J F Landaeta
email: javier.landaeta@cpfs.mpg.de

P Khanenko

D C Cavanagh

C Geibel

S Khim

S Mishra

I Sheikin

P M R Brydon

D F Agterberg

M Brando

E Hassinger
email: elena.hassinger@cpfs.mpg.de

Field-angle dependence reveals odd-parity superconductivity in CeRh 2 As 2

CeRh 2 As 2 is an unconventional superconductor with multiple superconducting phases. When H c, this material shows a field-induced transition from a low-field superconducting state SC1 to a high-field state SC2 with a large critical field of H c2 = 14 T and T c = 0.26 K. In contrast, for H ⊥ c, only the SC1 with H c2 = 2 T is observed. The critical field phase-diagrams and their anisotropy were consistently explained by the influence of Rashba spin-orbit coupling at the Ce sites where the inversion symmetry is broken locally. Here, we present a comprehensive study of the angle dependence of the upper critical fields using low temperature magnetic ac susceptibility, specific heat and torque on single crystals of CeRh 2 As 2 . The state SC2 is strongly suppressed when rotating the magnetic field away from the c-axis and disappears for an angle of 35 • . This angle dependence is dominated by the high anisotropy of the Pauli limit and thereby confirms the suggested odd-parity state with pseudospin triplet d vector in the plane.

I. INTRODUCTION

Odd-parity, or pseudospin triplet superconductivity is a rare phenomenon in nature. Only a few materials are promising candidates, including UPt 3 [1], the ferromagnetic superconductors UCoGe, URhGe, UGe 3 [2], and UTe 2 [3]. Theoretically, when spin-orbit coupling is strong, the angle dependence of the Pauli-limiting field H p offers a way to identify possible triplet states since H p should depend on the orientation of the applied magnetic field with respect to the direction of the spins of the Cooper pairs [START_REF] Sigrist | AIP Conference Proceedings[END_REF][START_REF] Machida | [END_REF][START_REF] Mineev | Introduction to unconventional superconductivity[END_REF]. However, the experimentally observed angle dependences of the upper critical fields in the above mentioned systems are often dominated by the orbital limit or by the interplay of field-enhanced spin fluctuations and superconductivity [2,[START_REF] Tada | [END_REF]. In the latter case, the critical field is believed to be governed by an Ising quantum critical point that appears only very near a specific field orientation [2,[START_REF] Tada | [END_REF]. Hence, a clear observation of the angle dependence of H p as evidence for triplet superconductivity is still lacking.

CeRh 2 As 2 was recently found to have a unique and extremely anisotropic superconducting (SC) state with a proposed field-induced pseudospin triplet state [8]. This conclusion was based only on measurements for the field parallel and perpendicular to the c axis. In particular, the unusual results for the field along the c axis may have another origin, either a change between different superconducting order parameters [9,10] or a quantum critical point. Here, we examine the full angle dependence of the superconducting magnetic field -temperature phase diagram and find it agrees with the ex-pected angular dependence of a pseudospin-triplet superconducting state.

CeRh 2 As 2 is a heavy-fermion compound with a Kondo temperature of about 30 K. Its electronic specific heat coefficient C/T keeps increasing below 4 K, a sign of quantum criticality, and attains a large value of 1 J/molK 2 at 0.5 K. A transition to an ordered state appears as a hump in the specific heat C/T at T 0 ≈ 0.4 K of probably quadrupolar character [11]. CeRh 2 As 2 enters an anisotropic superconducting state at T c = 0.26 K. In c axis magnetic fields, it has a unique phase diagram with two superconducting states, SC1 and SC2, and an upper critical field of 14 T, whereas for in-plane fields, only the SC1 state appears, with a critical field of 2 T. This state is strongly Pauli limited and the critical field is a factor of 2.5 -3 larger for c axis fields than for in-plane fields, both strongly exceeding the weak-coupling Pauli limit [12,13] of H p ≈ 0.5 T. The state SC2 however, seems to be purely orbitally limited for H c. The crystal structure of CeRh 2 As 2 is centrosymmetric, but the inversion point lies between the two Ce atomic positions of adjacent layers in the unit cell. In this structure, even and odd parity SC states can naturally appear from the same pairing interaction. A transition between them corresponds to a sign change of the order parameter in one of the two layers. The large anisotropy of the upper critical fields and the two superconducting phases were explained by the local inversion-symmetry breaking at the Ce sites enabling an anti-symmetric spin orbit coupling of Rashba type with alternating sign on neighboring Ce layers [8]. In this picture the zero-field even parity SC state is suppressed by a c axis field since it is Pauli limited, and transforms into an odd-parity state similar to the predictions in layered locally non-centrosymmetric systems [14]. The odd-parity state can be described as a pseudo-spin triplet state with d vector in the plane leading to the absence of a Pauli limit for H c [8,15] as in triplet superconductors in the helical state [START_REF] Sigrist | AIP Conference Proceedings[END_REF]. This com-bined with a large orbital limit can account for the large value of H c2 /T c observed in experiment. For in-plane fields, SC2 would be Pauli limited explaining the absence of SC2 in this field direction. In this paper, we study the superconducting phase diagram as a function of magnetic field direction by ac susceptibility χ, magnetic torque τ and specific heat C. We find that the angle dependence supports the picture that SC2 is an odd parity state with pseudo-spin d vector in the plane.

II. EXPERIMENTAL RESULTS

Figure 1(a) shows the magnetic field dependence of the absolute value of χ at the temperature of 45 mK for different angles. Details on the experimental methods can be found in [16]. We measured from θ = 0 • (H c) to 90 • (H ⊥ c here named H ab). The in-plane field orientation was [110] for torque but not defined for χ and C/T . A small but clear signature of the transition between SC1 and SC2 named H * appears for angles below 35 • . At 30 • a small anomaly is visible at H * in the derivative dχ/dH highlighted in the inset of Figure 1(a).

We define the upper critical field H c2 at the onset of the diamagnetic transition (horizontal dashed line in Figure 1(a) and H * at the maximum of the small bump from the field dependence of χ. The torque (τ) divided by H 2 (and scaled by sin (2θ ) -1 to remove the standard angle dependence in torque) given in Figure 1(b,c) displays similar step-like features at H * . The strong hysteresis loop in the superconducting state is characteristic of the magnetization in CeRh 2 As 2 [8,16]. H c2 is defined in the torque at the field where up and down sweep curves start to separate. Since this happens rather smoothly for small angles, there is a larger uncertainty on these points. The change in the hysteresis loop for 2.5 • visible in the inset of Figure 1(b) is related with a change in the magnetization anisotropy (see [16]).

For fields near the in-plane direction, an additional transition at H cr is observed at roughly 9 T (Fig. 1c and [16]), as published in reference [11]. H cr increases when the field is turned away from the ab plane towards the c axis until, for angles below 58 • , this anomaly cannot be resolved experimentally any more. As can be seen in the inset, it is strongly hysteretic indicating a first order transition, as also observed in the resistivity and magnetostriction [11], where it was associated with a change of the order below T 0 . No further transitions have been detected for in-plane fields up to 36 T and c axis fields up to 26 T [16].

From these data we find the angle dependence of H c2 , H * and H cr shown in Figure 2(a). Here, the upper critical field H c2 decreases rapidly as the angle is increased with respect to the c axis until it approaches the value of H * at about 35 • . From this point on, we only detect one superconducting state in χ and in τ in which the H c2 slowly decreases with angle until it reaches the expected value of ≈ 2 T for H ab.

For different magnetic field angles, temperature dependent ac-susceptibility (data in [16]) and specific heat at different fields give the full temperature-magnetic field phase diagrams. A selection of the specific heat data are depicted in Fig. 3, where a nuclear contribution has been removed. In this paper, these data are used to extract the superconducting transition temperatures and a qualitative behavior of T 0 (see below). A more detailed analysis of the specific heat is subject of future studies.

1 1 0 8 0 o 6 0 o 4 0 o 3 0 o 2 5 o 2 0 o 1 0 o 0 o ( c ) H * ؍ 0 H ( T ) H c 2 ( b )  a c ( a r b . u . ) C e R h 2 A s 2 4 5 m K ( a ) H * d  a c / d H 1 1 0 4 0 m K H c 2 7 4 o 6 6 o 5 0 o 5 8 o 4 6 o ؍ 0 H ( T ) 1 0 2 4 0 m K ؍ 0 H ( T ) H c 2 3 6 o 3 0 o 2 4 o 1 8 o 1 2 o ؔ | • H -2 • ( s i n 2 ؑ ) -1 ( a r b . u . ) H * 1 0 1 5 H c r 0 1 0 2 . 5 o
Here, we focus on the superconducting critical fields. Figure 4 shows the µ 0 H vs T phase diagrams for selected angles obtained from the temperature sweeps of C/T in Fig. 3, the temperature sweeps of the ac susceptibility [16] and the field sweeps from Fig. 1. Note that the discrepancy between the critical field from specific heat and ac-susceptibility at 20 • is ascribed to a difference in angle within the uncertainty be-

m 0 H | | a b m 0 H | | c ( b ) A n g l e ( θ) c a c t S C 1 m 0 H ( T ) C e R h 2 A s 2 T = 4 5 m K S C 2 H * H c 2 H c r ( a ) c a c H o r b C r i t i c a l f i e l d S C 1 C r i t i c a l f i e l d S C 2 H * c a l c . S C 1 m 0 H | | a b m 0 H ( T )
A n g l e ( θ) Since the transition at H q shows a strong hysteresis, only the critical fields from up sweeps are shown here. The critical fields from the down sweeps are typically around 1 T lower. (b) Angle dependence of the upper critical fields of SC1 and SC2 as well the orbital limit H orb of SC1 obtained from the phase diagrams in Fig. 4 and a fit of it using equation 1 (orange dashed line). Red and black lines are fits to equation 2 at 45 mK and the violet line reflects the calculated transition between SC1 and SC2, as detailed in the main text and [16].

m 0 H | | c S C 2
cause in this angle region, H c2 changes strongly even with only a few degrees. For all angles below 35 • , a kink appears in H c2 (T ) at a field that is close to H * obtained from the fieldsweeps in agreement with the fact that the H * line is almost temperature independent for all angles. As already observed for the high-symmetry directions [8], the phase diagrams determined by ac-susceptibility are fully consistent with those obtained from the specific heat and hence reveal the bulk properties.

The present torque and specific heat data also provide some new information on the phase diagram of the phases connected with T 0 and H cr , which were identified as a quadrupolar density wave [11]. Both T 0 and H cr present a clear angle dependence. For 10 • and 20 • , the hump at T 0 is suppressed with field, but remains visible up to roughly 4 T (Figure 3a,b), similar to what was observed for H c [8]. For 45 • T 0 stays approximately constant in applied fields up to 10 T, far above the superconducting critical field, similar to the behavior observed for H ab [8,11]. Because H cr shoots up for an- Here, a nuclear contribution has been removed (as in the supplementary information in [8]).

T 0 T ( K ) C / T ( J / m o l -K 2 ) 0 T 2 T 3 T 5 T 8 T 1 0 T 1 0 o T c ( a ) T ( K ) 0 T 1 T 2 T 3 T 4 T 7 T 2 0 o T 0 T c T ( K ) 0 T 1 T 1 . 5 T 1 . 8 T 2 T 3 T 4 5 o
gles from 90 • to 60 • , this suggests a tricritical point in the range 30 • < θ < 60 • and µH > 15 T. Furthermore, the absence of any further anomaly in the torque up to µH = 36 T for θ = 89.4 • (H a) [16] indicates that the phase forming at H > H cr is stable until very high field as observed e.g. for the quadrupolar phase II in CeB 6 in high magnetic fields [17]. Further high-field studies are necessary to determine the T 0 (H) boundary and the nature of this phase. Notably, the angle dependence of T 0 and H cr are quite different from those of H c2 and H * , suggesting the interaction between this phase and superconductivity to be weak.

III. SUPERCONDUCTING CRITICAL FIELDS

Let us first concentrate on the angle dependence of the critical field of the state SC1. Previous analysis along the two crystallographic directions showed that the orbital limit H orb in CeRh 2 As 2 is large and strongly exceeds the experimental critical fields of SC1. Therefore, this state is strongly Pauli limited with enhanced Pauli fields compared to the bare weak coupling value of H p = 1.84 T c ≈ 0.5 T [12,13]. We now proceed with the determination of the angle dependence of both the orbital limit H orb and the Pauli limit H p . In the clean-limit H orb is given by the slope of the critical field H c2 (T ) near T c as H orb (T = 0) = -0.73 T c dH c2 dT T =T c [18].

From the data in Fig. 4 we extract the values of the H c2 slopes near T c [16] and hence H orb for all angles, which are given in Figure 2b. We observe that the T c varies slightly even in zero field for different sample orientations, which is probably due to the remanent magnetic field in the superconducting magnet and a slightly different shapes of the ac susceptibility curves Magnetic field-temperature phase diagrams of CeRh 2 As 2 for different directions of the magnetic field. The experimental points are from ac susceptibility and specific heat, as indicated. The data show in (a) and (f) were taken from [8].

at different angles near the onset of the transition where we define T c . The values of T c are listed in [16]. Note that the uncertainty of the slope and hence H orb at each angle is quite large (error bars in Figure 2b). The angle dependence of H orb behaves as expected for an anisotropic bulk superconductor [START_REF] Tinkham | Introduction to Superconductivity[END_REF] according to

H c2 (θ ) = H c c2 √ Γ 2 sin θ 2 + cos θ 2 (1)
where

Γ = H c c2 /H ab c2 . We find Γ = H c orb /H ab orb = 2.
(0) = 0.18hV F /k B T c . Using v F = hk F /m * we find H c orb /H ab orb = m * 2 a /m * c m * a ⇒ m * a /m * c = 2.6
. This is comparable to the weak anisotropy in the magnetization at 2 K, where the in-plane value is a factor of 2 larger than the c axis value [8]. It will be interesting to see if band-structure calculations confirm this anisotropy in the future [11].

As a next step, the Pauli paramagnetic limit of SC1 is investigated. Here we consider the following expression for the upper critical field of a spin-singlet superconductor with both orbital and Pauli limiting

ln(t) = ∞ 0 du [1 -F θ + F θ cos( Hg θ u H P t )] exp( -Hu 2 √ 2H orb t 2 ) -1 sinh u (2)
where g θ is a field-angle dependent g-factor, t = T /T c , and F θ = 1 quantifies the pair-breaking due to Pauli limiting (as discussed later, this takes a different form for a pseudospintriplet order parameter). Using the H orb values from the fit of its angle dependence (in order to reduce the uncertainty at each angle), we find that H P /g θ exhibits an anisotropy similar to H c2 (θ ), that can also be described by Eq.1 with an effective Γ g = 2.8. For more details about the fitting procedure please refer to [16]. Within error bars, there is no temperature dependence of the H c2 anisotropy for SC1. Now let us turn to the critical field of SC2 with the aim to understand what is causing the strong suppression of H c2 when fields are turned away from the c axis and the disappearance of SC2 at an angle of 35 • . For H c, the temperature dependence of H c2 follows qualitatively -and even quantitatively, when a lower T c is assumedvery well the expectations for a pure orbital limit [8] without Pauli limiting effect [16]. To first order, the orbital limit of SC2 should be similar to the one of SC1 given in Fig. 2[20]. Therefore, we can make the first statement that the angle dependence of the orbital limit is not strong enough to describe the steep decrease of the experimental critical field H c2 with angle. Hence, the decrease must be related with the Pauli limit kicking in when the field is tilted towards the ab plane. As discussed in the context of SC1, one place where the Pauli field introduces anisotropy is through the spin-orbit coupling renormalized g-factor g θ . However, this anisotropy is also too small to account for the steep decrease of the experimental critical field H c2 with angle since any renormalized H p for a spin-singlet state should have the same anisotropy as in SC1. Consequently, there must be another source of anisotropy due to Pauli limiting. Indeed, this is exactly the behavior expected for triplet superconductors with d vector in the plane (helical state): an absence of Pauli limit for H c (infinite H c p ) and presence of Pauli limit for H ab. The latter is enhanced compared to the bare value [8,[START_REF] Frigeri | [END_REF], when Rashba spin-orbit coupling is included. Here we consider such a helical triplet state subject to an orbital critical field, for which the critical field is given by the expression of Eq.( 2) but now with

F θ = | d • ĥθ | 2 ,
where d is d/| d| and ĥθ is a unit vector that gives the direction of the Zeeman field projected onto to the pseudospin basis [8]. We note that when the orbital field energy (g θ µ B H orb ) is smaller than the spin-orbit coupling energy, this expression is equivalent to that found for an odd-parity spin-singlet state in which the order parameter has opposite sign on the two inequivalent Ce-layers. In Fig. 2, we show the calculated critical field for the state SC2. In the SM, we provide plots of the H -T phase diagrams for the different field angles. The agreement with experiment is excellent.

This leads us to the main conclusion of our paper: The angle dependence of the superconducting critical field is dom-inated by the huge anisotropy of the Pauli field of an odd parity state with d-vector in the plane, in agreement with the interpretation in [8] and in previous models of locally noncentrosymmetric SC [15], although here the SC state is a pseudospin triplet state with staggered dominant singlet intra-layer pairing.

As a final point, we have also calculated H * , the first-order transition between the SC1 and SC2 states. For H c, the H * transition was found to be a result of a competition between the Pauli-limited SC1 (with Pauli field H P,1 ) and the Pauli-limit free SC2, so that H * H P,1 . Here, we calculate the phase transition between SC1 and SC2 from the free energies taking only the Pauli limiting effect into account (violet line in Fig. 2b), with no additional parameters beyond those calculated from the fitting procedure. The neglect of the orbital limit leads to a slight overestimate of the critical field, but the angular dependence is in perfect agreement with experiment [16].

IV. DISCUSSION

We would like to emphasize that the simple model established in [8] and extended here to intermediate angles can reproduce all experimental observations based on only 3 open parameters that cannot be obtained experimentally: the critical temperature of the superconducting state SC2 T c,2 , the inplane Pauli limit H P,1 and the strength of the Rashba spin-orbit coupling relative to the interlayer hopping α. This model has the minimal number of bands in this crystal symmetry and naturally contains both even and odd parity superconducting states. Even though CeRh 2 As 2 certainly contains multiple bands [11], renormalized density functional theory calculations reveal the bulk of the density of states are on Fermi surfaces near the zone boundary -which justifies the single-band approach used here [11,22].

The angle dependence of the orbital limit of SC1 corroborates a rather 3D Fermi surface in agreement with the strongly warped cylinders calculated with renormalised bandstructure calculations [11]. Both the anisotropy of the effective mass given by the anisotropy of H orb as well as the anisotropy of the g factor (and the magnetic susceptibility) are rather small. Furthermore, in quasi 2D systems such as Sr 2 RuO 4 [23], CeCoIn 5 [24] or FeSe [25], the critical field is usually larger for in-plane fields than for c-axis fields, and in the 2D limit a cusp is expected for H orb for fields close to the a axis as observed for example in FeSe, K 2 Cr 3 As 3 or in superlattices of CeCoIn 5 /YbCoIn 5 [START_REF] Tinkham | Introduction to Superconductivity[END_REF][25][26][27], but not observed here. A previous theoretical study found that going from a quasi two dimensional Fermi surface to a three dimensional Fermi surface reduces the anisotropy of SC1 due to Rashba spin-orbit coupling, but shouldn't affect qualitatively the anisotropy of SC2 for the suggested scenario here [9]. However, they investigated a Fermi surface at the Brillouin zone center and the situation may change for a Fermi surface at the zone boundary. In ferromagnetic superconductors, which are the most prominent candidates of spin-triplet superconductivity, the critical fields are highly anisotropic [2,28], and the strong enhancements observed along certain directions or in the fieldreentrant phases are related with strong Ising-type spin fluctuations and quantum criticality influencing the orbital limit [2,[START_REF] Tada | [END_REF]. Here we find that this is not the case for CeRh 2 As 2 , where the anisotropy is accounted for by a pseudospin d that is oriented in the basal plane. An interesting open issue is why the orbital critical field and the Sommerfeld coefficient are so large for CeRh 2 As 2 . In the non-centrosymmetric superconductors CePt 3 Si and CeRhSi 3 the origin of this was proposed to be antiferromagnetic quantum critical fluctuations that enhance the electron effective mass [START_REF] Tada | [END_REF][29][30][31][START_REF] Bauer | Non-Centrosymmetric Superconductors : Introduction and Overview[END_REF]. This needs to be investigated further in CeRh 2 As 2 , where quadrupolar degrees of freedom are suggested to play a role [11] and a broadening of the As(2) NQR line below 0.25 K was interpreted as the onset of antiferromagnetic order [33]. Those systems show a similar anisotropy of the superconducting state to CeRh 2 As 2 with absence of Pauli limit for H c and strong but enhanced Pauli limit for H ab, but a full determination of the angle dependence hasn't been possible yet because the large anisotropy appears only under pressure, preventing an easy angle-dependent measurement.

V. SUMMARY AND CONCLUSION

The strong angle dependence of the upper critical fields of the high-field superconducting state SC2 determined via acsusceptibility, torque and specific heat reveals the unprecedented observation of the text-book like behavior of an odd parity state. Our discussion of the angle dependence of the critical fields presented above neglects an influence of the quadrupole density wave order below T 0 on the superconducting phase diagram, which has an anisotropic field dependence itself [11]. Future research is needed to understand both the interplay between the order below T 0 and the superconducting state in a unified picture.

VI. ACKNOWLEDGEMENTS

Figure 1 .

 1 Figure 1. Magnetic field dependence of magnetic susceptibility and torque for different field directions. (a) Absolute value of the ac susceptibility χ at 45 mK for different angles as indicated. θ = 0 • corresponds to µ 0 H c. The bump labelled as H * , is the transition between SC1 and SC2. The inset shows the derivative of the curve at 30 • , indicating that H * is still present at that angle. The dashed horizontal line indicates the value at which H c2 is defined. (b) Magnetic torque divided by H 2 sin(2θ ) at 40 mK, the inset shows the data for 2.5 • where the change in the hysteresis of τ is visible. (c) Torque divided by H 2 sin(2θ ) for angles close to the plane. The inset in (c) shows an additional phase transition appearing at about H cr ≈ 9 T. In b) and c) curves have been shifted for clarity.

Figure 2 .

 2 Figure 2. Angle dependence of the critical fields 45 mK. (a) different symbols represent different experimental techniques as indicated.Since the transition at H q shows a strong hysteresis, only the critical fields from up sweeps are shown here. The critical fields from the down sweeps are typically around 1 T lower. (b) Angle dependence of the upper critical fields of SC1 and SC2 as well the orbital limit H orb of SC1 obtained from the phase diagrams in Fig.4and a fit of it using equation 1 (orange dashed line). Red and black lines are fits to equation 2 at 45 mK and the violet line reflects the calculated transition between SC1 and SC2, as detailed in the main text and[16].

Figure 3 .

 3 Figure 3. Temperature dependence of the specific heat C/T in magnetic field at different angles. Here, a nuclear contribution has been removed (as in the supplementary information in[8]).

Figure 4 .

 4 Figure 4.Magnetic field-temperature phase diagrams of CeRh 2 As 2 for different directions of the magnetic field. The experimental points are from ac susceptibility and specific heat, as indicated. The data show in (a) and (f) were taken from[8].

6 and H c orb = 16 . 2 T

 162 as shown by the dashed orange line in Figure 2b. For a fully gapped 3D superconductor in the Bardeen Cooper Schrieffer theory, this angle dependence reflects the anisotropy of the normal state since H orb = Φ 0 /2πξ 2 (T ) and ξ

We thank Konstantin Semeniuk, Aline Ramirez, David Moeckli, Marc Fischer and Jörg Schmalian... for stimulating discussions. EH and JL acknowledge support from the Max-Planck society for funding of the Max Planck research group "Physics of unconventional metals and superconductors". Torque measurements were carried out at the European High Magnetic Field lab in Grenoble. CG and EH are also supported by the joint Agence National de Recherche (ANR) and DFG program Fermi-NESt through grant GE602/4-1. DFA was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0021971.


Shaden Shabayek

Héloïse Emmanuel Vincent

Héloïse Théro Digital

Digital Platforms' Governance: missing data & information to monitor, audit & investigate platforms' misinformation interventions

come

DIGITAL PLATFORMS' GOVERNANCE

What's the issue?

There is a growing concern in society about the spread of misinformation on online platforms and its potential impact on democratic debates and public health. To address this concern, online platforms have been expanding their rules in order to tackle the spread of misleading information. During the COVID-19 global health pandemic, platforms have shown a willingness to ensure the access to reliable health information by implementing further new policies. Moreover, regulators on a national and European level are making progress on the design of a legal framework specifically tailored to tackle disinformation 1 . Namely large platforms in operation have signed the "EU Code of Practice on Disinformation" (2018). This code lists a number of actions that large platforms have agreed to implement, such as to "reduce revenues of the purveyors of disinformation", "prioritize relevant, authentic, and accurate and authoritative information" or "dilute the visibility of disinformation by improving the findability of trustworthy content". Since then, several new regulatory guidelines have been adopted at the level of the European Union or are awaiting entry into force; such as the Strengthened Code of Practice on Disinformation (June 2022) and the Digital Services Act 2 (hereafter the DSA) which includes an obligation for very large platforms to give "access to data that are necessary to monitor and assess compliance with this Regulation" (see Article 31 of the DSA proposal) to vetted researchers 3 according to specified requirements by the act. Along similar lines, Trans-atlantic initiatives have emerged, such as the Platform Accountability and Transparency Act (PATA), a bipartisan bill introduced by US senators Coons, Portman and Klobuchar (December 2021). This bill requires that platforms make certain key information available to independent researchers 4 . At the European level, the DSA adds up to the GDPR applied since May 2018, which offers further guarantees for the respect of privacy and the ethical use of data for research purposes. In that context, a variety of actors are reflecting and organizing the practicalities of such legal frameworks to meet up with ethical concerns related to data circulation between platforms and many members of the society. In particular, the provisions of Article 40 of the GDPR encourage the drawing up of codes of conduct. The working group on Platform-to-Researcher Data Access of the European Digital Media Observatory (EDMO) has recently (May 2022) drafted such a code of conduct so that data circulation between platforms and researchers can be organized in practice. At a national level, regulators such as the ARCOM in France are gathering 5 information about the type of data that would be needed so that researchers can effectively investigate the impact of digital platforms on our informational ecosystem. Now from the perspective of researchers, assessing regularly the impact and pertinence of misinformation related interventions by online platforms and monitoring their implementation, as well as a careful investigation of the phenomenon of misinformation itself, are necessary safe-guards for democratic societies with growing digital spheres. Since their early days, online platforms have emerged as digital spaces where information and opinions can circulate freely. The task of ensuring a balance between freedom of expression and access to reliable information regarding political life or public health, is tremendously intricate. In spite of transparency efforts by digital platforms, a number of issues still remain. There is limited access to specific data and information which would enable the academic community, NGOs, the civil society and data journalists to successfully study online misinformation along with the related interventions. In what follows, we provide illustrations of ways to monitor most common misinformation related interventions with currently available data, which precisely demonstrate the scarcity of pertinent data.

We further lay out a list of missing data and information that would enable more effective monitoring, auditing and investigation of misinformation-related interventions by platforms, along with the breadth of misinformation. Clearly, this list intersects items which are present in the above mentioned legal Acts (e.g. Article 30 of the DSA on Additional online advertising transparency). However, our list is meant to not only enumerate missing data with precision but also propose a differential level of access to this data, ranging from exclusive access to vetted researchers within a legal framework when it comes to sensitive data, to a broader access by enriching the fields in currently available APIs. Designing different levels of access to different types of data is meant to attain two goals: (1) preserve privacy of users and address potential concerns of digital platforms regarding legal immunity when giving extended access to their data or information which might put at stake the functioning of their business model (2) provide access to richer data to a wider set of actors when ethical concerns are not at stake, because the task at hand is considerable and combining the results of a variety of actors using different tools of analysis and perspectives, ranging from vetted researchers to journalists and NGOs, can yield a richer understanding of the functioning of platforms and their impact on our informational ecosystem.

How do platforms action content related to misinformation?

Over the past years, growing concerns about the spread of misinformation have encouraged platforms to action content deemed as misleading. Qualifying a piece of content as misleading or false can be a challenging algorithmic task, and a human intervention is generally necessary, via fact-checking organizations, moderators, or users' reporting. For example, Facebook (Meta) is working with over 80 factchecking partner organizations and, according to the International Fact-Checking Network, the company represents the main source of revenue for many of these organizations. Twitter has a different approach where they focus on providing context rather than factchecking6 and the platform is testing a new crowd-based moderation system called "Birdwatch". As for YouTube (Google), this platform utilizes the schema.org ClaimReview markup, where fact-checking articles created by eligible publishers can appear on information panels next to the related content.

During the COVID-19 global health pandemic, platforms have upgraded their guidelines to include a set of rules to tackle the propagation of potentially harmful content. Those policies are enforced via existing actions such as: labeling content to Tweets 2. Twitter should provide context to help people make up their own minds in cases where the substance of a Tweet is disputed. Hence, our focus is on providing context, not factchecking." Tweet ID 1267986503721988096.

provide more context or indicate falsehood, publishing a list of claims that will be flagged or removed, suspending accounts, implementing strike systems, reducing the visibility of content, etc. Facebook's strategy to tackle misinformation is three fold : Remove, Reduce, Inform 7 . Twitter communicates about actions related to misinformation via their Twitter Safety account, such as testing a new feature to report Tweets that seem misleading to users or starting the automated labeling of Tweets that may contain misleading information about COVID19 vaccination 8 . On the YouTube Official Blog, the platform explains its "Four Rs of Responsibility" and how it raises authoritative content, reduces borderline content and harmful misinformation 9 . As each platform is a private company, those policies are not coordinated and are implemented in different ways across platforms. Nevertheless, there are common interventions against misinformation used by large digital platforms, which could be classified into three broad categories 10 : (i) informing users with flags, notices and information panels; (ii) reducing the visibility of some content, either at the post level or at the account level: and (iii) deleting content and suspending users temporarily or permanently in case of multiple rule violations.

Platforms make data available via official APIs (e.g. CrowdTangle, Twitter API V2, YouTube API V3), recent academic partnership programs (e.g. Social Science One 11 ) and transparency centers. But specific data and information to investigate misinformation interventions and their impact are scarce -such as data about whether a piece of content has a notice or

Can we investigate misinformation related interventions with currently available data? a. Account suspensions and content deletion

To date, investigating removed content and account suspensions, due to policy violations, is a burdensome task. This is because when a platform deletes a piece of content violating its rules or invites a user to delete a piece of content to regain access to the functionalities of the platform, the data disappears from official APIs12 and naturally is no longer visible on the platform. Hence the deleted content can no longer be investigated. Indirect methods could be designed to study suspensions and content deletion linked to misinformation13 . For at facilitating partnerships between the academic sphere and private companies who own informative data about people and society. Namely, this partnership allowed the release of a very large Facebook URLs Dataset and facilitated access to this dataset for the purposes of academic research.

instance, in order to study the volume of suspensions or deleted content, one can recollect data of pre-existing lists or collections from previous research of Facebook pages, groups or posts, YouTube channels or videos, or Twitter accounts or Tweets, and then investigate which accounts/content remain available and which have disappeared (if any). Similarly, using a crossplatform approach, researchers can gather some information about deleted content. Precisely, some users can deplore being targeted by a given platform's intervention (e.g. YouTube) via an account on a different platform (e.g. Twitter), or when a piece of content is simply removed from one platform (e.g. YouTube video) but information about that specific content remains on other platforms (e.g. title of a YouTube video along with the (inactive) link redirecting to it on YouTube). However, it should be noted that even when a platform displays a message indicating that a piece of content was removed for policy violation or that an account was suspended, to the best of our knowledge the specific policy violation is rarely indicated. Another indirect method consists in regularly monitoring and collecting data about accounts, pages, groups and channels who have previously shared content identified by fact-checkers as misleading, to be able to go back in time and analyze the content in case of an account suspension and investigate the pertinence and effectiveness of such intervention. Hence, access to this data needs to be provided in order to get a better understanding of the impact of content deletion directly linked to misinformation interventions and study potential indirect effects (e.g. users' migration to new platforms). Namely to address ethical and privacy concerns, access can be provided to vetted researchers for a fixed period of time, before the permanent deletion of the related metadata by platforms.

b. Reducing content visibility

platforms can be accessed via the Twitter Transparency center, see the section "industry transparency reports" (last accessed May 10, 2022).

Similarly, investigating how platforms reduce the visibility of problematic content via algorithmic recommendation systems can only be achieved with the design of models and experiments to simulate our understanding of how algorithms work. This method can yield incomplete and biased results, since there is no clear overview of how platforms integrate in their algorithms signals or variables to downrank or make problematic content less visible. Furthermore, very basic metrics such as the "reach" of posts on Facebook or Twitter (the number of actual viewers of a piece of content) are absent from official APIs and researchers have to resort to proxy measures, such as looking at the engagement received by pages or groups or accounts having shared multiple times a piece of content fact-checked as False, to then try to infer whether their visibility has been reduced. However, this approximation lacks precision. This is because the engagement rate (e.g. likes or comments numbers) reflects the intensity of the discussions on a given page or groups, but not the actual audience (reach) of a given piece of content. For example, pages linked to mainstream media outlets often have a very high audience and a low engagement rate, while highly politicized pages can have very high engagement rates without having a large audience. Finally, note that part of this information can be recovered from the Privacy-Protected Full URLs Data Set (see description in the next section), namely users' interactions on Facebook (e.g. views or clicks) with URLs that were "publicly" shared over 100 times. However, with this data, one cannot study the evolution over time of the reach (views or clicks) of a given Facebook public page or group that have repeatedly shared misleading content, especially those with a limited audience, because not all posts contain URLs, not all posts have been shared "publicly" over 100 times and noise added to the engagement count can heavily bias the analysis especially for low values.

c. Informing with banners, flags and notices

By contrast, information banners, flags and notices, can be studied since they are visible when searching posts or videos. This intervention was particularly adopted by many large platforms in direct relation with the diffusion of misleading information and is usually based on fact-checked content, moderators' intervention or users' reporting. In what follows, we design several exercises to show how this intervention consisting in informing users could be studied or monitored. We take a set of fact-checked links as a starting point and study the kind of interventions applied to them. 14 This means that for a link to be included in the dataset, it must have been shared at least 100 times by users who chose

Privacy-Protected Full URLs Data Set

We use a dataset extracted from the June 2021 version of the Facebook Privacy-Protected Full URLs Data Set, (Messing et al., 2021), which contains a column that indicates whether a rating was attributed to a given URL by a third-party fact-checking partner (see the field "tpfc_rating"). This very large data set constitutes a great resource for researchers because Facebook has the most substantial fact-checking program relative to other platforms and hence it provides aggregated data about which links contained in posts have been subject to a fact-check. It can be used not only to study misinformation on Facebook, but also on other platforms such as YouTube and Twitter, because of cross-platform traffic (e.g. sharing a YouTube video via a Facebook post or a Tweet). However it should be noted that the dataset is updated with a delay. Hence it cannot be used in real time to investigate ongoingevents. Furthermore in order to protect users' privacy, Facebook limited access to the dataset to URLs that have been shared publicly 14 over 100 times and this might create biases when trying to investigate the volume of misinformation.

the option "public" in their privacy settings (as opposed to "share to friends" for example).

Box 1: Systematic review: YouTube recommendations and problematic content.

This paper provides a systematic review of studies that have investigated the YouTube recommender system in relation with problematic content, such as radicalisation, conspiracy theories, misinformation and disinformation. Exactly 23 papers, which meet a set of eligibility criteria of inclusion, are analyzed. The authors find that 14 studies out of the 23 suggest that the YouTube recommender system is facilitating problematic content pathways, that is individuals are exposed to content via the recommender system that they might have not otherwise encountered. The remaining studies either produce mixed results (7 studies) or do not suggest that the YouTube recommender system is facilitating exposure to problematic content (2 studies). Finally, the authors discuss the limitations of these studies, in terms of methods and modeling choices. These limitations stem from the lack of a clear understanding of how YouTube recommender systems actually work, since such information is not fully disclosed, but also from limited access to relevant data. Figure 1 displays the breakdown of links that were reviewed by third-party fact-checking partners, by rating categories: fact checked as false, not eligible, fact checked as true, etc. Figure 2 shows the number of links fact checked as false grouped by the country where the link was most shared. We restrict the present investigation to the set of 2109 links flagged as False since January 1, 2020 and that were most shared in the ten European countries 15 for which we have over 100 links in the dataset. As of April 5, 2022 only 1436 among the 2109 links are still active (status 200). 15 The ten countries are: France, Germany, Greece, Spain, Poland, Hungary, Great-Britain, Italy, Netherlands, Lithuania.

Box 2: Examining potential bias in largescale censored data

This paper conducts a cross-dataset analysis over the month of December 2018, to compare findings based on (i) the Facebook Privacy-Protected Full URLs Data set and (ii) data from a nationally representative desktop web panel from the company Nielsen. They found that 10% of clicks went to fake news domains in that month when using the Facebook dataset, against 2.5% of clicks when using the Nielsen dataset. By matching URLs between both datasets, along with a CrowdTangle investigation and an internal Facebook investigation, the authors show that this overestimation (4X difference) is due to the 100public-share threshold introduced in the Facebook dataset for privacy-protective procedures. Hence, they argue that censoring part of this large Facebook dataset can dramatically affect conclusions about misinformation drawn from the data. We show the volume per rating category of links for which the field "tpfc_rating" in the data set is not empty. The category "other" includes exactly three rating categories: 'fact checked as missing context' (821 links), 'prank generator' (142 links) and 'fact checked as altered media' (1 link).

Case Study 1: YouTube videos factchecked as False

We found 293 links that correspond to YouTube videos, among the 2109 links rated as False by a third party fact-checking partner, from ten EU countries where those links were most shared. We wanted to know whether these videos have been actioned by YouTube. To that end, we searched on the YouTube API v3 for these videos and found that only 76 videos (~26%) were still available. However, we were unable to find on the YouTube API v3, a field indicating whether the available video contained an information panel or any metadata related to the videos that were no longer available. Hence, we searched for this information by scraping the content of information panels when the videos were active and any message that appears when clicking on the links of unavailable videos (see Figure 3).

As summarized in Figure 4, we found that only 20 videos (out of 76 active videos) contained an information panel (about COVID19) and 12% of the remaining videos without an information panel had the comments functionality deactivated. Furthermore, among the 217 inactive videos around ~20% were removed and the most common reason (86% of those videos) was "for violating YouTube Community Guidelines" (see panel a, Figure 3), without clearly indicating which specific policy violation. The remaining 80% of inactive videos displayed a message saying that the video is unavailable and for ~53% of these videos no reason was provided (see panel b, Figure 3). Finally, for active videos, we found that the average view and like count of videos was higher for videos without an information panel, relative to videos containing an information panel (see panel a, Figure 5). However, the median view and like count of videos containing an information panel was higher than those without an information panel (see panel b, Figure 5). This indicates that for videos containing an information panel, there is a long tail of relatively "low" view and like count bringing the mean down more than the median.

Case Study 2: Tweets containing links fact-checked as False

For this second case study, we take the 2109 links "fact-checked as False" since January 1, 2020 and that were most shared in ten European countries (see the subsection Privacy-Protected Full URLs Data Set), and collect Tweets which have shared at least one of these links. We aimed to see whether those tweets contained a notice (see panel a, Figure 6) or an interstitial (see panel b, Figure 6). On the Twitter API v2, to the best of our knowledge, there does not exist a field which indicates whether a notice was attributed to a Tweet; only fields related to the interstitials "possibly sensitive" and "withheld" can be recovered from the Twitter API v2 16 .

Hence, we collected Tweets using minet, a web mining command line tool 17 , in order to be able to recover Twitter "notices" whenever they exist. We found ~72k Tweets (excluding retweets) having shared at least one of the 2109 links flagged as False (see Figure 7). Among these Tweets, only 11 contained a notice (e.g. "Stay informed") and 2910 Tweets had the interstitial "possibly sensitive". According to the Twitter rules, the interstitial "possibly sensitive" is used to advise viewers "that they will see sensitive media, like adult content or graphic violence". Manually checking Tweets marked as "possibly sensitive" we found no adult content nor graphic violence (see example in panels b and c of Figure 6) -but either links (from our initial list) or quoted tweets of other users 18 . Inspecting the ten Tweets that contained a notice (e.g., "Stay informed"), we found that: 1) there exists a big variation in terms of follower count of the eleven users linked with the eleven Tweets 19 , 2) there exists other Tweets without a notice, containing the exact same link and some keywords as the Tweets containing a notice. Both remarks suggest 16 See https://help.twitter.com/en/rules-and-policies/noticeson-twitter. 17 See https://github.com/medialab/minet. 18 The placement of an interstitial can depend on accounts settings and we noticed that the field "possibly_sensitive" returned "True" for Tweets for which we could no longer see an interstitial when inspecting them manually directly on Twitter. Hence we suspect that the interstitial might be placed temporarily. Moreover, we suspect that these interstitials might result from users reporting, see that this process might not be automated and might be the result of users' reporting.

In addition, we compared engagement (sum of likes, retweets and replies) for Tweets containing an interstitial "possibly sensitive" and Tweets without an interstitial (see Figure 8). We found that that the average engagement for Tweets with an interstitial "possibly sensitive" were lower (around 2) when compared to tweets without an interstitial (around 6), suggesting that attributing an interstitial to a Tweet might contribute to lowering its visibility and hence engagement. However, it should be noted that in absolute values, the engagement for the collected tweets containing a link factchecked as false is low; the median of total engagement for those Tweets is zero and the 75th percentile is equal to one.

Finally, we used a cross-platform approach and studied engagement for Tweets having shared a YouTube video marked as False by a fact-checking partner (see Case Study 1). We found that the average engagement (likes, replies, retweets) on Twitter for YouTube videos that got removed for violating YouTube community guidelines, was higher than the average engagement for YouTube videos without an information panel and that were still available. https://help.twitter.com/en/safety-and-security/sensitivemedia. 19 Among the eleven unique Twitter users having created a Tweet to which a notice was attributed, four Twitter users had between 4 and 300 followers, two users had between 1k and 6k followers and finally four users had between 64k to 400k followers.

Recommendations: data & information needed to monitor and audit digital platforms' misinformation related interventions

The previous section illustrates and discusses that currently available data does not allow us to monitor most of the misinformation-related actions platforms take. In this section we list our recommendations regarding which data and information should be made available to effectively monitor, audit, and investigate misinformation related platforms' interventions.

Many of the following data and information requests can be achieved via differential access that accounts for the sensitivity of the data and information:

(1) For highly sensitive data, official APIs can be utilized by creating an extended specific data access to vetted members of the academic community or via academic partnerships similar to Social Science One. Such access would occur within a legal framework (e.g. Article 31 of the DSA) and according to a rigorous code of conduct to preserve privacy and address ethical concerns (e.g. Article 40 of the GDPR).

(2) For data that do not raise ethical concerns and with very minimal risk to privacy, current official APIs can have enriched fields, allowing a wider audience to conduct research and investigate misinformation related issues.

Data needed to measure the amount of misleading content in circulation and its visibility

Access to pertinent data needs to be provided in order to measure the scale of the issue and the impact of platforms' actions on the total amount of attention misinformation gets. Data needs to be available timely, without a delay of several months and it needs to be complete. For example, the "Privacy-Protected Full URLs Data Set" only includes URLs with more than 100 "public" shares, as part of their privacy-protective procedures (see box 2); so one cannot study websites with limited audiences. Moreover, there is a delay of 6 to 18 months so researchers cannot use it to study on-going events.

Data needed

• The "reach" of a piece of content, which is its actual number of views.

Collectible via a new field in existing APIs

• list of all content (including internal posts and external fact-checked URLs) that a platform has identified as sharing misleading information, including recent content and low virality content.

Data needed to investigate platforms' labeling actions

Labels added by platforms to provide context on problematic content can only be obtained by scraping or visual inspection so far and a programmatic access is needed.

Data needed

Data and information needed to investigate platforms' downranking actions

To quantify the impact of interventions consisting in reducing the visibility of a piece of content or all content produced by a given source (e.g. downranking), researchers need to be able to know when the intervention (e.g. strike) has occurred.

Data needed

• Indication, for a website or an account (Facebook group or page, Twitter accounts, Youtube channels etc.), of the number of "strikes" it received for a given misinformation-related policy violation and the specific policy violated.

Collectible via a new field in existing APIs.

• list of all accounts/websites that have been down ranked by the platform and the periods for which the intervention was in effect.

Information needed

• the definition of the strike system of platforms when it exists and the policy violations that lead to a strike as well as the consequences of having strikes for an account.

To the best of our knowledge, this information exists for Twitter (as part of their "Civic Integrity Policy" and "COVID 19 misleading information policy") and for Youtube for any community guidelines violation. • details about further actions which are used to reduce the visibility of content, such as 1) excluding a piece of content from appearing via a direct search on a platform (e.g. search box of Twitter), 2) prohibiting users from sharing specific domain names in a post.

Data needed to monitor platforms' suspension/deletion of content/accounts and to study misinformation over time

Digital platforms can either directly remove a piece of content that violates their rules or invite users to delete it themselves to regain access to their account for example. Lost data linked to deleted content can bias the study of long-term trends of users' behavior and/or the impact of platforms' moderation policies. It can disrupt ongoing research projects, because when a page or account is suspended by a platform, researchers must adapt their protocols to deal with the missing data.

Data needed

• Indication of the specific policy violation that led to the suspension of an account and the content that violated the stated policy.

Collectible via a new field in existing APIs.

Data needed to study algorithmic recommendations of misleading content

Researchers need to be able to understand whether engagement (e.g., following a page or an account) with accounts identified as repeatedly sharing misinformation or misleading content, comes from direct search by users or from algorithmic recommendations.

Data needed

• Proportion of views of identified misleading content that results from algorithmic recommendation: This can take the form of a field indicating the proportion of views resulting from a direct search for the content or an external link versus the proportion of views resulting from an algorithmic recommendation within the platform. • Proportion of the total number of views on all content shared by known misinformation sources that comes from the platform's recommendation algorithm. For example, the proportion of views on all Youtube videos published by a channel that regularly publishes misinformation that come from the Youtube "watch next" recommendation algorithm.

• Proportion of followers gained by a given account (notably known misinformation sources) that come from the platform's recommendation algorithm: This can take the form of a field indicating the share of followers gained via direct search and the share of followers gained via an algorithmic recommendation to follow an account or page.

Information needed

• whether and how a platform's recommendation algorithm excludes or downranks i) content that was found to be misleading information or ii) accounts that have repeatedly shared misinformation.

Tracking demonetization of content/accounts spreading misinformation

As the EU Code of Practice on Disinformation asks that platforms "reduce revenues of the purveyors of disinformation", independent researchers would need access to data to verify this intervention.

Data needed

• indicating whether an account (e.g., a

YouTube channel or Facebook page) was demonetized for policy violations and indication of which policies were violated.

Collectible via a new field in existing APIs. • list of content demonetized by a platform due to its identification as misinformation; • list of accounts demonetized by a platform because they were identified as repeatedly spreading misleading content; • list of content/accounts that have been considered for demonetization by the platform (e.g., following reports by the platform's users) but have not been demonetized.

Annex 1: Summary table -data & information needed to monitor and audit digital platforms' misinformation related interventions

  Missing data & information to monitor, audit & investigate platforms' misinformation interventionsShaden Shabayek, Emmanuel Vincent and Héloïse Théro Sciences Po médialab -June 2022 Draft version Digital Platforms' Governance Missing data & information to monitor, audit & investigate platforms' misinformation interventions 1. What's the issue? .......................................................................................................... 2. How do platforms action content related to misinformation? ................................ 3. Can we investigate misinformation related interventions with currently available data?.................................................................................................................................... a. Account suspensions and content deletion ................................................................... b. Reducing content visibility ............................................................................................... c. Informing with banners, flags and notices ..................................................................... Privacy-Protected Full URLs Data Set .................................................................................................. Figure 1: Third Party Fact-Checked URLs in the dataset broken down by rating ................................. Figure 2: Links fact-checked as false, by country where it was most shared ....................................... Case Study 1: YouTube videos fact-checked as False .........................................................................

Figure 4 :

 4 YouTube videos fact-checked as False ............................................................................... Figure 3: Messages displayed for inactive videos fact-checked as False ..........................................

Figure 5 :

 5 View and like count of active YouTube videos "fact-checked as False" .............................. Case Study 2: Tweets containing links fact-checked as False ...........................................................

Figure 6 :

 6 "Stay Informed" notice and "possibly sensitive" interstitial on Twitter (Screenshots taken on May 11, 2022) ......................................................................................................................................

Figure 7 :

 7 Tweets containing at least one link fact-checked as false ...................................................

Figure 8 :

 8 Total engagement for (left) suspended YouTube videos shared within Tweets and (right) Tweets marked as possibly sensitive .................................................................................................. 4. Recommendations: data & information needed to monitor and audit digital platforms' misinformation related interventions ........................................................ 1. Data needed to measure the amount of misleading content in circulation and its visibility ..................................................................................................................................... 2. Data needed to investigate platforms' labeling actions .................................................. 3. Data and information needed to investigate platforms' downranking actions ............ 4. Data needed to monitor platforms' suspension/deletion of content/accounts and to study misinformation over time ............................................................................................. 5. Data needed to study algorithmic recommendations of misleading content .............. 6. Tracking demonetization of content/accounts spreading misinformation ................... Summary table.......................................................................................................................table -data & information needed to monitor and audit digital platforms' misinformation related interventions ................................................................. Annex 2: Quick access to community guidelines & platform misinformation policies, for Facebook, Twitter and YouTube ............................................................................................

  Yesilada, M. & Lewandowsky, S. (2022). Systematic review: YouTube recommendations and problematic content. Internet Policy Review, 11(1).

  Allen, J., Mobius, M., Rothschild D. M., & Watts, D. J. (2021). Research note: Examining potential bias in large-scale censored data. Harvard Kennedy School (HKS) Misinformation Review.

Figure 1 :

 1 Figure 1: Third Party Fact-Checked URLs in the dataset broken down by rating

Figure 2 :Figure 3 :Figure 4 :

 234 Figure 2: Links fact-checked as false, by country where it was most shared (See the field "public_shares_top_country" in the dataset)

Figure 7 :Figure 6 :

 76 Figure 7: Tweets containing at least one link fact-checked as false

  For a detailed list of interventions of multiple platforms, we invite the reader to navigate through the following airtable compiled by Slatz and Leibowicz (2021). 11 Social Science One is an academic organization based at Harvard University and founded by Facebook in 2018. It aims an information panel, or fields indicating the specific policy violation when an account, page or group is suspended. Furthermore, when navigating through the categories of policy areas, to the best of our knowledge,

		misinformation is absent from the data
		available on the transparency centers of
		key platforms, such as Facebook, Twitter
		and YouTube. Finally, platforms' official
		communication	about	misinformation
		interventions is rare and the academic
		community, NGOs and data journalists,
		usually discover interventions related to
		misinformation via monitoring social media
		accounts related to domain names with
		several failed fact-checks or via articles in
		news outlets.
	7	See about.fb.com/news/2019/04/remove-reduce-inform-
	new-steps/ (last accessed May 16, 2022).
	8	See
	twitter.com/TwitterSafety/status/1379515615954620418
	and twitter.com/TwitterSafety/status/1483076718730649607
		(last accessed May 16, 2022).

9

See blog.youtube/inside-youtube/the-four-rs-ofresponsibility-remove/ (last accessed May 16, 2022). 10

  • list of content/accounts deleted by a platform in relation to misinformation or hate speech policies. • count of views/engagement related to removed content following a policy violation, o including views/engagement for all the content produced by suspended accounts, and not just the problematic content. o including data that was deleted by users themselves following a notification from the platform.

& information to monitor, audit & investigate platforms' misinformation interventions. 2022. hal-

For example, the requirements for vetted researchers are given in paragraph

of Article 31 of the Proposal for a

Regulation on a Single Market for Digital Services (Digital Services Act), 15 December 2020.4 For an update on this discussion, watch the May 4, 2022 Subcommittee Hearing, presiding Chair Coons on "Platform Transparency: Understanding the Impact of Social Media" judiciary.senate.gov/meetings/platform-transparencyunderstanding-the-impact-of-social-media 5 See the call https://www.arcom.fr/consultationspubliques/consultation-publique-sur-lacces-aux-donneesdes-plateformes-en-ligne-pour-la-recherche

To the best of our knowledge, Twitter does not have a page which summarizes its fact-checking strategy, if any. The Twitter Safety Team tweeted on June 3, 2020 the following: "We heard: 1. Twitter shouldn't determine the truthfulness of

Application Programming Interface.

To the best of our knowledge, aggregate figures of account suspensions and content deletion directly related to misinformation rarely exist, with the exception of COVID-19 misleading information on the Twitter transparency center. Transparency reports of other

Summary table

See Annex 1 Ethics: the data collection and processing complied with the EU General Data Protection Regulation (GDPR). The case studies use the Facebook Privacy-Protected Full URLS Data set and have been submitted for pre-publication review as indicated in the updated (April 2022) Research Data Agreement. The review concluded that no Personal Information or Confidential Information was found.

Further readings


Wafia Benhamlaoui
email: w.benhamlaoui@univ-skikda.dz

Mounira Rouainia
email: rouainia_m@yahoo.fr

NATURAL GAS TRANSPORTATION BY PIPELINE: HAZARDS AND CONSEQUENCES CASE OF GK2 NATURAL GAS PIPELINE, SKIKDA REGION

Keywords: transport of hazardous materials, accident scenario, risk assessment, pipeline, natural gas transportation

The hazardous materials transportation by pipelines is the most used means of transport for long distance links for liquid and gas. This mode of transport is not without risk and accidents, which can be due to internal origin as the corrosion of the pipeline, or of external origin such as an activity close to the pipeline (public works ...). Our study is done on a natural gas pipeline, this pipeline is part of a pipeline network of the EST Pipeline transportation (TRC) in Skikda region, with a terminal of 5 pipelines (3 of natural gas, 1 of crude oil, 1 of condensate) which is located close to urban areas and makes the impact of a leak on a pipeline of gas or oil significant. In this study, our objective is to assess all risks related to natural gas transportation by pipeline and their possible consequences. In addition, we will determine critical events related to different type of leaks to show the possible impacts and damages that a breach on natural gas pipeline can have in the presence of a source of ignition.

INTRODUCTION

The transport of hazardous materials by pipelines is used at a large-scale level to transport liquid or gaseous hydrocarbons for long distance links. Pipelines have been widely constructed around the world, compared with other methods of transportation, its safety is the highest [START_REF] Feng | Revelation of Oil and Gas Pipeline Failure[END_REF], but this mode of transport is subject to different type of accidents; like internal origin as the corrosion of the pipeline, or of external origin such as an activity close to the pipeline (public works ...). As the SKIKDA region is home to the EST Pipeline transportation (TRC) headquarters, with a terminal of five pipelines (3 of natural gas, 1 of crude oil, 1 of condensate), and it is located close to urban areas, which increases the degree of impacts and damages.

In this case, study, we consider a leak on a GK2 natural gas pipeline, with a breach of 500 mm that crosses an urban area before reaching the TRC terminal. Our objective is to determine the possible impact and damage that this leak can have in the presence of a source of ignition, with the help of a software of calculations and modelling of the effects.

POSSIBLE CAUSES OF THE TRANSPORT OF HAZARDOUS MATERIALS BY PIPELINES

Pipeline transportation consists of a set of pressure pipes of variable diameters used to move liquids or liquefied gases continuously or sequentially. This mode of transport is used to transport natural gas (gas pipelines), liquid or liquefied hydrocarbons (oil pipelines), certain chemical products (ethylene, propylene, etc.) [START_REF] Safadi | Contribution to the risk assessment of transport of hazardous materials taking into account uncertainties[END_REF].

A pipeline is a complex system, geographically spread on a wide territory, requiring technologies and methodologies to support the identification of pipeline segments that are highly potentially at risk of failure.

Several types of accidents have been identified by the gas and oil pipeline industry in the past according to US Department of Transportation (DOT) Office of Pipeline Safety, 1991 and CONCAWE 1996. They are most frequently classified in five cause categories:

-Third parties that represent a damage caused by operations carried out by others in the pipeline vicinity and not related to its management; -Corrosion, when pipeline is subject to two types of corrosion, the first one is an inside corrosion, derived from water or other substances transported with hydrocarbons (viscosity and temperature are crucial information for the accident analysis), the second one is an outside corrosion related to the pipe coating and cathodic protection; -Mechanical that are fractures or cracks that occur when efforts go beyond the efforts of the system permits; -Operational error, which are caused by excessive pressure or system malfunction; -Natural events such as landslides, floods, erosion in general, subsidence, earthquakes, frost or lightning [START_REF] Chiara | Accident occurrance evaluation in the pipeline transport of dangerous goods[END_REF].

EXAMPLES OF LARGE-SCALE ACCIDENTS OF HAZARDOUS MATERIALS TRANSPORTATION

-On 12 September 2011, international media sources reported a major fuel pipeline explosion and fire in the Mukuru-Sinai slum of Nairobi, Kenya. Over 100 people were killed, while an equal amount of people were hospitalized with serious burn wounds.

Based on an analysis carried out by UNOSAT1, using imagery of the situation before and after the explosion and fire, an estimated area of 10 600m² had been seriously affected by the explosion. A further estimated 57 dwellings located in the area had been destroyed and 20 had been seriously damaged. The UNOSAT report also indicated that the Ngong River, downstream of the explosion site, appeared to be affected by the release of a large amount of petroleum products [START_REF]Fuel Spill and Fire Rapid Environmental Emergency Assessment Mukuru-Sinai slum[END_REF].

-On 18 January 2019, a pipeline transporting gasoline exploded in the town of Tlahuelilpan, in the Mexican state of Hidalgo. The blast killed at least 135 people and injured dozens more. Mexican authorities blamed fuel thieves, who had illegally tapped the pipeline. The explosion was particularly deadly because large crowds of people had gathered at the scene to steal fuel. Security forces tried to persuade people to move away from the scene, but they were outnumbered and asked not to engage with civilians for fear of causing a violent confrontation. The leak was reported at 17:04 CST (11:04 UTC), and the explosion occurred two hours later at 19:10. It took about four hours for responders to extinguish the fire [5].

-On November 16, 2017, at 4:34 a.m. mountain daylight time, a TransCanada Corporation, Keystone Pipeline (Keystone) ruptured near Amherst, South Dakota, between the Ludden, North Dakota, (Ludden) and Ferney, South Dakota, (Ferney) pump stations. Keystone's Operational Control Center (OCC), in Calgary, Alberta, Canada, was monitoring Keystone's Supervisory Control and Data Acquisition system that detected the leak and shut down the pipeline. Keystone's field staff traveled to the indicated leak location confirmed that the pipeline had ruptured, and initiated their spill response plan. The approximate spill area was comprised of about 5,000 barrels of crude oil. The first indication of the pipeline rupture occurred at 5:33 a.m., when an abrupt drop in discharge pressure and a corresponding increase in flow rate were observed at the Ludden pump station. In addition, at 5:34 a.m., a corresponding pressure drop was observed at the Ferney pump station. The controller at Keystone's OCC initiated an emergency shutdown of the pipeline at 5:36 a.m. and commenced isolation of the pipeline. By 5:45 a.m., the failure location had been isolated by using remotely operated valves. The NTSB determines that the probable cause of the failure of the Keystone Pipeline was a fatigue crack, likely originating from mechanical damage to the pipe exterior by a metal-tracked vehicle during pipeline installation that grew and extended in-service to a critical size resulting in the rupture of the pipeline [6].

HAZARDOUS MATERIALS TRANSPORTATION BY PIPELINE IN THE REGION OF SKIKDA

Sonatrach -RTE (East Transport Region), manages pipeline transport in the Skikda region. It transports crude oil, condensate and natural gas respectively from Haoud El Hamra and Hassi R'Mel to Skikda Terminal [START_REF]Data Sheets[END_REF]

Risk assessment of hazardous materials transportation by pipelines

Risk analysis techniques specific to hazardous materials transportation have been developed over the years. However, while fixed-site risk analysis is framed by well-defined methods, the case of hazardous materials transportation is often absent from formal discourse. Some actions are undertaken by the authorities, but the actual risk analysis seems to be of more interest to researchers than to legislators, because of its inherent complexity [START_REF] Leroux | Logistics Strategies for Companies Working in the Hazardous Materials Field[END_REF].

Some examples of risk assessment in hazardous materials transportation

-

The study by Jo and Ahn takes into account pipeline transport and considers a model that is intended to reduce the level of risk as a key variable that should be taken into account in the planning and building stages of a new pipeline. It stresses the importance of considering not only individual but also societal risk due to cumulative fatal length and failure rate. The dataset used in the paper is based on data at the European level [START_REF] Jo | A method of quantitative risk assessment for transmission pipeline carrying natural gas[END_REF].

-The PRA is a well-established technology, where PRA analysts aim to estimate parameters used to determine the frequencies and probabilities of different events. According to [START_REF] Muhlbauer | Pipeline risk management manual[END_REF] [START_REF] Muhlbauer | Pipeline risk management manual[END_REF], the probabilistic risk assessment usually answers three questions: What can go wrong? How likely is it? What are the adverse consequences? The two methods normally used to answer these questions are the "Event Tree Analysis" and the "Fault Tree Analysis". [START_REF] Muhlbauer | Pipeline risk management manual[END_REF] 10] suggests also a way to facilitate the understanding of the PRA by combining each hazard with a Likelihood-Consequence matrix.

Presentation and application of the Quantitative Risk Assessment method:

The first step of the QRA method consists in determining the hazards related to an installation, in our case of study we use the method called "preliminary risk analysis APR", the table below summarizes the results of the analysis:

N° CAUSES FAILURE

. Preliminary Risk Analysis of Transportation by Pipelines

The second step is to use a method of quantification of these hazards, we operated for the use of the method 'bowtie', and that because it has the principle of bringing together the causes as well as the consequences centred on the same dreaded event central, the table below summarizes the critical feared events options that can be found in a pipeline risk assessment:

CRITICAL FEARED EVENTS Commentaries 1 pipeline leak in Liquid phase
Corresponds to a hole of diameter equal to a certain percentage of the nominal diameter of a pipe carrying a flammable liquid. It can be a '' functional '' opening on the pipeline: leaks from seals on pumps, on valves ...

pipeline leak in gas phase

Corresponds to a hole of diameter equal to a certain percentage of the nominal diameter of a pipe carrying a gas. The ERC can be a '' functional '' opening on the pipeline: leaks from seals on pumps, on valves… 3

Breakage of a pipe

The rupture is the loss of equipment leading to a significant and instantaneous release of the substance. In most cases, the catastrophic rupture, can lead to the ejection of missiles, thermal flows and a surge wave.

Collapse of the pipe

Reservoir collapse is the complete loss of equipment, leading to a complete and instantaneous release of the substance. It is due to a reduction of pressure of the capacity, leading to its collapse by action of the atmospheric pressure.

TABLE 3. Feared events

In our study case the pipeline transports natural gas, according to the referential of the QRA Method [START_REF]Guideline for quantitative risk assessment[END_REF], we note that the selected risked event is 'breakage of a pipe: it's a loss of containment, the following step consists to apply the Bowtie Method on this critical feared event, the interest in this step is to allow the visualization of all the roads, going from basic events to damage. Then we will determine the effects of damage with PHAST modeling software [START_REF][END_REF]. The purpose of using this type of modeling software is to model the magnitude of the damage that a natural gas pipeline (GK2) leak can have in an urban environment in the Skikda region; the figure below shows the path of the pipeline passing through an urban area before arriving at the RTE terminal: To modelize the effect of a possible, we need some data related the pipeline, external data as meteorological data, the

FIGURE 1 .

 1 FIGURE 1. Risk assessment of the LOC by the method Bowtie

FIGURE 2 .

 2 FIGURE 2. Representation of GK2's path[START_REF]RTE -Skikda document[END_REF]

FIGURE 4 .

 4 FIGURE 4. intensity radiation for Jet fire on map

TABLE 1 .

 1 has: Materials transported by the RTE-Skikda

	Name of the	Length Length in	Type of	Caractéristiques
	pipe		Skikda	product
				transported
	NK1	645.5	40.880	Condensate	Start-up year: 2009
		KM	km		-Main line NK1 30 ''
					-Place of departure: Haoud El Hamra
					-Arrival point: Skikda land terminal
					-Diameter: 30 ''
					-Theoretical transport capacity: 11.4
					million tons / year
					-actual current transport capacity: 11.4
					million tonnes / year
	OK1	645 KM 109 km	Crude oil	-Date of entry into production (Date
					first loaded): 27 April 1972
					-Main line OK.1 34 ''.
					-Place of departure: Haoud El Hamra
					-Arrival point: Skikda land terminal
					• Diameter: 34 ''.
					• Theoretical transport capacity: 30
					million tons / year.
					-Actual Transport Capacity: 30 million
					tons / year.
	GK1 40''	574.87	41 km	Natural gas	Date of commissioning: March 1971
		KM.			-Departure point: CNDG Hassi R'mel
					-Arrival point: Arrival terminal Skikda
					-Diameter: 40 ''
	GK2 42''	575,545	40.879	Natural gas	-Commissioning year: December 2001
		KM	km		-Departure point: CNDG Hassi R'mel
					-Arrival point: Arrival terminal Skikda
					-Diameter: 42 ''
					-Theoretical Capacity: In compression:
					14.2 X 109 CM3 / year
					year
					-Actual capacity: In compression: 14.2
					* 109 CM3 / year
					year
	GK3 48''	785 KM 55.198	Natural gas	-Start of construction year: 2010
			km		-Year of production: 2012
					-Place of departure: CNDG Hassi
					R'mel wilaya de Laghouat
					-Place of arrival: TASO Skikda
					(Terminal Skikda) and TA-KO El Kala
					(Arrival Terminal El Kala)
					-Diameter: 48 ''

TABLE 4 .

 4 table bellow sumerizes all these parameters : SCENARIO'S PARAMETERS

	Material	Natural gas (methane)
	Pipe length	1400 m
	Pipe diameter	42"
	Internal temperature	30 °C
	Internal presure	50 bar
	External temperature	24 °C
	Wind speed	18.7 Km/h
	Pumped inflow	173,8
	Breach size	500 mm

Path Scenario Distance to UFL [m] Distance to LFL [m]

		FIGURE 3. Side view of disperssion cloud
	Path	Scenario		Weather	Flame length [m]
	GK2 leak\Long pipeline	Location specific breach day	196,485
					Distance to LFL
					fraction [m]
	GK2 leak\Long pipeline Location specific	5,74763	38,4284	400,184
		breach
		TABLE 5. Distance downwind to defined concentrations
		Mass flow rate 1382,84 kg/s
			Release	62,9182 s
			duration
		TABLE 6. Calculated Quantities

TABLE 7 .

 7 Jet Fire Results-Distance downwind to defined radiation levels

TABLE 9 .

 9

Late Explosion Results-Distance downwind to defined overpressures FIGURE 6. Worst case late explosion FIGURE 7. Late explosion worst case radiation

CONCLUSIONS

We know that the risk zero does not exist, although the RTE terminal has set controls measures to prevent all type of risks related to pipeline transportation, the population is in a considerable increasing, as now they live near a pipeline. The risk of a leak or rupture is always present; even it is caused by internal components as corrosion, or external source like external activity or an act of sabotage.