published absence of another simultaneous eruption | SUPPORTED |
| Same front surface | Published EUV/radio interpretation; agreement of radio-derived heights and EUV front evolution | SOURCE INTERPRETATION, with density-model dependence |
| Same local patch | No localized radio position and uncertainty registered to the selected PA116 EUV patch | NOT ESTABLISHED |

Ma et al. use San Vito dynamic spectra. Kozarev et al. use Learmonth spectra and a Newkirk density-to-height relation. The retained Gopalswamy analysis uses HiRAS spectra. These records contain valuable spectral constraints, but the relevant analyses do not provide the independent radio image needed for a local match.

The Gopalswamy discussion explicitly states the absence of radio imaging and identifies emission near the nose as an assumption. Its approximate 4% height difference for a flank alternative addresses sensitivity of the inferred height under the adopted morphology. It is not a positional confidence region for the radio source, does not identify PA116 and does not bound upstream flow. A common height does not determine a common local surface patch.

Likewise, model-dependent agreement between the radio and EUV heights cannot validate the same density profile, same local geometry and same source assignment independently. The lane-to-upstream/downstream interpretation and harmonic identification remain separate dependencies even if an eventual sky-position match becomes available.

## Physical conclusion and closure criterion

Under the frozen R135 construction,

    w1 = Vn - u1n
    wcrit = sqrt[5 (p1/rho1) r / (4-r)].

These are the inherited equations, not a new calculation. For the fixed G0 speed and full retained domain, a supported upper u1n below 277.5 km/s would satisfy the requested sufficient regular-SLOW exclusion test. **That bound has not been measured in the retained material.**

Observational closure requires both:

1. An independent bounded pre-front plasma velocity along the same local normal, with tracer identity, timing, calibration and geometry uncertainties included. Its full supported upper bound must be below 277.5 km/s when the frozen Vn and pressure/source domain are retained.
2. Independent localization of the compression-bearing radio source to that same outer-front patch, with sufficient temporal and spatial uncertainty control and a justified lane/state assignment. Spectral radio imaging is one possible route; an equivalently strong independent localization could serve the same purpose.

If Vn or the source tuple is uncertain beyond the frozen construction, preserve their joint dependencies and test the full supported set using

    inf_supported[(Vn - u1n) - wcrit] > 0.

A central-value comparison is insufficient. Failure to establish this sufficient inequality does not itself prove SLOW or reject FAST. Exact degeneracies and the limits of ordinary-shock classification remain as documented in R135.

The present closure test has **two independent missing requirements**. Measuring only flow would leave local radio association unresolved; localizing only the radio source would leave flow unresolved. A global nose, quiet-corona prior, catalogue family label or assumed small wind cannot close either gap by itself.

## Final required summary

**E11 R136 RESULT:** UPSTREAM FLOW NOT SUFFICIENTLY CONSTRAINED — FAMILY SELECTION UNRESOLVED.

**Supported upstream-normal-flow interval:** none independently bounded by the retained E11 observations; recorded as null.

**Relation to the 277.5 km/s threshold:** not observationally testable with the retained inputs. No upper bound below the threshold is established.

**Radio/EUV association level:** same eruption supported; same surface is a published, model-supported interpretation; same local patch is not established.

**Admissible families:** the frozen R135 conditional FAST and SLOW families remain. No observed outer-front family is selected.

**Why SLOW is excluded or survives:** it is not observationally excluded. Neither the flow bound nor the local radio assignment needed to apply the joint exclusion is independently established.

**Remaining bottleneck:** an independently associated local upstream/jump measurement: normal plasma flow plus localization of the radio compression to the same outer patch.

## Evidence and reproducibility

The audit uses retained Ma (2011) Sections 2 and 3.2–3.3; Kozarev (2011) Sections 2.2, 3.1–3.2 and 3.4; Gopalswamy (2012) Section 2.3 and the discussion of radio-source location; and the E11 portion of Lee (2019) Section 3.3. R108/R109 preserve the diagnostic/state assignments; R119 and R135 preserve the conditional exclusion requirements. R94 is consulted only to verify that its flow values were scenario parameters, not measurements.

R136_FROZEN_INPUTS.json records each exact saved file identity. R136_EVIDENCE.json provides section locators, short text anchors and line numbers for the retained extractions. Original PDFs remain inherited unchanged. RMO adds this independence and association audit while preserving the original authors' scientific credit.

No new solar data, literature, MHD roots, image fits, spectral fits or numerical sensitivity map are produced. The inner front, E05 and other events are not reopened. File-integrity verification is separate from this observational conclusion. R134 and R135 remain frozen.

**MHD admissibility determines what observational precision is required; observational analysis determines whether that precision is achievable.**