Thomas Arbez
email: thomas.arbez@edu.mnhn.fr

Christian A Sidor

J.-Sébastien Steyer

Laosuchus naga gen. nov. sp. nov., a new chroniosuchian from Southeast Asia (Laos) with internal structures revealed by micro-CT scan and discussion of its palaeobiology

Keywords:

Chroniosuchians were a clade of non-amniotic tetrapods known from the Guadalupian (middle Permian) to Late Triassic, mainly from Russia and China. The rarity of complete or articulated remains means that relatively little is known about this group in terms of its anatomy, palaeobiology, or evolutionary history. Based on a nearly complete skull with a left hemimandible, we describe the first chroniosuchian from Laos from rocks preserving the Permian-Triassic boundary in the Luang Prabang Basin, which is located on the tectonic Indochina Block. This specimen is referred to a new genus and species, Laosuchus naga, based on numerous diagnostic features, including an extremely reduced pineal foramen; absence of palatal dentition; well-developed transverse flange of the pterygoid that contacts the maxilla; internal crest on and above the dorsal side the palate; otic notch closed by the tabular horn and the posterior part of the squamosal, forming a continuous wall; thin and high ventromedial ridge on parasphenoid. A phylogenetic analysis of 51 characters and 25 taxa reveals a basal position for Laosuchus naga among Chroniosuchia. In addition, CT scan data reveal internal structures and provide new insights about the anatomy and palaeobiology of chroniosuchians. Laosuchus naga was likely amphibious and spent most of its time in water, rather than in terrestrial environments. As chroniosuchians are nonmarine tetrapods previously known on the North China Block, South China Block, and Laurussia, the occurrence of Laosuchus naga on the Indochina Block supports the hypothesis of physical connections between all these tectonic plates by the time of the Permo-Triassic boundary.

Introduction

The chroniosuchians were a clade of non-amniotic tetrapods that survived the Permian Triassic mass-extinction [START_REF] Shishkin | Permian and Triassic anthracosaurs from Eastern Europe[END_REF][START_REF] Buchwitz | On the use of osteoderm features in a phylogenetic approach on the internal relationships of the Chroniosuchia (Tetrapoda: Reptiliomorpha)[END_REF]. They occupied fresh water environments and some species were potentially terrestrial as their system of osteoderms suggests an adaptation to terrestrial locomotion [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF][START_REF] Buchwitz | Osteoderm microstructure indicates the presence of a crocodylian-like trunk bracing system in a group of armoured basal tetrapods[END_REF]. Chroniosuchians are divided in two families, the Bystrowianidae and the Chroniosuchidae, but both share a similar geographic range. The Bystrowianidae is the more recent of the two families, with Triassic taxa, although most of these are mainly known from fragmentary and/or disarticulated material. They present a weakly fenestrated skull (e.g. absence of preorbital fenestrae), narrow osteoderms ventrally fused with the neural spine, and ball-shaped intercentra [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF]. In the other side, the Chroniosuchidae are represented by mainly Permian taxa and present elongated preorbital fenestrae, long slit-like choanae, and larger osteoderms [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF]. Phylogenetically important variability occurs in the shape of their intercentra, which could be disc-, horseshoe-or ball-shaped. This variability would explain why this Chroniosuchidae does not always form a monophyletic group according to the phylogenetic analyses of [START_REF] Buchwitz | On the use of osteoderm features in a phylogenetic approach on the internal relationships of the Chroniosuchia (Tetrapoda: Reptiliomorpha)[END_REF].

The first chroniosuchian was discovered in 1929: it consists of ribs and osteoderms from the upper Permian of the Russian fore-Ural region and was first attributed to the seymouriamorph Kotlassia prima by [START_REF] Hartmann-Weinberg | The dermal ossifications of the Russian seymouriamorphs[END_REF]. Later, Vjushkov (1957a, b) recognized chroniosuchians as a distinct group [START_REF] Buchwitz | On the use of osteoderm features in a phylogenetic approach on the internal relationships of the Chroniosuchia (Tetrapoda: Reptiliomorpha)[END_REF]. The clade Chroniosuchia was erected by [START_REF] Tatarinov | Seymouriamorphen aus der Fauna der UdSSR[END_REF] who classified them among anthracosaurs (=Anthracosauromorpha sensu Ivachnenko & Tverdochlebova, 1980), but a recent study placed them among stemamniotes, close to lepospondyls and diadectomorphs [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF]. However, according to [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF], who included Chroniosaurus dongusensis in their phylogenetic analysis, Chroniosuchia forms a polytomy with Silvanerpeton miripedes, Embolomeri and another clade comprising Seymouriamorpha, Gephyrostegidae, Lepospondyli and the amniote Paleothyris acadiana. Currently, 22 valid species of chroniosuchians are recognized, known from 1) the middle Permian to Middle Triassic of the Russian fore-Ural region [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF][START_REF] Buchwitz | On the use of osteoderm features in a phylogenetic approach on the internal relationships of the Chroniosuchia (Tetrapoda: Reptiliomorpha)[END_REF], 2) the middle to upper Permian of China (e.g., [START_REF] Young | A new Late Permian fauna from Jiyuan, Honan[END_REF][START_REF] Li | New anthracosaur and temnospondyl amphibians from Gansu, China[END_REF][START_REF] Jiang | First record of Bystrowianid Chroniosuchians (Amphibia: Anthracosauromorpha) from the Middle Permian of China[END_REF], 3) the Middle Triassic of Germany [START_REF] Witzmann | A relic basal tetrapod from the Middle Triassic of Germany[END_REF], and 4) the Middle or Upper Triassic of Kyrgyzstan [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF]. Because of the poor preservation of the material (mostly consisting in disarticulated specimens such as isolated osteoderms), the group is poorly known in terms of its general anatomy, phylogeny, and palaeobiology [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF]. This is especially true for the Bystrowianidae.

Systematic palaeontology

Superclass Tetrapoda [START_REF] Goodrich | Studies on the structure and development of vertebrates[END_REF] Order Reptiliomorpha Säve-Soderbergh, 1934 (sensu [START_REF] Benton | Vertebrate Paleontology[END_REF] Suborder Chroniosuchia [START_REF] Tatarinov | Seymouriamorphen aus der Fauna der UdSSR[END_REF](sensu Witzmann & Schoch, 2017) Family incertae sedis Genus Laosuchus gen. nov.

This published work and the nomenclatural acts it contains have been registered with Zoobank:

Etymology: from the country of origin (Laos) and the ancient greek soûkhos, "crocodile" for its crocodilian-like appearance.

Diagnosis: as for the species

Laosuchus naga sp. nov.

This published work and the nomenclatural acts it contains have been registered with Zoobank:

Holotype: MDS-LPQ 2005-09, a nearly complete skull (260 mm of maximum length, 160 mm of maximum width and 85 mm high) with its left hemi-mandible partly articulated.

Etymology: from the mythological monster "Naga" (or Phaya Naga) believed to live in the Mekong River, which is close to the type locality.

Type locality: Ban Houaytan District, right bank of the Mekong River, Luang Prabang Province, northern Laos (GPS coordinates available to qualified researchers).

Type horizon: Reddish volcaniclastic siltstone with a maximum age of 251.0 ± 1.4 My according to U-Pb dating of detrital zircons [START_REF] Rossignol | The volcaniclastic series from the Luang Prabang Basin, Laos: A witness of a triassic magmatic arc[END_REF], Tan South section [START_REF] Bercovici | Permian continental paleoenvironments in southeastern Asia: new insights from the Luang Prabang Basin (Laos)[END_REF], Purple Claystones Formation ("Zone des Argiles violettes" sensu [START_REF] Counillon | Documents pouvant servir à l'étude géologique des environs de Luang Prabang (Cochinchine)[END_REF], see also [START_REF] Steyer | The geological and palaeontological exploration of Laos; following in the footsteps of J. B. H. Counillon and A. Pavie[END_REF]. Characters supporting an assignment to Reptiliomorpha (according to [START_REF] Benton | Vertebrate Paleontology[END_REF] character states in our phylogenetic analysis, see below): (1) parietal and tabular sharing a narrow suture (angustitabular condition); (2) premaxillae less than half of the skull width [START_REF] Benton | Vertebrate Paleontology[END_REF]; (3) vomers strut-like, narrow.

Diagnosis

Characters supporting an assignment to

Description Preservation and computed tomography scan

Overall, the specimen is well preserved, except for its left side, which is partially crushed and weathered. In addition, it was slightly compressed dorsoventrally during fossilization, which has deformed the interorbital part of the skull roof. The left hemimandible is also well preserved and found in natural articulation. There is only a little displacement of the left hemimandible towards the right side, likely due to the compression, and its lateral surface is partly weathered, especially the posterior part.

To supplement the visible external anatomy, the holotype was scanned at the AST-RX facility of the MNHN with the following parameters: microfocus beam 240 kV; voltage 210 kV; current 410 μA; voxel size 0.09464315 mm; and slices resolution 1790 x 2024 pixels. 3157 virtual slices, reconstructed using GE Sensing & Inspection Technologies Phoenix|x-ray datos|x rec, were cropped to 1251 x 2014 pixels to render the data more manageable and imported in the 3D reconstruction software Mimics 17.0 and 18.0 (Materialise, Leuven, Belgium). The 3D model, performed by segmentation using the "thresholding" function with grayscale from 50 to 255, was produced with the same voxel resolution and with a "Smooth Factor" of 1.0 and five iterations, in order to reduce surface irregularities due to manual segmentation. Data produced by segmentation were exported in the software 3matic 9.0 for PDF 3D creation (see in Supplementary Information).

General features

In dorsal view, the skull is subtriangular (260 mm length, 170 mm width and 85 mm height)

with an elongated snout (antorbital length 165 mm; postorbital length 80 mm) whose tip is rounded (Fig. 2). The skull roof is pierced by a subtriangular premaxilla fontanelle, rounded naris and elevated oval orbits. Most of the cranial sutures are not visible because they are covered by the strong degree of ornamentation (Fig. 2). A system of ridges runs along the skull roof, and the pineal foramen is nearly indistinct (1 mm diameter), which is unique in chroniosuchians. The dentition is composed of conical teeth on the hemimandible, premaxillae, and maxillae in addition to numerous denticles on the palate (see below). The palate is mostly flat, especially in its anterior region. However, its posterior region shows a high vertical flange of the pterygoid. The palate is pierced by large and elongated choanae and presents subrectangular adductor fossae. The skull roof of Laosuchus naga shows dermal ornamentation consisting of pits and ridges of around 1 mm height, with a honeycomb pattern [C2(1)] (i.e., character 2, state 1). This highly pronounced ornamentation obscures most sutures and suggests an adult stage for the specimen (e.g. [START_REF] Steyer | Ontogeny and phylogeny in temnospondyls: a new method of analysis[END_REF]. Dermosensory canals are visible inside the dermatocranial bones, but not on their surface (see below) [C1(2)]. This skull roof also shows paired parasagittal and oblique ridges of 3-10 mm in height [C3(1)]: the parasagittal ridges are straight and run from the tabular, along the medial border of the orbits and naris, to the anterior tip of the snout. The oblique ridges are straight and run from the anterior border of the orbit to the lateral border of the skull at around mid-length between the orbit and the naris.

On the left side, the external naris is ovoid (13-16 mm length, 12-14 mm width) [C5(0)] and slightly enlarged anteriorly, as is the case in Madygenerpeton pustulatus [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF].

By contrast, Chroniosaurus dongusensis [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF] and Chroniosuchus paradoxus [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF] have a slit-like naris. The nares are well separated and lateralized with an elevated medial margin framed by the anterior ends of the sagittal ridges.

Well separated and lateralized external nares are found in chroniosuchians (when preserved), except Bystrowiella schumanni where nares are close together and located almost at the tip of the snout [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF]. A subtriangular premaxillary fontanelle (18 mm length, 10 mm width) is present between the premaxillae [C4(1)], and represents a synapomorphy of Chroniosuchia, with only Madygenerpeton pustulatus [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF]) lacking it. The fontanelle covers almost half of the interpremaxillary suture. The premaxillae are elongated, with a lateral area contacting the naris, and form the anterior end of the snout. Contrary to Bystrowiella schumanni, no lateral crest and edentulous part lateral to the choanae have been found [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF].

The orbits are slightly oval (28 mm length, 25 mm height) and raised well above the skull roof, as in Madygenerpeton pustulatus [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF]. However, in Laosuchus naga the orbits are proportionally smaller than those of Madygenerpeton pustulatus [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF],

Chroniosaurus dongusensis [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF] or Chroniosuchus paradoxus [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF] (the ratio orbit length/skull length is 0.11 compared to 0.14, 0.14 and 0.18, respectively). The prefrontal-jugal suture seems to emerge from the anterior border of the orbits.

Posterior to the right orbit, a rounded bone is visible; which we interpret as the postorbital (or possibly the postfrontal). The parietal foramen is circular and extremely small (slightly less than 1 mm in diameter). Its size is conspicuously smaller than in other chroniosuchians (e.g., around 2.5 mm in Chroniosaurus dongusensis [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF], 2 mm in Madygenerpeton pustulatus [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF], 3.5 mm in Bystrowiella schumanni [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF]) for a skull length around 61 mm, 100 mm, 84 mm respectively).

The postparietals are subrectangular in dorsal view (11 mm length, 21 mm width), heavily ornamented and partly extend on the occiput (see below). They do not present a posterior articulation surface, free of dermal sculpture, for the first osteoderm as in Bystrowiella schumanni [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF]. In dorsal view, they delimit a central embayment in the posterior margin of the skull table along with the tabulars. This central embayment forms a rectangular space (28 mm length, 44 mm width), which is narrower and more elongated than that of Chroniosuchus paradoxus (Novikov et al. 2000, fig. 4.1) and Chroniosaurus dongusensis (Tverdokhlebov et al. 2005, fig. 17) in which the embayment has a parabolic outline. Interestingly, Madygenerpeton pustulatus [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF] shows two small and rounded embayments between the postparietal and the tabulars.

In Laosuchus naga, the tabulars are subrectangular (50 mm length, 16 mm width) and delimit the lateral border of the central embayment. Their lateral margin is completely in contact with the squamosal, thereby eliminating any indication of a tabular horn and otic notch, a unique situation in Chroniosuchia. The tabular also lacks a ventromedial portion free of dermal sculpture as in Bystrowiella schumanni [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF].

The squamosals are subrectangular in lateral view (55 mm length, 29 mm width) with, as an otic notch is absent, a straight posterior margin. Apart from the lack of an otic notch, the overall shape of the squamosal is similar to Chroniosaurus dongusensis [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF].

However, in Laosuchus naga, its sutures are unclear, and what is drawn in Figures 2 and3 might also encompass the supratemporal.

The jugals are elongated subtriangular bones (155 mm length, 28 mm width) similar to Bystrowiella schumanni [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF] and Bystrowiana permira [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF]. In Laosuchus naga, the jugal shows a dermal sculpture also found on the whole skull roof: this ornamentation does not present elongated ridges radiating from a centre, as mentioned for Bystrowiella schumanni [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF] and Bystrowiana permira [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF].

The quadratojugal is subtriangular in lateral view (21 mm length, 33 mm width) and relatively short compared to other chroniosuchians, as it does not reach the maxilla [C15(1)]. In

Laosuchus naga the quadratojugal is clearly different from Bystrowiana permira, where the quadratojugal shows dorsal and ventral curvatures [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF].

Unfortunately, the suture between the maxilla and the premaxilla is not visible in ventral view.

However, together these bones form a long and slender structure (215 mm length, 5 mm width and 12 mm height): this structure is curved in its most anterior part and delimits the choanae laterally, the vomer anteriorly, and the ectopterygoid and the pterygoid posteriorly.

Palate (Fig. 4, 5, 6B)

The palate is fragmented and incompletely preserved, especially the left side. This renders the sutures between the palatal bones difficult to determine with confidence. An anterior palatal fenestra is not present in Laosuchus naga, similar to the condition in anthracosaurs like

Anthracosaurus russelli [START_REF] Panchen | On Anthracosaurus russelli Huxley (Amphibia: Labyrinthodontia) and the family Anthracosauridae[END_REF] or Pholiderpeton attheyi [START_REF] Panchen | The skull and skeleton of Eogyrinus attheyi Watson (Amphibia: Labyrinthodontia)[END_REF]) and the chroniosuchian Chroniosaurus dongusensis [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF]. However, Laosuchus naga In ventral view, the vomer is rectangular and elongated (60 mm length, 20 mm width). It thickens laterally and medially, delimiting a flat central depression. The anterior margin of the vomer is convex ventrally. Its lateral margin is concave and borders the choana, whereas its medial margin is straight. Its posterior region is not preserved.

The palatine is subrectangular (40 mm length, 25 mm width). Its posterior limit is not very clear. Its lateral margin, which is slightly concave, thickens dorsally to form a vertical wall that forms the lateral margin of the choana. This bony wall begins in the first one-third of the palatine's length and its height increases posteriorly and regularly up to 8 mm. The outline of the ectopterygoid forms an elongated triangle in ventral view (175 mm length, 25 mm width) with a posteriorly directed tip. It is proportionally wider than that of Chroniosaurus dongusensis [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF] and Chroniosuchus paradoxus (Novikov et al. 2000) and does not reach the subtemporal window. However, this bone is very fragmented and consequently its suture with the palatine remains hypothetical (as represented by a dotted line in Fig. 4D).

The pterygoid covers most of the palatal surface (150 mm length, 60 mm width) and consists of five parts: the horizontal palatal ramus, the internal wall, the articular area, the transverse process including the descending flange, and the quadrate ramus including the ascending flange.

The right pterygoid is well preserved except in its anterior extremity, which may partly cover the vomer, as in Chroniosaurus donguensis [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF]. The palatal ramus is triangular and elongated, as in Chroniosaurus donguensis [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF]. Its medial margin extends dorsally and forms a broad inturned flange, called here the "internal wall", which becomes progressively more vertical anteriorly, as in Archeria crassidisca [START_REF] Holmes | The skull and axial skeleton of the Lower Permian anthracosauroid amphibian Archeria crassidisca Cope[END_REF]) and Chroniosaurus dongusensis [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF]. The most posterior rim of the internal wall is marked by a medial groove bordered by two crests in which the parasphenoid basal plate is inserted, forming an elongated basicranial articulation. This is different from Chroniosaurus donguensis [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF] and Chroniosuchus paradoxus (Novikov et al. 2000), where a well-developed process of the pterygoid forms the basicranial articulation.

The basicranial articulation of Laosuchus naga also contrasts with the common hemispherical basipterygoid process seen in various early tetrapods (e.g. [START_REF] Klembara | The cranial anatomy of Discosauricsus Kuhn, a seymouriamorph tetrapod from the Lower Permian of the Boskovice Furrow (Czech Republic)[END_REF]. In Laosuchus naga, the transverse process of the pterygoid projects laterally until it articulates with the medial surface of the lower jaw. This transverse process forms a thick and straight ramus with a descending flange laterally directed, making it triangular in anterior view, and similar to that of Bystrowiana permira [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF], after Ivakhnenko & Tverdokhlebova 1980). The posterior surface of the right descending flange shows seven grooves, which may correspond to the insertion of ligaments of the musculus pterygoideus [START_REF] Carroll | Problems of the origin of reptiles[END_REF][START_REF] Holmes | The skull and axial skeleton of the Lower Permian anthracosauroid amphibian Archeria crassidisca Cope[END_REF]). The quadrate ramus of the pterygoid bears the ascending flange ('lamina ascendens' sensu [START_REF] Bystrow | Benthosuchus sushkinia labyrinthodont from the Eotriassic of Sharzhenga River[END_REF], which is hooked, posteriorly directed, and with a rounded extremity contacting the quadrate.

Dorsally, the vertical flange sutures to the descending flange ('lamina descendens' sensu [START_REF] Bystrow | Benthosuchus sushkinia labyrinthodont from the Eotriassic of Sharzhenga River[END_REF] of the squamosal. Ventrally, the quadrate ramus is slightly thicker, and the ascending flange extends anteriorly into the posterior part of the basicranial articulation area. A recess is visible at the base of the anterior part of both ascending flanges (Fig. 5), which we interpret as the basicranial recess. This recess is similar to the basicranial recess of Kotlassia prima [START_REF] Bystrow | Kotlassia prima Amalitzky[END_REF] and Discosauriscus austriacus [START_REF] Klembara | The cranial anatomy of Discosauricsus Kuhn, a seymouriamorph tetrapod from the Lower Permian of the Boskovice Furrow (Czech Republic)[END_REF], where the internal morphology of the skull is well known. Just dorsal to this recess is a bony extension whose shape is reminiscent of the epipterygoid. However, it is unclear if this extension is the epipterygoid itself or a part of the lamina ascendens with a badly preserved basicranial recess at its base.

The parasphenoid is known by its basal plate (150 mm length, 60 mm width) and a small, disarticulated fragment of the cultriform process. The basal plate has a diamond shape in ventral view. Its posterior portion is subtriangular, deeper than its anterior part, as preserved, and divided by a thin and high median ridge, as in Discosauriscus austriacus (Klembara 1997, fig. 20). The crista muscularis, visible in the mid-region of the basal plate, is oriented transversely and is straight (this crest is curved in Chroniosaurus dongusensis; [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF]. The The subtemporal fenestrae are relatively large and subrectangular (58 mm length and 38 mm width). Their anatomy differs from that of Chroniosaurus dongusensis [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF] and Chroniosuchus paradoxus [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF], where an anterior extension of the fenestra is found between the ectopterygoid and the maxilla.

Interestingly, CT data reveal a pair of long internal crests running along on dorsal surface of the palate (Fig. 7B). The left one is better preserved and arises from the posterolateral region of the vomer. It follows the margin of the choana and forms a vertical crest of a variable thickness on the palatine and ectopterygoid (1.5-4 mm). Posteriorly to the choana, this crest contacts the maxilla on which it turns posteromedially and overlies the ectopterygoid and pterygoid, but without making contact. It is not possible to say if this crest is formed by several palatal bones or if it consists of a single unit. Regardless, no equivalent has been found in other taxa.

Occiput (Fig. 7,8)

The occiput of Laosuchus naga is well preserved (160 mm width, 85 mm height and 50 mm depth). The foramen magnum is broadly oval in outline (18 mm width, 8 mm height), which is similar to other anthracosaurs where the foramen magnum is circular (e. OEA is trapezoidal in outline. Its lateral side consists of a buttress that may be the paraoccipital process. This resembles the condition found in Embolomeri sensu [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF].

The internal side of the OEA is concave, possibly to accommodate the otic capsule (Fig. 8).

Below this ventral extension of the tabular and dorsolaterally to the exoccipital column, a shallow (1-2 mm) and small ovoid (3 x 4 mm) depression is visible: this post-temporal depression may be homologous to the post-temporal fenestra observed in other stegocephalians, such as temnospondyls (e.g. [START_REF] Arbez | Exceptional endocranium and middle ear of Stanocephalosaurus (Temnospondyli: Capitosauria) from the Triassic of Algeria revealed by micro-CT scan, with new functional interpretations of the hearing system[END_REF].

An oblique fissure passes through the postparietals and the OEA, and reaches the foramen magnum, likely passing though the suture between the two postparietals and the synotic tectum of the supraoccipital. The left opisthotic, which is well preserved, has a bean-shape in posterior view. It is fused with the OEA and forms the paroccipital flange, a common feature observed in various early tetrapods such as Anthracosauroideae (e.g. [START_REF] Panchen | On Anthracosaurus russelli Huxley (Amphibia: Labyrinthodontia) and the family Anthracosauridae[END_REF][START_REF] Smithson | The morphology and relationships of the Carboniferous amphibian Eoherpeton watsoni Panchen[END_REF],

Seymouriamorpha (e.g. [START_REF] Laurin | A redescription of the cranial anatomy of Seymouria baylorensis, the best known seymouriamorph (Vertebrata: Seymouriamorpha)[END_REF], Diadectomorpha (e.g. [START_REF] Romer | The primitive reptile Limnoscelis restudied[END_REF]) and Lepospondyli (Caroll & Gaskill 1978). As in others chroniosuchians, the sphenethmoid is not visible (even with the CT scan), reinforcing the pattern of a strong reduction of the endocranial ossification characteristic of the group [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF].

The basioccipital is reduced posteriorly, a situation similar to Gephyrostegus bohemicus [START_REF] Carroll | The ancestry of reptiles[END_REF] and Asaphestera intermedia [START_REF] Carroll | The order Microsauria[END_REF]. In Laosuchus naga, it is limited by the space between the occipital condyles and forms a rectangular thick plate. As this basioccipital is not well developed ventrally (as is the case in anthracosaurs such as Archeria crassidisca, [START_REF] Holmes | The skull and axial skeleton of the Lower Permian anthracosauroid amphibian Archeria crassidisca Cope[END_REF]Palaeoherpeton decorum, Panchen 1964), it likely did not articulate with the cervical vertebrate. Its dorsal surface is posteriorly marked by two rounded depressions (Fig. 8). As they are congruent with the concavities on the internal surface of the OEA (see above), they may correspond to the emplacement of the otic capsule.

The exoccipitals are laterally flattened and ovoid, as in Chroniosaurus dongusensis [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF]) and Discosauriscus austriacus [START_REF] Klembara | The cranial anatomy of Discosauricsus Kuhn, a seymouriamorph tetrapod from the Lower Permian of the Boskovice Furrow (Czech Republic)[END_REF]. They are almost reduced to forming just the occipital condyles (17 mm height and 8 mm width), but remain distinctly separated by the basioccipital. The foramen for cranial nerves IX -X, visible dorsally, is located on the suture between the left exoccipital and its corresponding opisthotic. The foramen for cranial nerve XII is slightly more ventral and visible on the lateral surface of the condyle. These foramina are rounded (~ 1 mm diameter), which is similar with those of Archeria crassidisca [START_REF] Clack | The braincase of the anthracosaur Archeria crassidisca with comments on the interrelationships of primitive tetrapods[END_REF] and Discosauriscus austriacus [START_REF] Klembara | The cranial anatomy of Discosauricsus Kuhn, a seymouriamorph tetrapod from the Lower Permian of the Boskovice Furrow (Czech Republic)[END_REF].

The quadrate is difficult to distinguish from the squamosal, and so both bones were 3D modeled as a single structure. The right quadrate shows two condyles: the medial one (10 mm in anteroposterior length) is rounded, and the lateral one is much smaller. Anterolaterally, the dorsal process of the quadrate interlocks with the posterior part of the quadrate ramus of the pterygoid and extends into the subtemporal fenestra. The dorsal process has a small depression on the medial side, marking the contact with the tip of the pterygoid quadrate ramus. In ventral view, the quadrate is relatively short, as in Chroniosuchus paradoxus [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF] and

Chroniosaurus dongusensis [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF]. A short quadrate seems to be characteristic of chroniosuchians. However, as the quadrate is only depicted in ventral view in Chroniosuchus paradoxus [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF] and Chroniosaurus dongusensis [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF]), this should be taken with caution. The quadrate of Laosuchus naga is located substantially ventral to the exoccipital condyle [C32(0)].

Dentition (Fig. 9)

The dentition of Laosuchus naga includes both marginal teeth and palatal denticles. The marginal dentition preserves 45 teeth, closely set on the premaxillae, maxillae, and dentary.

Where complete, these teeth are typically conical, but certain teeth can be slightly curved posteriorly, and anteroposteriorly or laterally flattened according to their position. The tooth height is relatively constant along the jaw, as in Chroniosaurus dongusensis [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF] and in contrast to Bystrowiella schumanni [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF]. In Laosuchus naga, this tooth height is of 9 mm in average (with rare extremes between 6 to 14 mm). CT data suggest that the marginal teeth are labyrinthodont, with infolded enamel and a central pulp cavity (Fig. 9D), as observed also in Bystrowiella schumanni [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF].

On the palatal surface, numerous small denticles are scattered irregularly, notably on the ectopterygoids and the palatal rami of the pterygoids, as is the case in Chroniosuchus paradoxus [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF] and Chroniosaurus dongusensis [START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF]. Palatal tooth row or tusks (or alveoli) have not been found.

Left hemimandible (Fig. 9)

The left hemimandible is partially articulated with the skull (Figs. 3,4). It is relatively narrow and elongate, with a slight anteromedial curvature, measuring 265 mm in length and 11-16 mm in width. Anteriorly, the mandible measures only 8mm in height, but this measurement increases to a maximum of 28 mm in the region of the angular. In overall shape, the mandible of Laosuchus naga is most similar to that of Chroniosuchus paradoxus [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF].

In Laosuchus naga, the labial surface of the hemimandible is ornamented by pits and ridges but this ornamentation is partly weathered and makes it difficult to trace the sutures in places.

However, a close examination under UV light reveals thin depressions in the posterior and ventral regions of the dentary which suggests the locations of sutures with the postsplenial and angular, respectively.

CT data allow for visualization of the glenoid region of the mandible (Fig. 9), which is otherwise obscured because it is in articulation with the skull (Fig. 3). The articular presents a glenoid fossa formed by two concave ovals facets for the articulation with the quadrate condyles. The larger facet (16 mm length, 7 mm width) is lingually situated to the smaller one (8 mm length, 4 mm width). When compared to the condition seen in the anthracosaurs Pholiderpeton attheyi [START_REF] Panchen | The skull and skeleton of Eogyrinus attheyi Watson (Amphibia: Labyrinthodontia)[END_REF], Proterogyrinus scheelei [START_REF] Holmes | The Carboniferous amphibian Proterogyrinus scheelei Romer, and the early evolution of tetrapods[END_REF], and Archeria crassidisca [START_REF] Holmes | The skull and axial skeleton of the Lower Permian anthracosauroid amphibian Archeria crassidisca Cope[END_REF]), the jaw articulation in Laosuchus naga is positioned relatively ventrally. In Laosuchus naga, the adductor fossa (58 mm length, 17 mm width) is located on the posterior one-quarter of the mandible and has a relatively low lateral margin, nearly reaching the height of its medial margin. This organization contrasts with Chroniosuchus paradoxus, where the medial margin is well below the lateral one [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF], and with the condition in anthracosaurs in general (e.g. Pholiderpeton attheyi, Panchen 1972;

Proterogyrinus scheelei, Holmes 1984 and Archeria crassidisca, Holmes 1989). At the anterior limit of the adductor fossa, a bony extension (15 mm length) is posterodorsally directed but this could be due to the deformation of the specimen. The lingual side of the mandible presents a shallow and elongate Meckelian fenestra (24 mm length, 6 mm height), but its reduced height could be related to the overall flattening of the specimen. The Meckelian fenestra is unique as reported in Chroniosaurus dongusensis [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF] and Bystrowiella schumanni [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF]. On the lingual side of the hemimandible, an elongated depression (48 mm length, 10 mm height) is present posteroventrally, likely for the attachment of jaw adductor musculature.

The parasymphyseal dental plate is visible in dorsal view: this small and hook-shaped extension of the dentary (26 mm length, 10 mm of maximum width) is posteriorly directed but does not bear teeth or tusks, as is the case in many stegocephalian taxa (e.g., Ichthyostega stensioei, [START_REF] Jarvik | The Devonian tetrapod Ichthyostega[END_REF]Archeria crassidisca, Holmes 1989;Watsonisuchus madagascariensis, Steyer 2003).

Dermo-sensory and/or nutritive canals (Fig. 6)

Thanks to the CT-scan, dermo-sensory and/or nutritive canals were observed within the premaxilla, maxilla, prefrontal, jugal, and dentary. The premaxillary canal is well developed: it corresponds to a large primary canal (1-3 mm in diameter) which ramifies into smaller secondarily canaliculi (of sub-millimeter diameter) connected to the surface of the bone by tiny foramina. Interestingly, such foramina are also found in Bystrowiella schumanni [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF]. The dentary canal is also well developed and ramified: its primary canal separates from the Meckelian space to follow it in the anterior direction, then it bifurcates anteriorly in secondarily straight canaliculi also emerging and reaching the lateral surface of the hemimandible. These internal canals may result from an internalization of the lateral-line system, as noted in other chroniosuchians [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF][START_REF] Golubev | Revision of the Late Permian chroniosuchians (Amphibia: Anthracosauria) from Eastern Europe[END_REF]). Their possible function is discussed below.

Phylogeny (Fig. 10) To potentially reinforce the results of using the matrix of [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF] in our phylogenetic analysis, we also tested a preliminary analysis using the matrix of Buchwitz et al. Laosuchus naga (premaxilla short and blunt, C29(1) in [START_REF] Buchwitz | On the use of osteoderm features in a phylogenetic approach on the internal relationships of the Chroniosuchia (Tetrapoda: Reptiliomorpha)[END_REF]. For these reasons, we found the matrix of [START_REF] Buchwitz | On the use of osteoderm features in a phylogenetic approach on the internal relationships of the Chroniosuchia (Tetrapoda: Reptiliomorpha)[END_REF] not useful for determining the systematic position of Laosuchus naga.

In
We therefore used the matrix of [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF] by adding Laosuchus naga and Bystrowiella schumanni [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF], by combining their previous characters 1 and 2 (into our current character 1), and by recoding 28 character states (see Supplementary Information). We also used the name of the only microsaur Asaphestera instead of 'microsauria' as [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF] did. The slightly modified matrix contains 25 taxa and 51 characters (see Supplementary Information) and was analysed by the branch and bound algorithm and ACCTRAN optimization of PAUP 4.0, with all the character states unordered (except for numbers 35 and 48 because they correspond to a morphological transformation series) and equally weighted. We used Ichthyostega stensioei [START_REF] Jarvik | The Devonian tetrapod Ichthyostega[END_REF] as the outgroup.

These parameters correspond to those of [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF]. Silvanerpeton (which is here a stem-anthracosaur), and Jarilinus (which may not be strictly related to Chroniosuchus, as both form a polytomy with other chroniosuchians).

Laosuchus naga and Bystrowiella schumanni fall at the base of the chroniosuchian clade (Fig. 10), with which they share the following synapomorphies: Unequivocal C7(1); C35(2); C36(1); C48(1); Equivocal C51(1); and the following symplesiomorphies: Unequivocal C14(1);

Equivocal C33(0); C42(0). The assignment of Laosuchus naga to Chroniosuchia is also supported by a strong Bremer index of 4. Within chroniosuchians, Laosuchus naga is sistertaxon to the clade (Bystrowiana (Chroniosuchus, Jarilinus (Chroniosaurus, Madygenerpeton))).

Discussion

Taxonomic assignment

The assignment of Laosuchus naga to Chroniosuchia could be questionable if the definition of the clade by Witzmann & Schoch (2017) was strictly followed. Indeed, Laosuchus naga is unfortunately not represented by vertebrae or osteoderms which bear typical characters diagnosing the clade Chroniosuchia [START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF]. However, in our phylogenetic analysis, of the nine character states to be found supporting the clade These features also exclude Laosuchus naga from the other stem-amniote groups, i.e. from the Embolomeri (which do not present the features 1-4 and 7-10 mentioned above), the Gephyrostegidae (Gephyrostegus bohemicus [START_REF] Carroll | Problems of the origin of reptiles[END_REF]) used in our analysis does not present the features 1, 5, 6, 9, 10 mentioned above), and the Seymouriamorpha (which do not present the features 1, 5, 6 mentioned above, based on Discosauriscus austriacus [START_REF] Klembara | The cranial anatomy of Discosauricsus Kuhn, a seymouriamorph tetrapod from the Lower Permian of the Boskovice Furrow (Czech Republic)[END_REF], Kotlassia prima [START_REF] Bystrow | Kotlassia prima Amalitzky[END_REF], Seymouria baylorensis [START_REF] Laurin | A redescription of the cranial anatomy of Seymouria baylorensis, the best known seymouriamorph (Vertebrata: Seymouriamorpha)[END_REF]). For these reasons, we consider Laosuchus naga to be a chroniosuchian. As mentioned above, two families are present within the clade, the Chroniosuchidae and the Bystrowianidae:

-As for the Bystrowianidae, Laosuchus naga shares with Bystrowiella schumanni an elongated jugal only, and with Bystrowiana permira a distinct transverse process with a descending flange and an elongated jugal only: these similarities, compared with the many differences observed between Laosuchus naga and these Bystrowianidae respectively (see description above), are therefore not sufficient to assign Laosuchus naga to this family.

-As for the Chroniosuchidae, Laosuchus naga does not show the preorbital fenestra typical of the family. It does share palatal characters with Chroniosaurus dongusensis and Chroniosuchus paradoxus (see comparison above), but as the palate is not known in Bystrowianidae, it is not possible to know if these characters are typical of Chroniosuchia or Chroniosuchidae.

Moreover, Laosuchus naga does not fall close to a chroniosuchid in our phylogenetic analysis.

For all these reasons mentioned above, we consider Laosuchus naga to be a Chroniosuchia, but of unknown familial affiliation.

Chroniosuchian interrelationships

The position of Chroniosuchia within early tetrapods varies according to the authors:

- Luang Prabang Basin, which has also yielded dicynodont material described by [START_REF] Battail | Late Permian dicynodont fauna from Laos[END_REF] and analysed in detail by Olivier et al. (submitted). No other vertebrates are known from this basin so far. As the holotypic specimen was found in-situ, in a volcaniclastic siltstone layer of the Luang Prabang Basin (see above), it is not geologically reworked. As such, the maximum age of Laosuchus naga is that of its host strata, which were radiometrically dated of 251.0 ± 1.4 My according to the U-Pb dating of [START_REF] Rossignol | The volcaniclastic series from the Luang Prabang Basin, Laos: A witness of a triassic magmatic arc[END_REF] based on detrital zircons. This age estimate overlaps with the Permian-Triassic (PT) boundary according to most recent studies [START_REF] Shen | Calibrating the end-Permian mass extinction[END_REF]. The occurrence of a chroniosuchian in this part of the world and at this time brings interesting implications in term of palaeobiogeography and evolution.

Asia is composed of a mosaic of tectonic plates including the North China Block (hereafter NCB), the South China Block (SCB), and the Indochina Block (IB; where Laos is located). As these plates have very complex histories during the Permian and the Triassic (e.g. Metcalfe 2011), the reconstruction of Pangea remains highly debated concerning this part of the world.

Two different palaeogeographic scenarios of eastern Pangea have been proposed for the PT interval: the first scenario suggests that the NCB, the SCB and the IB were at least partly separated by ocean(s) (e.g. Zhang et al. 2013), whereas the second scenario suggests that these blocks were connected like a peninsula linked to Laurussia (e.g. [START_REF] Buffetaut | The contribution of vertebrate palaeontology to the geodynamic history of South East Asia[END_REF][START_REF] Metcalfe | Palaeozoic and Mesozoic tectonic evolution and palaeogeography of East Asian crustal fragments: the Korean Peninsula in context[END_REF][START_REF] Metcalfe | Tectonic framework and Phanerozoic evolution of Sundaland[END_REF][START_REF] Vuong | U/Pb and Sm/Nd dating on ophiolitic rocks of the Song Ma suture zone (northern Vietnam): evidence for upper paleozoic paleotethyan lithospheric remnants[END_REF]).

As mentioned above, chroniosuchian fossils are known from the middle Permian to Middle Triassic of Russia, middle to upper Permian of China, Middle Triassic of Germany and Middle/Upper Triassic of Kyrgyzstan (e.g. [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF][START_REF] Young | A new Late Permian fauna from Jiyuan, Honan[END_REF][START_REF] Witzmann | A relic basal tetrapod from the Middle Triassic of Germany[END_REF]Schoch et al. 2010, respectively). The new occurrence of the amphibious Laosuchus naga in nonmarine rocks therefore supports the second palaeogeographic scenario, as previously proposed by [START_REF] Buffetaut | The contribution of vertebrate palaeontology to the geodynamic history of South East Asia[END_REF]. This scenario also fits with the discovery of dicynodont material (terrestrial species) in the same Purple Claystones Formation of Laos [START_REF] Battail | Late Permian dicynodont fauna from Laos[END_REF]Olivier et al. submitted).

Possible function(s) of the dermo-sensory and/or nutritive canals

Two kinds of canals have been found in Laosuchus naga: simple canals in the skull roof (Fig. 6A) and ramified canals in the premaxilla, maxilla and mandible (Fig. 6A,C).

The simple canals are interpreted as internalized sulci belonging to the lateral line system, considering their 1) location on the skull roof, 2) close proximity with the bone surface, and 3) shape. As in most modern fish, the lateral line system allows the animal to perceive displacements in surrounding water (i.e. a water flow). Similar canals have been found in other non-amniote tetrapods, with a similar function inferred (e.g. [START_REF] Ahlberg | The first tetrapod finds from the Devonian (Upper Famennian) of Latvia[END_REF][START_REF] Jarvik | The Devonian tetrapod Ichthyostega[END_REF][START_REF] Clack | The dermal skull roof of Acanthostega gunnari an early tetrapod from the Late Devonian[END_REF].

The ramified canals observed in Laosuchus naga are the first ones found in a fossil amphibian.

As the structure differs from sulci and are deeper in the bone, they likely had a different function from the lateral line system. Their diameter and ramified structure are consistent with a vascular system, hence suggesting a blood irrigation function. As these ramifications are located at the tip of the snout and mandible, this possible irrigation may be associated with a sensory function.

Similar canals, called "neurovascular canals", are also known in living species where they have various sensorial functions in addition to irrigation: mechanoreception in crocodiles and birds [START_REF] Soares | Neurology: an ancient sensory organ in crocodilians[END_REF][START_REF] Leitch | Structure, innervation and response properties of integumentary sensory organs in crocodilians[END_REF][START_REF] Schneider | Neuronal mechanism for acute mechanosensitivity in tactile-foraging waterfowl[END_REF], thermoreception in lizards and snakes (e.g. [START_REF] Seebacher | Physiological mechanisms of thermoregulation in reptiles: a review[END_REF], electroreception in platypus [START_REF] Gregory | Electroreceptors in the platypus[END_REF]. In crocodiles, these canals are used when the head of the animal is half-emerged to detect surface waves (i.e., pressure waves) generated by prey moving in water which help with prey capture, especially in low-visibility conditions (e.g. turbid waters, crepuscule/night period) [START_REF] Soares | Neurology: an ancient sensory organ in crocodilians[END_REF][START_REF] Leitch | Structure, innervation and response properties of integumentary sensory organs in crocodilians[END_REF].

There is some evidence suggesting that mechanoreception is a plausible function for the canals via nervous structures associated to the significant blood irrigation. The numerous small conical and curved teeth indicate that Laosuchus naga was a predator. Moreover, the sediments that yielded Laosuchus naga suggest a fluviatile river environment [START_REF] Bercovici | Permian continental paleoenvironments in southeastern Asia: new insights from the Luang Prabang Basin (Laos)[END_REF]) under a tropical, warm and wet climate (e.g. [START_REF] Fluteau | The Late Permian climate. What can be inferred from climate modelling concerning Pangea scenarios and Hercynian range altitude? Palaeogeography[END_REF][START_REF] Bercovici | Permian continental paleoenvironments in southeastern Asia: new insights from the Luang Prabang Basin (Laos)[END_REF]. These characteristics suggest a similar ecology with living crocodiles, which also share morphological cranial convergences with Laosuchus naga (e.g. elevated skull table and orbits, long triangular snout, predator dentition). Hence, regarding morphological and ecological similarities, the ramified canals may have had the same additional function of mechanoreception. This possible function seems redundant with that of its internal sulci, but both systems (neurovascular and lateral line) are not sensitive to the same stimuli, both in nature (particle displacement versus pressure waves) and efficiency area (underwater versus water surface). Hence, the pressure waves system would have been complementary to the internal sulci.

Surviving the Permian-Triassic crisis?

Chroniosaurus dongusensis is one of the earliest chroniosuchians [START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF] but not the most basal one, according to our phylogenetic analysis (Fig. 8). Additionally, the microsaur Asaphestera intermedia (from the Upper Carboniferous) was found as the sistertaxon to the chroniosuchian clade. This relationship suggests a long ghost lineage of the chroniosuchians, as suggested by [START_REF] Buchwitz | On the use of osteoderm features in a phylogenetic approach on the internal relationships of the Chroniosuchia (Tetrapoda: Reptiliomorpha)[END_REF]. However, this clade is known to have survived the PT mass extinction (e.g. [START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF][START_REF] Buchwitz | On the use of osteoderm features in a phylogenetic approach on the internal relationships of the Chroniosuchia (Tetrapoda: Reptiliomorpha)[END_REF]. If Laosuchus naga can be confirmed as Triassic in age, its lineage must have also crossed the Permo-Triassic boundary. Even if some factors such as those involving palaeoclimates and/or palaeogeography can be put forward to explain these survival cases, it seems that more and more tetrapods survived the largest mass extinction of the Phanerozoic.

Conclusion

Laosuchus naga gen. et sp. nov., is described as the first chroniosuchian from Laos on the basis of a well-preserved skull and a left hemimandible found in natural articulation. The radiochronologic age of the sediments yielding the specimen gives a late Permian-Early

Triassic age, which suggests that this new taxon may have survived the Permian-Triassic mass extinction. Laosuchus naga is represented by one of the best preserved chroniosuchian skulls.

However, it remains of unknown familial relationships because the holotype does not preserve any postcranial elements. As a nonmarine tetrapod, Laosuchus naga also has important palaeobiogeographic implications: its occurrence on the Indochinese Block and its phylogenetic position suggest that the Indochinese Block was connected to the surrounding tectonic blocks during late Permian-Early Triassic times. Laosuchus naga was analysed by computed microtomography and is the first chroniosuchian for which the internal anatomy has been described.

This 3D analysis revealed in particular new ramified canals inside the dentary, maxillae and premaxillae: they are interpreted as nutritive and/or dermo-sensory canals, probably linked with pressure receptors. Our phylogenetic analysis pointed out an important ghost lineage between Chroniosuchia and their close stem-amniote relatives. However, chroniosuchians remain a rare and poorly known clade: further studies will provide essential information to better understand the evolution of stem-amniotes.

Figure 1 .

 1 Figure 1. Geographical and geological context of Luang Prabang Basin. A. Sedimentary log from "Tan South" Section (after Bercovici et al. 2012; see theirTable 1 for more details about lithofacies), scale in meters; B. Map of Southeast Asia; C. Map of Laos with the Mekong River in grey.

:

  Laosuchus naga has the following autapomorphies: (1) pineal foramen extremely reduced (1 mm of diameter); (2) absence of palatal dentition (no tusks, dental rows or dental alveoli); (3) well-developed transverse flange of the pterygoid that contacts the maxilla; (4) internal crest on and above the dorsal side the palate (vomer, ectopterygoid and pterygoid); (5) otic notch closed by the tabular horn and the posterior part of the squamosal, forming a continuous wall; (6) thin and high ventro-medial ridge on parasphenoid. Diagnostic characters, but not exclusive to Laosuchus naga: (1) absence of paired preorbital fenestrae; (2) presence of a premaxillary fontanelle; (3) maxilla and quadratojugal separated by jugal; (4) absence of anterior palatal vacuity; (5) pterygoid with transverse process and descending flange; (6) jaw with parasymphyseal dental plate.

  Chroniosuchia (according to the character states in our phylogenetic analysis and anatomical comparisons, see below for details and discussion): (1) skull roof with elaborate system of oblique transverse and sagittal ridge; (2) presence of premaxillary fontanelle; (3) prefrontal and jugal in contact anterior to orbit; (4) pterygoid flange well developed; (5) very narrow parasphenoid with a crest between the basicranial joint; (6) braincase poorly ossified.

Figure 2 .

 2 Figure 2. Laosuchus naga gen. et sp. nov. (specimen MDS-LPQ 2005-09) from the Permian/Triassic boundary of Laos in dorsal view. A. specimen photograph; B. 3D model produced with Mimics ® ; C. anatomical drawing; D. interpretive drawing. Scale bar = 100 mm

Figure 3 .

 3 Figure 3. Laosuchus naga gen. et sp. nov. (specimen MDS-LPQ 2005-09) from the Permian/Triassic boundary of Laos in left lateral view. A. specimen photograph; B. 3D model produced with Mimics ® ; C. anatomical drawing; D. interpretive drawing. Scale bar = 100 mm

  shows very large trapezoidal choanae (75 mm length, 20 mm width) with rounded posterior extremities. These openings are especially large and elongated compared to those of other chroniosuchians and anthracosaurs (the ratio between choanae length and skull length is 0.34 in Laosuchus naga compared to 0.14 for Anthracosaurus russelli, Panchen 1977; 0.14 for Proterogyrinus scheelei, Holmes 1984; 0.17 for Chroniosuchus paradoxus,[START_REF] Novikov | Permian and Triassic anthracosaurs from Eastern Europe[END_REF] and 0.16 for Chroniosaurus donguensis,[START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF].

Figure 4 .

 4 Figure 4. Laosuchus naga gen. et sp. nov. (specimen MDS-LPQ 2005-09) from the Permian/Triassic boundary of Laos in palatal view. A. specimen photograph; B. 3D model produced with Mimics ® ; C. anatomical drawing; D. interpretive drawing. Scale bar = 100 mm

  median ridge and the crista muscularis delimit two subtriangular muscular pockets, which are exceptionally deep in comparison with those of others stem-amniotes (e.g. Chroniosaurus dongusensis,[START_REF] Klembara | The anatomy of palate of Chroniosaurus dongusensis (Chroniosuchia, Chroniosuchidae) from the Upper Permian of Russia[END_REF] Chroniosuchus paradoxus, Novikov et al. 2000; Discosauriscus austriacus, Klembara 1997; Archeria crassidisca, Holmes 1989).

Figure 5 .

 5 Figure 5. 3D model of left and right pterygoids in anterior view of Laosuchus naga gen. et sp. nov. (specimen MDS-LPQ 2005-09) produced with Mimics ® . Scale bar = 50 mm.

Figure 6 .

 6 Figure 6. 3D model of the internal canal system and cranial structures of Laosuchus naga gen. et sp. nov. (specimen MDS-LPQ 2005-09) produced with Mimics ® . Skull roof and left hemimandible are transparent. A. dorsal view of the skull roof. Scale bar = 60 mm; B. dorsal view with skull roof removed. Scale bar = 60 mm; C. Lateral view of left hemimandible (scale bar = 60 mm) with close up on the anterior extremity of the left hemimandible in dorsal (scale bar = 10 mm).

Figure 7 .

 7 Figure 7. Laosuchus naga gen. et sp. nov. (specimen MDS-LPQ 2005-09) from the Permian/Triassic boundary of Laos in occipital view. A. specimen photograph; B. 3D model produced with Mimics ® ; C. anatomical drawing. Scale bar = 100 mm

  Figure 8. 3D model of the occipital area in anterolateral view of Laosuchus naga gen. et sp. nov. (specimen MDS-LPQ 2005-09) produced with Mimics ® . Scale bar = 20 mm

Figure 9 .

 9 Figure 9. Left hemimandible of Laosuchus naga, gen. et sp. nov. (specimen MDS-LPQ 2005-09) from the Permian/Triassic boundary of Laos. 3D model in A, labial view; B, dorsal view; and C, lingual view. Scale bar = 50 mm; D. tomography of the anterior extremity of the left mandible. Scale bar = 5 mm

  order to determine the phylogenetic position of Laosuchus naga among early tetrapods, we conducted a phylogenetic analysis. The recent and most exhaustive phylogenies dealing with early tetrapods including reptiliomorphs are those of Schoch et al. (2010), Buchwitz et al. (2012), and Witzmann & Schoch (2017), which take into account 5, 12 and 2 chroniosuchian taxa respectively. As the matrix of Schoch et al. (2010) also contains the largest proportion of cranial characters compared with postcranial ones (i.e. 65.4%, contra 48.6 and 35.3% for the matrices of Buchwitz et al. (2012) and Witzmann & Schoch (2017) respectively), it is believed to be the most relevant dataset here to test the relationships of Laosuchus naga within chroniosuchians.

Figure 10 .

 10 Figure 10. Phylogenetic position of Laosuchus naga mapped on a stratigraphic scale. Strict consensus (L = 139 steps; CI = 0.417; RI = 0.645) of 18 MPTs based on 25 taxa and 51 characters. Black numbers represent Bremer Index.

(

  2012), adding Laosuchus naga and Bystrowiella schumanni[START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF], and using the heuristic search algorithm and ACCTRAN optimization of PAUP 4.0[START_REF] Swofford | PAUP*, Phylogenetic analysis using parsimony (*and other methods)[END_REF]: we obtained 416 most parsimonious trees (MPTs) of 158 steps (CI = 0.519; RI =0.759), the strict consensus of which (see Supplementary Information) placed Laosuchus naga as sistertaxa to Madygenerpeton pustulatus[START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF] but based on optimization of missing characters mostly. Moreover, on nine characters supporting the monophyly of Chroniosuchidae (six based on osteoderms, three based on skull), only one unambiguous symplesiomorphic character is coded in Laosuchus naga (quadrates well posterior to condyles, C55(0) in Buchwitz et al. 2012); and on eight characters supporting the monophyly of Bystrowianidae (five based on osteoderms, three based on skull), only one ambiguous synapomorphic character is found in

  Our analysis resulted in 18 MPTs of 130 steps (CI = 0.446; RI = 0.692), the strict consensus of which is shown in Figure 10. Our results are mostly congruent with those of Clack & Klembara (2009), Schoch et al. (2010) and Witzmann & Schoch (2017), as anthracosaurians (including Silvanerpeton or not) and chroniosuchians form two distinct clades. Compared with Schoch et al. (2010), our results are almost the same except for the position of Greererpeton (which forms a polytomy with Eucritta, Balanerpeton, Cochleosaurus and the stem-amniote clade here),

  Chroniosuchia [C7(1); C14(1); C33(0); C35(2); C36(1); C42(0); C48(1), C51(1)], three are known in Laosuchus naga [C14(1); C33(0); C51(1)]. Moreover, although none of the following anatomical features are exclusive to Chroniosuchia, their combination is characteristic and strengthens the attribution of Laosuchus naga to Chroniosuchia: 1, elaborated system of oblique, transverse, and sagittal ridges; 2, absence of external sulci; 3, elongated choanae; 4, well-developed transverse process of pterygoid; 5, internal flange of pterygoid; 6, extremely thin cultriform process of the parasphenoid; 7, thin quadrate (in ventral view); 8, strong reduction of the braincase ossification; 9, single Meckelian fenestra; 10, low surangular crest.

  [START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF] and[START_REF] Buchwitz | On the use of osteoderm features in a phylogenetic approach on the internal relationships of the Chroniosuchia (Tetrapoda: Reptiliomorpha)[END_REF] (using a modified version of the matrix of[START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF]), Chroniosuchia have a relatively derived position close to the lepospondyl Asaphestera intermedia.-In[START_REF] Clack | An articulated specimen of Chroniosaurus dongusensis, and the morphology and relationships of chroniosuchids[END_REF] and[START_REF] Witzmann | Skull and postcranium of the bystrowianid Bystrowiella schumanni from the Middle Triassic of Germany, and the position of chroniosuchians within Tetrapoda[END_REF] (all using a modified version of the matrix ofRuta & Clack, 2006), Chroniosuchia form a polytomy with Silvanerpeton miripedes, Embolomeri and another clade comprising Seymouriamorpha, Gephyrostegidae, Lepospondyli and the amniote Paleothyris acadiana. As the matrix ofRuta & Clack (2006), used as starting point in these analyses, includes more characters and stem-tetrapod taxa than that of[START_REF] Schoch | A chroniosuchid from the Triassic of Kyrgyzstan and analysis of chroniosuchian relationships[END_REF] (except for the number of chroniosuchian taxa), these results are believed to be more relevant concerning the interrelationships of Chroniosuchia. It is however the opposite for the intrarelationships of the chroniosuchians (see above).Interestingly, all the analyses of mentioned above suggest similar relationships (i.e., Embolomeri, (Gephyrostegidae (Seymouriamorpha, Lepospondyli))), with only Chroniosuchia variably positioned among these taxa. Consequently, it is evident that these problematic chroniosuchians require further studies and phylogenetic analyses: one idea could be to integrate the best preserved chroniosuchian taxa in the exhaustive matrix ofRuta & Clack (2006) -or a modified version of it -to better test their intra-and inter-relationships at the same time. But such an analysis would require first-hand examination of a large number of stemamniote taxa, and goes beyond the scope of this study.Palaeobiogeographic implications (Fig. 11)Laosuchus naga is the first chroniosuchian from Laos. It was found in the Permo-Triassic

Figure 11 .

 11 Figure 11. Stratigraphic and geographic distribution of chroniosuchian fossils. A. Presentday geographic map B. Late Permian palaeogeographic map (modified from Metcalfe 2011).

Acknowledgements

-We thank B. Battail, M. Véran, P. Richir (MNHN), R. Damiani (ex. BPI Johannesburg), J.-P. Porte (CERN), B. Khenthavong (Autorité Nationale pour la Science et la Technologie, Musée des Dinosaures, Savannaketh), B. Phanmongkhoune (Bureau de la Culture, Luang Prabang Province), S. Lorrain and M. Boulay (Cossima Productions) for field assistance, P. Richir (MNHN) for the extraction, R. Vacant (CR2P CNRS) for the preparation, P. Loubry (CR2P CNRS) and L. Caze (MNHN) for the photos, S. Vongphamany (Department of Patrimony, Museums and Archeology, Vientiane) for field authorization and exportation permit. We thank the Governor of the Luang Prabang Province for assistance, J.-P. Cuomo and F. Engelmann (Luang Prabang) for their support. NGS grant 7655-04 (to JSS), and a MESR Doctoral grant (to TA) supported this research. We thank M. Buchwitz and an anonymous reviewer for their useful comments.


Satyanarayana Bade

Lionel Djadaojee

Manuel Andia

Pierre Cladé
email: pierre.clade@lkb.upmc.fr

Saïda Guellati-Khelifa

Observation of Extra Photon Recoil in a Distorted Optical Field

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Light carries momentum which induces on atoms a recoil for each photon absorbed. In vacuum, for a monochromatic beam of frequency ν, the global momentum per photon is bounded by general principles and is smaller than hν/c leading to a limit on the recoil. However, locally this limit can be broken. In this paper, we give a general formula to calculate the recoil in vacuum. We show that in a laser beam with a distorted optical field, there are regions where the recoil can be higher than this limit. Using atoms placed in those regions we are able to measure directly the extra recoil.

Light exerts upon a surface a pressure called the radiation pressure. From a classical perspective, this pressure is described by a linear momentum with a density that is proportional to the energy flux, the Poynting vector [START_REF] Jackson | Classical electrodynamics[END_REF]. From a quantum mechanical point of view, the pressure corresponds to momentum carried by photons. The momentum p is defined only for a plane wave and has an amplitude proportional to the energy (or the frequency ν) of the photon || p|| = hν/c.

When an atom of mass m absorbs a photon, the momentum of the photon induces a recoil on the atom. The recoil velocity, v r = hν/mc, plays an important role in atomic physics (laser cooling and atom interferometry). The recoil velocity has been measured with a very high accuracy for the determination of the fine structure constant [START_REF] Bouchendira | [END_REF][3][4][5]. Measuring the recoil of atoms is also a tool to probe the local momentum of light. Even though the absorption of photons is quantized, the best way to calculate the recoil velocity is to use the classical momentum given by the ratio between the density of linear momentum and the photon density. This approach reveals interesting properties of light, such as in the evanescent regime where a recoil velocity larger than hν/mc (i.e an extra recoil velocity) is expected [6,7].

In this paper, we show that the extra recoil is actually not limited to the case of an evanescent wave: even in a beam propagating in vacuum the momentum of a photon can be locally higher than hν/c. Using atoms placed in these locations, we have been able to confirm experimentally this effect.

For a linearly polarized beam and under the paraxial approximation one can use the scalar diffraction theory to describe the optical field [START_REF] Born | Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (7th Edition)[END_REF]. The momentum of a photon is given by the canonical momentum p = ∇φ, where φ is the spatial phase of the laser [START_REF] Antognozzi | [END_REF][10]. Let us consider a laser beam propagating along the z axis of which we know the amplitude A(x, y, z 0 ) and phase φ(x, y, z 0 ) on the plane z = z 0 . One can use the Helmholtz equation to propagate the wavefront along the z axis and therefore deduce the z component p z of the momentum at position

z 0 , p z = k(1 + δk rel ) with δk rel = - 1 2
∇ ⊥ φ k 2 + 1 2k 2 ∆ ⊥ A A (1)
where ∆ ⊥ and ∇ ⊥ are evaluated in the plane z = z 0 and k = 2πν/c. The first term related to the phase gradient corresponds to a tilt in the propagation direction with respect to the z axis due to a local distortion of the wavefront. The second term gives a correction to the momentum even in the case of a plane wavefront. This counter intuitive term is actually a generalization of effects already identified in situations where an analytical solution exists, such as evanescent and Gaussian beams.

In the case of an evanescent wave A 0 e αy-iβz , the longitudinal momentum, proportional to β, is usually obtained with the dispersion relation (β 2 -α 2 = k 2 ). At first order in α (paraxial approximation), this equation leads to β/k = 1 + α 2 /2k 2 , the value obtained by calculating the Laplacian of the amplitude. In [7], the extra recoil observed in the saturation spectroscopy was explained by the pseudo-momentum of the photon in the refractive medium used to generate the evanescent wave. We should notice that the extra recoil can be explained by Eq. (1) which does not imply to be close to the surface of the refractive medium. As we will see, even in vacuum, positive correction to the recoil could be observed.

For a Gaussian beam, at the position of the waist, ∇ ⊥ φ = 0, and the momentum of light is given by the Laplacian of the amplitude. This leads to a correction of the momentum

p z k = 1 - 2 k 2 1 w 2 - r 2 w 4 (2)
which gives a correction to the atomic recoil, the well known Gouy phase correction [3,11,12], calculated using the analytical value of the phase of a Gaussian beam. Atoms being placed usually at the center of a Gaussian beam experience a negative correction. This correction is interpreted with the dispersion in momentum of the plane wave decomposition of the laser beam [13]. Each plane wave tilted by an angle θ with respect to the z-axis gives a negative correction -θ 2 /2. The average longitudinal momentum reduction is δk rel = -1/(kw) 2 . Locally, the correction is different: at the center the correction is twice this value and at large distances, the sign of the correction changes: even for a Gaussian beam, an extra recoil can be observed.

In this paper we consider a more general case of distorted optical field with amplitude noise and phase noise. We should first note that the spatial phase and amplitude fluctuations are mixed during propagation. Even a wave-front distortion caused by optics will appear as amplitude fluctuations after propagation. Furthermore both the relative fluctuations of the amplitude (σ A /A) and the phase fluctuations (σ φ ) have the same standard deviation. In Eq. ( 1), the term due to wave-front distortions (which scales as σ 2 φ ) is therefore negligible compared to the term due to amplitude fluctuations, which scales as σ A /A. This leads to a counter intuitive result: the term due to spatial intensity fluctuations, which is usually ignored, is dominant over the term due to wave-front distortions. In the rest of the paper, the latter is always neglected.

In order to estimate the correction due to the local fluctuations of the amplitude we consider, for the sake of simplicity, an optical wave with an auto-correlation function of the amplitude given by σ 2 i e -(x 2 +y 2 ) 2 /l 2 /4. The parameter l is the correlation length that gives the scale of the second term of Eq. ( 1) and σ i is the RMS relative intensity noise. Using the wave-vector power spectral density (WV-PSD) we estimate σ(δk rel ) at √ 2σi (kl) 2 (for details see [14]). It is important to note that this term is different from the average momentum of the photons that can also be calculated from the WV-PSD, yielding -

σ 2 i 2(kl) 2 .
This result is related to the previous one: even though the typical value of the longitudinal momentum of plane-wave photons scales as σ 2 i /(kl) 2 , due to coherence between the different plane waves, the local momentum fluctuates with a much higher amplitude. Let us take for example l = 100 µm and RMS amplitude of σ i = 0.05 for a light wave-length of λ = 780 nm. This corresponds to typical values when using poor quality optical elements. The RMS value of δk rel is 100 ppb. The amplitude of this effect is much larger than the sensitivity of atom recoil measurements performed using atom interferometry. However it has never been observed yet because experiments measure the average recoil and are not sensitive to local fluctuations.

To observe this effect one can take advantage of the correlation between local light momentum and light-field intensity: indeed, this correlation arises from the Laplacian term in equation 1, which changes sign between minima and maxima of intensity. To illustrate and understand this correlation and how the experiment takes advantage of it, we have performed a numerical simulation of the propagation of a noisy light profile. We generated a field on the (x, y) plane with a uniform intensity and a random phase noise with a typical correlation length l = 100 µm and RMS amplitude of 0.07 rad. Figure 1 shows a slice of this beam taken in the (x, z) plane after a propagation of 50 cm. The high or low intensity regions have a typical width of l = 100 µm and a typical length of z l = l 2 /λ 1 cm. On the right of the picture, we have plotted the phase of the laser beam only for those regions. For high intensity regions (continuous contour), the phase evolves from typically 0.05 rad on the top to -0.05 rad at the bottom (red to blue, or σ i to -σ i ): there is a negative correction to the photon momentum with a relative amplitude that scales as σ i /kz l , i.e. σi (kl) 2 as calculated above. The opposite occurs for low intensity regions (dashed line).

Therefore, in order to see this effect, one has to select atoms in regions of relatively high or relatively low intensity. For that let us consider an experiment sensitive to the momentum of light: if the probability P (I) to transfer light momentum to the atoms depends on the intensity, the spatial distribution of atoms is filtered and is therefore correlated to the local photon momentum. This gives rise to a correction with respect to the average momentum δk rel = δk rel P (I)

P (I) (3)
As I and δk rel are anti-correlated (see [14]), the correction due to local fluctuations of the light momentum can be negative or positive depending on whether P (I) is a decreasing or an increasing function of intensity. This is what we observed in the experiment described below.

Our experiment uses Bloch oscillations (BO) in an accelerated optical lattice [15,16] to transfer a large number of recoils to ultra-cold 87 Rb atoms. The recoil velocity is then measured via the Doppler effect using atom interferometry. A detailed description of the experimental set-up can be found in [START_REF] Bouchendira | [END_REF]. We use an atomic cloud of nearly 10 6 atoms with a 2 mm radius and at a temperature of 4 µK. The interferometer is operated in the usual Ramsey-Bordé configuration with a Ramsey time of 10 ms. It uses two pairs of π/2 light pulses that drive a Raman transitions between the hyperfine levels F = 1 and F = 2. The first pair selects atoms which are then coherently accelerated with 250 BO in 3.5 ms, followed by the second pair that measures the total momentum transferred between the two pairs of pulses. Interference fringes are obtained by scanning the frequency δ meas of the last pair of pulses (see Fig. 2) and by measuring the relative population in each hyperfine level (F = 1 and F = 2) using time-of-flight technique.

The efficiency of BOs depends sharply on the intensity of the laser. If the intensity is lowered, due to Landau-Zener losses only the atoms in the higher intensity regions survive the BO and are involved in the interferometer. For instance, if 50% of the atoms are lost during BO, the remaining atoms are mainly in the regions where the intensity is larger than the average and a negative effect of the order of σi (kl) 2 should be observed. We repeat the recoil measurement by scanning the intensity of the Bloch beams (see Fig. 2.a), we measure also the fraction of atoms that survive BOs, this fraction gives the efficiency η of BOs. Dots in Fig. 3 show the relative recoil velocity with respect of the value obtained in [START_REF] Bouchendira | [END_REF] as function of η. We choose this representation because, as we will see latter, in our model this curve is FIG. 3. The relative recoil velocity variation δvr/vr as a function of efficiency η. Dots correspond to experimental data which are obtained in two cases: with and without clipping one of the Bloch beams. The deviation in the momentum from the ideal plane wavefront is larger when the beam is clipped due to amplified fluctuations. Line: calculated correction due to the change in momentum δk rel as a function of the efficiency of BOs (from Eq. 5). In our model, this curve is universal. The only parameters are the RMS intensity fluctuations σi and the correlation length l of those fluctuations which give the amplitude factor (σi/(kl) 2 ) of the correction.

universal. As the intensity is lowered, the BOs efficiency decreases (see [14]) and the deviation becomes larger. In order to confirm the effect, one of the two Bloch beams is clipped with an aperture of diameter 3 mm to amplify the intensity fluctuations. Here, we clearly observe an increased deviation from the plane wave momentum when the beam is clipped for a given η.

In order to observe an extra recoil, one has to place atoms in regions of relatively low intensity. To this end, we have changed the temporal sequence of the experiment (Fig. 2.b): just before the acceleration, we perform 10 BOs with a tunable intensity (Bloch pulse-A) in such a way that atoms performing BOs are removed (pushed away, they do not participate in the subsequent recoil measurement). At low intensities, no atoms are removed and hence no effect should be observed. When the power of this first Bloch beam is increased, atoms are removed from the experiment, starting with the ones that are at maxima of intensity. For higher power, only atoms at minima survive. The first Bloch pulse, used to filter the spatial distribution of atoms, is then followed by the 250 BOs at a fixed and high power which are normally used to measure precisely the recoil velocity (Bloch pulse-B on Fig. 2

.b).

Figure 4 shows the results. This experiment was performed with one of the beams being clipped by a 3 mm aperture. Without losses, we observe a momentum slightly smaller than k, this is the same effect described earlier. However, when the number of atoms is reduced by the selecting BOs, the measured photon momentum increases, leading to an effect larger than 4 × 10 -8 . One would expect to see a correction with an opposite sign and the same amplitude in comparison with the data shown in Fig. 3, but we observe a reduction of the amplitude of the effect that can be explained by the motion of atoms between the selection and measurement pulses: even if they are selected at low intensity, the transverse motion of the atoms brings them to regions of higher intensity, leading to a reduction of the correction.

Let us now discuss quantitatively the experimental data. For BOs, the probability P (I) is governed by the Landau-Zener losses. As it varies sharply with the intensity, we model it with a Heaviside function centered around a critical intensity I c [17,18]. Using this model, one can calculate an analytical expression for the efficiency η and average δk rel (from Eq.3) as a function of

I rel = (I c -I)/(Iσ i ) η = erfc(I rel / √ 2) 2 (4)
δk rel = - 1 k 2 l 2 σ i π/2 e -I 2 rel /2 η (5)
From these two quantities a parametric curve can be drawn and is used to fit the data in Fig. 3. A single parameter is used, the quantity σi (kl) 2 . For the data without beam clipping, we obtain σi (kl) 2 = 8 × 10 -8 , this corresponds to 5% of fluctuations at a scale of l = 100 µm, which is compatible with an independent measurement of the phase profile.

Since BOs are a pure coherent quantum phenomenon, one can think that the effect described and observed in this paper is rather a signature of processes which cause a decoherence of the system (spontaneous emission, interatomic interactions or disordered light potential). Since the first observation of BOs of cold atoms in optical lattices an important work has been devoted to investigate the question of decoherence [19][20][21][22][23][24][25][26]. In particular, the dynamics of BOs in disordered optical lattices has been investigated in detail in [24]. Both theory and experiment [23][24][25] have shown that even a very small disorder results in broadening of the quasi-momentum distribution that causes a damping of the center-of-mass motion. In our experiment during the Bloch acceleration atoms move by about 5 mm, this distance is smaller than the characteristic length of the intensity fluctuations along the z-axis (see figure 1). In addition, we analyzed in detail our raw experimental data (time-of-flight signals and the atomic fringes), as shown in [14] we do not observe any signature of the scattering of the quasi-momentum underlying a damping of BOs. Furthermore, we used a dilute atomic gas and the Bloch laser frequencyl is fardetuned from the resonance, thus inter-atomic interactions and spontaneous emission are negligible [START_REF] Bouchendira | [END_REF].

In this paper, we have calculated and measured locally the momentum of light using the recoil of atoms. We have been able to measure a recoil higher than the fundamental limit of hν/mc per absorbed photon. Even though the photon absorption is quantized and the velocity of the atom is well measured, it is not possible to give a precise meaning to the local momentum of the photon. For a photon, like any other particle, the momentum is defined only for a plane wave. Any other field can be decomposed as a sum of plane waves. An atom placed in this field perceives all those photons, however the transferred recoil is not the average momentum of those photons. This leads to the following result: a superposition of photons each with a momentum equal to hν/c may result in a recoil velocity larger than hν/mc for the absorption of one photon. To the best of our knowledge, we report the first ever observation of this effect. Finally, this work is also of special interest for applications of BOs and atom interferometry for high precision measurements [START_REF] Bouchendira | [END_REF]5,[27][28][29][30][31][32][33][34][35][36]

FIG. 1 .FIG. 2 .

 12 FIG.1. Simulation of a slice of the intensity (left) and phase (right) of a laser beam taken along the propagation axis (vertical axis in the figure). Random phase fluctuations with a typical size of 100 µm were generated on the (x, y) plane and propagated over 50 cm. The continuous (resp. dashed) contour shows regions of relatively high (resp. low) intensity. In the high intensity region (resp. low intensity), the phase evolves along the z direction, from a typical value of 50 mrad to -50 mrad (resp. -50 mrad to 50 mrad), leading to a local variation of the photon momentum.

8 FIG. 4 .

 84 FIG. 4. Measurement of the relative recoil in a distorted field obtained by removing atoms in the high intensity regions of the Bloch beams, following the protocol described on Fig. 2.b.

ACKNOWLEDGMENTS

This work was supported by the Agence Nationale pour la Recherche, INAQED Project No. ANR-12-JS04-0009, the Cluster of Excellence FIRST-TF and the National Institute of Standards and Technology's Precision Measurement Grant.