Velocity-Field Disagreement (VFD)

• Velocity-Field Disagreement (VFD) is the mismatch between an observed or inferred velocity field and a reference structure, revealing hidden physical or model inconsistencies.
• It applies across fields such as sunspot penumbrae, robotic action models, spectroscopic PPV analysis, and Galactic filaments, each adapting the metric to specific physical constraints.
• VFD informs both scientific inquiry and practical methodologies, enabling uncertainty quantification, failure detection, and refined physical interpretations in complex systems.

Searching arXiv for papers that use or contextualize “Velocity-Field Disagreement” across the domains represented in the provided data. Velocity-Field Disagreement (VFD) is a term used in multiple research contexts to denote a mismatch between an observed or inferred velocity field and another physically relevant structure, constraint, or reference. In sunspot penumbrae, it denotes plasma flows whose direction is not aligned with the local magnetic field vector (Balthasar et al., 17 Nov 2025). In flow-based vision-language-action models, it denotes disagreement among ensemble velocity fields and functions as an estimator of epistemic uncertainty (Römer et al., 16 Jun 2026). In spectroscopic studies of interstellar turbulence, the term is used for the mismatch between structures seen in spectroscopic cubes and the true underlying turbulent velocity field, a mismatch addressed by the Velocity Decomposition Algorithm (VDA) (Yuen et al., 2020). In magnetic-field inference from molecular-line data, closely related usage refers to misalignment between VGT-inferred magnetic-field directions and a reference direction such as the Galactic Plane or dust polarization, with large disagreement indicating localized dynamical disruption (Zhao et al., 2023). The term therefore does not identify a single invariant quantity across disciplines; rather, it designates a family of discrepancy concepts centered on the interpretability, consistency, or uncertainty of velocity-derived structure.

1. Terminological scope and domain-specific definitions

In the context of sunspot penumbrae, “Velocity-Field Disagreement” denotes the occurrence of plasma flows whose direction is not aligned with the local magnetic field vector (Balthasar et al., 17 Nov 2025). The defining case is one in which high line-of-sight velocities of opposite sign are observed in adjacent penumbral filaments while the magnetic field vector remains essentially unchanged and almost horizontal. The details specify that if $\mathbf{B}$ is the local magnetic field vector and $\mathbf{v}$ the plasma velocity vector, VFD requires $|\mathbf{v}|$ large, on the order of $\sim1$–$2\ \mathrm{km\ s^{-1}}$, and $$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$ locally, while $\gamma\simeq90^\circ$ and $B_{\mathrm{total}}$ varies only weakly between regions of opposing $\mathbf{v}$ (Balthasar et al., 17 Nov 2025).

In flow-matching models for robotic action generation, VFD is defined over an ensemble of independently trained velocity fields $\{v_{\theta_i}\}_{i=1}^M$ and measures their pairwise disagreement (Römer et al., 16 Jun 2026). The paper writes a conditional flow-matching model as a time-indexed velocity field $\mathbf{v}$0 and uses disagreement among ensemble members as an uncertainty signal. In that setting, VFD is not a physical misalignment but an ensemble-dispersion quantity that is mathematically related to inter-model KL divergence (Römer et al., 16 Jun 2026).

In spectroscopic PPV analysis, the summarized formulation states that VFD arises when high-contrast filaments seen in narrow HI slices are misinterpreted as density features unconnected to true velocity eddies (Yuen et al., 2020). The proposed remedy is the Velocity Decomposition Algorithm, which constructs a component $\mathbf{v}$1 that faithfully represents velocity crowding, or “caustics,” and separates it from the density-dominated contribution $\mathbf{v}$2 (Yuen et al., 2020). In this usage, VFD names an interpretive mismatch between observable structures in channel maps and the actual turbulent velocity field.

In studies of giant Galactic filaments using the Velocity Gradient Technique, the supplied details state that where the disagreement between the VGT-inferred field direction $\mathbf{v}$3 and a reference direction is large, one says the “velocity-field disagreement” is significant (Zhao et al., 2023). The relevant discrepancy is quantified through offset angles and the Alignment Measure, and it is associated with “magnetization gaps,” localized zones of strong magnetic-field discontinuity (Zhao et al., 2023).

A plausible implication is that VFD functions as an umbrella term for disagreement between a velocity-derived representation and a physical reference: magnetic geometry, density structure, or model consensus.

2. Sunspot penumbrae: disagreement between flow direction and magnetic geometry

The sunspot application studies an active region with two mature sunspots, where one of them formed several days later than the main one, and where flux emergence is still ongoing between the two spots (Balthasar et al., 17 Nov 2025). Observations of NOAA 12146 on 2014-08-24 were obtained with the GREGOR Fabry–Pérot Interferometer in spectroscopic mode, the Blue Imaging Channel of the GREGOR solar telescope, and SDO/HMI context data (Balthasar et al., 17 Nov 2025). The GFPI observations used the Fe I 709.0 nm line, with 24 wavelength points, $\mathbf{v}$4 steps, eight accumulations per step, 31 s cadence, and pixel scale $\mathbf{v}$5 (Balthasar et al., 17 Nov 2025). HMI vector magnetograms and Dopplergrams in Fe I 617.3 nm provided $\mathbf{v}$6, $\mathbf{v}$7, inclination $\mathbf{v}$8, and line-of-sight velocity at mid-photospheric heights (Balthasar et al., 17 Nov 2025).

The line-of-sight velocity was derived from the line shift $\mathbf{v}$9 determined by either a fourth-order polynomial fit to the line core or a Fourier-transform method. The supplied expression is

$|\mathbf{v}|$0

with $|\mathbf{v}|$1 and $|\mathbf{v}|$2 the speed of light (Balthasar et al., 17 Nov 2025). The magnetic field was derived through the VFISV Milne–Eddington inversion, which retrieves $|\mathbf{v}|$3, $|\mathbf{v}|$4, and $|\mathbf{v}|$5, with derived quantities

$|\mathbf{v}|$6

(Balthasar et al., 17 Nov 2025).

The observed VFD signature consists of blueshifts up to $|\mathbf{v}|$7 intruding into the limb-side penumbra of the new spot and adjacent redshifts up to $|\mathbf{v}|$8 following the regular Evershed pattern (Balthasar et al., 17 Nov 2025). The two high-speed streams are separated by only $|\mathbf{v}|$9–$\sim1$0 and cross both the outer penumbral boundary and the photospheric polarity-inversion line (Balthasar et al., 17 Nov 2025). In both the blue and red flow regions, $\sim1$1–$\sim1$2, $\sim1$3–$\sim1$4, and $\sim1$5 within a few percent, with no sharp change at the velocity sign reversal (Balthasar et al., 17 Nov 2025).

The study states that the case satisfies the VFD criteria because high-velocity streams of $\sim1$6 occur where the magnetic field remains horizontal and shows no reversal or discontinuity at the velocity boundary, while Local Correlation Tracking on BIC images yields horizontal proper motions $\sim1$7 and $\sim1$8 along the high-$\sim1$9 trajectories (Balthasar et al., 17 Nov 2025). The Doppler shifts are therefore interpreted as genuine laminar flows along nearly horizontal field lines of opposite direction rather than image-plane advection (Balthasar et al., 17 Nov 2025).

The physical interpretation given is a flux-emergence scenario in which flux tubes rooted in the newly emerged region channel inward blueshifted flows while adjacent penumbral flux tubes of the pre-existing spot carry the normal outward redshifted Evershed flow (Balthasar et al., 17 Nov 2025). The two flux systems run nearly parallel, but their flow directions are set by the anchoring footpoints rather than by local field polarity (Balthasar et al., 17 Nov 2025). The implications listed in the details are that penumbral dynamics must accommodate multiple co-spatial flux tubes with independent flow directions, that overturning convection alone may not explain sustained counter-flows, and that siphon or pressure-driven flows along emerging loops likely contribute (Balthasar et al., 17 Nov 2025).

A common misconception in this context would be to identify nearly horizontal magnetic fields with a unique flow direction. The reported observations instead show that opposite Doppler streams can coexist under nearly unchanged field inclination and strength (Balthasar et al., 17 Nov 2025).

3. Flow-matching models: VFD as an epistemic uncertainty estimator

In flow-based vision-language-action models, the core object is a conditional flow-matching model written as a time-indexed velocity field

$2\ \mathrm{km\ s^{-1}}$0

that transports a base distribution $2\ \mathrm{km\ s^{-1}}$1 to the data distribution $2\ \mathrm{km\ s^{-1}}$2 via

$2\ \mathrm{km\ s^{-1}}$3

(Römer et al., 16 Jun 2026). The paper specifies a Gaussian optimal-transport conditional path

$2\ \mathrm{km\ s^{-1}}$4

with exact velocity $2\ \mathrm{km\ s^{-1}}$5, and the standard flow-matching loss is given explicitly in the details (Römer et al., 16 Jun 2026).

Given an ensemble of $2\ \mathrm{km\ s^{-1}}$6 independently trained flow models $2\ \mathrm{km\ s^{-1}}$7, a simple VFD score at a single state is

$2\ \mathrm{km\ s^{-1}}$8

(Römer et al., 16 Jun 2026). The details further state that Theorem 3.1 shows the KL divergence between two models is exactly

$2\ \mathrm{km\ s^{-1}}$9

(Römer et al., 16 Jun 2026). This establishes a direct relation between velocity-field disagreement and inter-model distributional divergence.

The practical uncertainty score is then the discretized quantity

$$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$0

where trajectories satisfy

$$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$1

(Römer et al., 16 Jun 2026). The implementation described in the details starts from one pre-trained base VLA $$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$2, fine-tunes it $$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$3 times on random shuffles of the same pre-training data $$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$4, and computes VFD by integrating each model’s flow while accumulating pairwise squared differences (Römer et al., 16 Jun 2026). The supplied optimizations are that discrete ODE integration with $$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$5 is enough, that $$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$6 often suffices in practice, and that all flows and trajectories run in parallel on GPU (Römer et al., 16 Jun 2026).

The evaluation reported on LIBERO uses Spearman’s rank correlation, Pearson correlation, and reliability diagrams. Table 1 in the details lists negative Spearman and Pearson correlations between uncertainty and downstream success for several baselines, with VFD reported as $$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$7, exceeding Action-L2 at $$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$8, ACE at $$(\mathbf{v}\cdot\mathbf{B})/(|\mathbf{v}||\mathbf{B}|)\neq \pm1$$9, DECU at $\gamma\simeq90^\circ$0, GU at $\gamma\simeq90^\circ$1, Entropy at $\gamma\simeq90^\circ$2, and Perplexity at $\gamma\simeq90^\circ$3 (Römer et al., 16 Jun 2026). The paper states that VFD yields better-calibrated uncertainty estimates predictive of downstream performance and remains well-calibrated even when only the language prompt is varied (Römer et al., 16 Jun 2026).

For deployment-time failure detection, the procedure is to compute $\gamma\simeq90^\circ$4 at each action-generation timestep, calibrate a one-sided threshold $\gamma\simeq90^\circ$5 per task from 10 successful runs via conformal prediction, and declare failure as soon as $\gamma\simeq90^\circ$6 (Römer et al., 16 Jun 2026). The reported metrics are accuracy $\gamma\simeq90^\circ$7, true-positive rate $\gamma\simeq90^\circ$8, normalized detection time $\gamma\simeq90^\circ$9, and timestep-wise accuracy $B_{\mathrm{total}}$0 (Römer et al., 16 Jun 2026). The same uncertainty signal drives SAVE, an uncertainty-guided active multitask fine-tuning framework. SAVE computes per-task uncertainties, forms the sampling distribution

$B_{\mathrm{total}}$1

queries expert demonstrations from the most uncertain states, and fine-tunes each ensemble member on a mixture of pre-training and newly collected data (Römer et al., 16 Jun 2026). The quantitative gains reported are that to reach $B_{\mathrm{total}}$2 success, Random needs $B_{\mathrm{total}}$3 rounds versus $B_{\mathrm{total}}$4 for SAVE/VFD; to reach $B_{\mathrm{total}}$5, Random needs $B_{\mathrm{total}}$6 versus $B_{\mathrm{total}}$7 for SAVE/VFD; final success is $B_{\mathrm{total}}$8 for Random versus $B_{\mathrm{total}}$9 for SAVE/VFD; and compared to the second-best uncertainty-driven method, VFD saves at least $\mathbf{v}$0 of expert demonstrations (Römer et al., 16 Jun 2026).

This usage makes VFD a model-selection and safety signal rather than a direct observable. A plausible implication is that the term has broadened from physical mismatch to a statistically grounded disagreement functional over learned vector fields.

4. Spectroscopic PPV analysis: resolving disagreement between channel structure and turbulent velocity

The VDA-based usage begins from the PPV description of an emitting turbulent volume characterized by density $\mathbf{v}$1 and LOS velocity $\mathbf{v}$2 (Yuen et al., 2020). The observed density in a velocity channel centered at $\mathbf{v}$3 of width $\mathbf{v}$4 is written as

$\mathbf{v}$5

with $\mathbf{v}$6 the thermal variance (Yuen et al., 2020). The channel-map correlation $\mathbf{v}$7 depends on the LOS velocity structure function $\mathbf{v}$8 and the density correlation $\mathbf{v}$9 (Yuen et al., 2020). Under a power-law density correlation, the channel statistics split into a pure “velocity caustics” term $\{v_{\theta_i}\}_{i=1}^M$0 and a density-dominated term $\{v_{\theta_i}\}_{i=1}^M$1 (Yuen et al., 2020). Thin and thick channels are distinguished by

$\{v_{\theta_i}\}_{i=1}^M$2

(Yuen et al., 2020).

The VDA decomposition is formulated so that each channel slice satisfies

$\{v_{\theta_i}\}_{i=1}^M$3

(Yuen et al., 2020). In the summarized derivation, one forms the 2D intensity map $\{v_{\theta_i}\}_{i=1}^M$4, assumes that in the thick limit $\{v_{\theta_i}\}_{i=1}^M$5, and writes

$\{v_{\theta_i}\}_{i=1}^M$6

with $\{v_{\theta_i}\}_{i=1}^M$7 (Yuen et al., 2020). The details emphasize the approximate orthogonality condition $\{v_{\theta_i}\}_{i=1}^M$8 in the subsonic case and note that it breaks down at high $\{v_{\theta_i}\}_{i=1}^M$9 but is correctable via a supersonic variant (Yuen et al., 2020).

In this framework, VFD arises when filamentary structures in narrow HI slices are interpreted as density structures although they are actually produced by velocity crowding (Yuen et al., 2020). VDA is designed to restore the one-to-one link between structures seen in spectroscopic slices and the true turbulent velocity field by separating density and caustic contributions (Yuen et al., 2020). The numerical tests summarized in the details report that in an isothermal subsonic cube, the correlation between the recovered $\mathbf{v}$00 and the true caustics $\mathbf{v}$01 is $\mathbf{v}$02 in all slices, with power-spectrum slopes matching to within $\mathbf{v}$03; in an isothermal supersonic cube, wing slices give $\mathbf{v}$04–$\mathbf{v}$05; and in multiphase HI, VDA recovers velocity caustics with $\mathbf{v}$06 even when CNM is supersonic and heavily thermally broadened (Yuen et al., 2020).

Applications to GALFA-DR2 data are summarized for a high-velocity cloud and for high-latitude diffuse HI. In HVC 186+19−114, $\mathbf{v}$07 versus $\mathbf{v}$08 shows a characteristic double peak away from line center, while $\mathbf{v}$09 peaks at the center; in the central channel, $\mathbf{v}$10 at $\mathbf{v}$11 for CNM and $\mathbf{v}$12 for WNM (Yuen et al., 2020). In high-latitude diffuse HI, one region is described as “sub-thermal,” where density and velocity are comparable in the center and the wings are velocity-dominant, while another is “thermally broad,” where VCA on $\mathbf{v}$13 recovers a 3D slope $\mathbf{v}$14 (Yuen et al., 2020).

A closely related controversy concerns the orthogonality of the VDA components. The paper “Correlation of velocity and density contributions to spectroscopic channel maps: Reality check on Kalberla et.al (2022)” states that a criticism of VDA based on negative correlation between $\mathbf{v}$15 and $\mathbf{v}$16 is invalid because the quantities are naturally orthogonal by construction and the correct application of VDA to any data must provide zero correlation (Yuen et al., 2022). It further states that the likely mistake was an incorrect VDA expression, and that 14 out of 15 figures in the criticized work are invalid (Yuen et al., 2022). This controversy is not about whether disagreement exists in the interpretive sense, but about whether the decomposition used to resolve it preserves the defining orthogonality relation.

5. Velocity Gradient Technique: disagreement as magnetic misalignment and “magnetization gaps”

The VGT application is rooted in the theory of strong magnetized turbulence, according to which eddies become elongated along the local magnetic field, so the gradient of intensity in thin velocity channels tends to be perpendicular to $\mathbf{v}$17 (Zhao et al., 2023). For a PPV cube $\mathbf{v}$18, finite-difference gradients are computed, the raw gradient orientation is

$\mathbf{v}$19

dominant sub-block gradient directions $\mathbf{v}$20 are extracted, and pseudo-Stokes parameters

$\mathbf{v}$21

are formed, yielding

$\mathbf{v}$22

(Zhao et al., 2023).

Agreement or disagreement between the VGT-inferred $\mathbf{v}$23 and a reference direction $\mathbf{v}$24 is quantified using the offset angle

$\mathbf{v}$25

and the Alignment Measure

$\mathbf{v}$26

(Zhao et al., 2023). The details state that $\mathbf{v}$27 implies perfect parallelism, $\mathbf{v}$28 perfect perpendicularity, and $\mathbf{v}$29 random or mixed. When comparing $\mathbf{v}$30 to the Galactic Plane direction, the fraction of area with $\mathbf{v}$31 is

$\mathbf{v}$32

(Zhao et al., 2023). Where VFD is large, such as $\mathbf{v}$33 or large $\mathbf{v}$34, the disagreement is called significant (Zhao et al., 2023).

The six giant filaments studied divide into two groups. G29, G47, and G51 have $\mathbf{v}$35, $\mathbf{v}$36, and $\mathbf{v}$37 and show no magnetic-field gaps; G24, G339, and G349 have $\mathbf{v}$38, $\mathbf{v}$39, and $\mathbf{v}$40 and do exhibit gaps (Zhao et al., 2023). In G29, G47, and G51, offset-angle histograms are sharply peaked at $\mathbf{v}$41, giving $\mathbf{v}$42 and $\mathbf{v}$43, with continuous, disk-parallel fields (Zhao et al., 2023). In G24, G339, and G349, “magnetization gaps” are narrow zones, a few beam widths and $\mathbf{v}$44, where $\mathbf{v}$45 abruptly jumps by tens of degrees, often coincident with local density dips or velocity-component crossings in position–velocity diagrams (Zhao et al., 2023).

The mechanisms proposed in the details are Galactic shear, turbulent stability, filament reassembly, gravitational collapse, and stellar feedback (Zhao et al., 2023). The fact that most filaments and their magnetic fields lie parallel to the disk midplane over lengths $\mathbf{v}$46–$\mathbf{v}$47 is attributed to differential rotation stretching both gas and field into coherent strands (Zhao et al., 2023). At the VGT resolution, $\mathbf{v}$48–$\mathbf{v}$49, the turbulent crossing time $\mathbf{v}$50–$\mathbf{v}$51 is much shorter than the shear time $\mathbf{v}$52, yet the field remains ordered, implying that small-scale turbulence alone cannot randomize $\mathbf{v}$53 (Zhao et al., 2023). Local disagreement is therefore interpreted as tracing reassembly, collapse, or feedback rather than ordinary turbulent disorder (Zhao et al., 2023).

This usage differs from the sunspot case because the disagreement is not between $\mathbf{v}$54 and $\mathbf{v}$55 directly, but between a magnetic field inferred from velocity gradients and an external reference geometry.

6. Comparative framework and conceptual distinctions

The following table organizes the principal usages represented in the supplied sources.

Context	What disagrees	Representative quantity
Sunspot penumbra	Plasma flow direction and local magnetic field vector	$\mathbf{v}$56 locally (Balthasar et al., 17 Nov 2025)
Flow-based VLAs	Ensemble velocity fields from independently trained models	$\mathbf{v}$57 and $\mathbf{v}$58 (Römer et al., 16 Jun 2026)
PPV turbulence analysis	Structures in spectroscopic slices and the true turbulent velocity field	$\mathbf{v}$59, $\mathbf{v}$60, and $\mathbf{v}$61 in VDA (Yuen et al., 2020)
Giant filaments with VGT	VGT-inferred field direction and reference direction	$\mathbf{v}$62, $\mathbf{v}$63, and $\mathbf{v}$64 (Zhao et al., 2023)

These usages share a common logic: a velocity-derived quantity is compared against a target structure that is treated as physically meaningful. What changes from field to field is the target of comparison. In sunspots, the target is the local magnetic field measured from spectropolarimetry (Balthasar et al., 17 Nov 2025). In robotic action models, it is ensemble consensus and the induced trajectory distribution (Römer et al., 16 Jun 2026). In PPV turbulence, it is the true underlying turbulent velocity field rather than density-caused morphology in channel maps (Yuen et al., 2020). In VGT analyses, it is a reference magnetic orientation, such as the Galactic Plane or Planck polarization (Zhao et al., 2023).

A potential source of confusion is to assume that VFD always refers to a scalar diagnostic with a standard formula. The supplied literature does not support such a uniform definition. In one case the disagreement is geometric, in another probabilistic, in another interpretive, and in another based on alignment statistics. The term is therefore context-dependent.

A second misconception is to equate any observed negative correlation or mismatch with a valid VFD diagnostic. The VDA controversy summarized in (Yuen et al., 2022) shows that the validity of a disagreement claim can depend on whether the underlying decomposition has been applied correctly. In that case, the paper argues that the derived quantities $\mathbf{v}$65 and $\mathbf{v}$66 are orthogonal by construction, so nonzero correlation signals an error in implementation rather than a physical failure of the method (Yuen et al., 2022).

7. Scientific significance and methodological implications

Across the cited domains, VFD serves as a diagnostic of latent structure that is not obvious from raw observations alone. In the sunspot case, it exposes co-spatial or adjacent penumbral flux systems with independent flow directions, implying that penumbral dynamics during flux emergence cannot be reduced to a single overturning-convective Evershed picture (Balthasar et al., 17 Nov 2025). In flow-based VLAs, it converts inter-model disagreement into a deployable uncertainty estimate that supports failure detection and sample-efficient active fine-tuning (Römer et al., 16 Jun 2026). In PPV turbulence, it motivates explicit separation of density and velocity contributions so that filamentary structure in channel maps is not conflated with density structure (Yuen et al., 2020). In giant filaments, it localizes dynamical events such as reassembly, collapse, and feedback through abrupt changes in inferred field orientation (Zhao et al., 2023).

The methodological role of VFD is correspondingly varied. It can be a criterion for identifying physically anomalous regions, as in penumbral counter-flows (Balthasar et al., 17 Nov 2025). It can be a mathematically grounded uncertainty estimator, as in ensemble flow matching (Römer et al., 16 Jun 2026). It can be a problem statement that motivates a decomposition algorithm, as in VDA (Yuen et al., 2020). It can also be an alignment-based comparative statistic, as in VGT studies of Galactic filaments (Zhao et al., 2023).

This suggests that the enduring value of the term lies less in a single formalism than in a recurring research problem: velocity information often admits multiple interpretations, and disagreement with an external physical constraint or with model consensus can reveal either hidden structure or methodological error. The papers surveyed here show both possibilities. Sunspot penumbrae and giant filaments treat disagreement as a physically informative phenomenon (Balthasar et al., 17 Nov 2025, Zhao et al., 2023), whereas the VDA controversy treats one reported disagreement as an artifact of incorrect expressions rather than a real inconsistency (Yuen et al., 2022). In machine learning for control, disagreement is elevated from an inconvenience to a calibrated operational signal (Römer et al., 16 Jun 2026).