{"id":"49af833b-b956-4bc7-9413-e0ecc358af11","arxiv_id":"2607.05540","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"low","formal_verification":"none","parameter_count":2,"one_line_summary":"Tomographic boundary layers in a Corbino disk enhance the quadratic magnetoresistance coefficient via curvature-dependent slip and superballistic electrode conductance, yielding three B-field regimes with anomalous T/n scaling.","lead":"Tomographic electron flow in a Corbino disk creates an extended non-hydrodynamic boundary layer near electrodes that superballistically injects current and enhances azimuthal slip, parametrically boosting the quadratic magnetoresistance. The boost depends on electrode curvature and produces three magnetic-field regimes whose anomalous temperature and density scaling may explain recent viscosity measurements.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified beyond the reader's already-flagged collision-model assumption.","rationale":"The central claim is an asymptotic kinetic-theory result for Corbino magnetotransport under a standard tomographic collision model. The matched expansion, boundary-layer construction, superballistic electrode condition (Eq. 14), curvature-dependent slip (Eq. 13), and the resulting non-monotonic α(B) are internally consistent and numerically corroborated. The only load-bearing modeling choice is precisely the one the reader already flagged; no additional soft spot (e.g., incompressibility failure, neglected higher harmonics, or curvature expansion breakdown) rises to the same level. Therefore the CONDITIONAL verdict with high confidence stands without adjustment.","tokens_in":14134,"tokens_out":467,"duration_ms":4706,"concrete_test":"Re-solve the tomographic-layer ODE (17) and the resulting slip condition (13) with a non-diagonal microscopic collision operator taken from the exact-diagonalization spectra of Refs. [26,39] (instead of the constant-γe / γ'm^p model); if the superballistic electrode conductance or the leading ko-dependent slip coefficient changes by more than ~20%, the parametric enhancement of α is model-sensitive.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The reader's weakest_assumption correctly isolates the softest point: the fixed-rate even/odd collision model (paragraph after Eq. (3), with p=0 or 4) is assumed to remain valid inside the curved electrode layers where h is far from local equilibrium. The paper already mitigates this by (i) deriving the layer equations from the same operator, (ii) showing that the leading electrode conductance saturates the model-independent Raichev bound, and (iii) validating the asymptotic profiles against full numerical solutions of Eq. (1) for p=0 (Figs. 2–3, error ≤9%). No stronger internal inconsistency or hidden assumption that would overturn the three-regime structure or the curvature-tuned slip appears. The experimental link remains qualitative, as the reader notes, but that does not undermine the theoretical claim.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper develops a matched asymptotic expansion of the linearized Fermi-liquid kinetic equation for tomographic electron flow in a Corbino disk, treating even- and odd-parity modes with disparate mean free paths. It identifies an extended tomographic boundary layer of thickness √(ℓ_e ℓ_o) near the electrodes that produces superballistic electrode conductance saturating twice the Sharvin value and a curvature-dependent azimuthal slip velocity. These effects parametrically enhance the quadratic magnetoresistance coefficient α, which exhibits three magnetic-field regimes (tomographic at weak B when r_c ≳ k_o, hydrodynamic at intermediate fields, and Ohmic at large B). The weak-field tomographic corrections carry anomalous density and temperature scalings that may reconcile the non-Fermi-liquid viscosity extracted from recent Corbino experiments.","tokens_in":14352,"tokens_out":970,"duration_ms":13472,"significance":"If correct, the work supplies a concrete, geometry-tunable mechanism that converts the long-lived odd modes of a 2D Fermi liquid into measurable magnetoresistance signatures, thereby offering a route to extract both even- and odd-mode mean free paths from a single device. Strengths include a systematic O(k_e) expansion that recovers known bulk Stokes–Ohm equations while deriving new electrode boundary conditions, analytic bulk solutions in terms of modified Bessel functions, numerical layer functions, and direct benchmarks against full kinetic-equation solutions (error ≤9 % at k_e=0.1). The superballistic conductance result saturates a model-independent upper bound, and the predicted non-monotonic α(B) is a sharp, falsifiable signature of tomography.","major_comments":[{"comment":"Paragraph after Eq. (3) and End Matter: the fixed-relaxation-time collision model (constant γ_e for even m≥2, γ_MC_m=(γ'm^p+γ_e)^{-1} for odd m≥3) is assumed to remain accurate inside the curved electrode layers where the distribution is far from local equilibrium. While the leading electrode conductance saturates the model-independent Raichev bound and the p=0 asymptotics match full numerics of Eq. (1) to ≤9 %, the more realistic p=4 case is shown only for the layer functions Y_E and T_E; a corresponding full-device magnetoresistance comparison for p=4 would strengthen that the three-regime structure and curvature-tuned slip survive a more faithful collision operator.","section":null},{"comment":"Discussion of experimental link (final two paragraphs): the claim that tomographic corrections “may account for” the anomalous viscosity scaling reported in Ref. [21] remains qualitative. The paper correctly notes that the relative weight of the (τ'_η)^{-1}∼n^4/T^4 term can be tuned by electrode curvature, yet no explicit fit or estimate of the prefactors for the device parameters of [21] is provided; without this, the connection stays suggestive rather than diagnostic.","section":null}],"minor_comments":[{"comment":"Fig. 2 caption and main text: the hydrodynamic reference curve is shown only for 1/r_c=0.1; adding the corresponding hydrodynamic curve for 1/r_c=0.2 would make the shaded tomographic correction easier to compare across panels.","section":null},{"comment":"Eq. (13) and surrounding text: the conventional slip length ℓ_slip=(32/15π)ℓ_e is quoted without a brief reminder of its origin (diffuse-wall kinetic theory); a short parenthetical citation would help non-specialist readers.","section":null},{"comment":"End Matter, Eq. (21b): the finite-wavelength correction u^{(1)}_{FW|θ} is stated to lack a closed form; noting that it vanishes identically for G→∞ (as used in the main figures) would clarify why the clean-limit analytics remain simple.","section":null},{"comment":"References: the recent channel-geometry companion papers [34,35] are cited, but a one-sentence contrast of the electrode-driven versus wall-driven boundary layers would orient the reader more quickly.","section":null}],"recommendation":"minor_revision","confidential_remarks":"Solid, carefully executed kinetic-theory paper that cleanly isolates a new electrode-layer effect. The collision-model caveat is real but already partially mitigated by the authors; a short additional p=4 magnetoresistance panel would remove most remaining doubt. Suitable for the journal after minor revision."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The punchline is that tomographic odd-mode lifetime produces an extended electrode boundary layer of thickness sqrt(ell_e ell_o). That layer gives superballistic electrode conductance (exactly twice Sharvin, saturating Raichev’s bound) plus a curvature-dependent azimuthal slip that parametrically boosts the quadratic magnetoresistance coefficient alpha. The same calculation yields three regimes: tomographic at weak B (rc > ko), hydrodynamic once rc drops below the long odd mfp, and Ohmic once rc reaches the short even mfp. The weak-field scaling of alpha can look non-Fermi-liquid and may explain the anomalous viscosity extracted in Zeng et al.\n\nWhat is actually new is the perfect-transmission electrode layer (not the diffuse-wall case from their earlier papers), the explicit curvature term in the slip condition, the superballistic result, and the full Corbino magnetoresistance formulas. The bulk Stokes-Ohm expansion is recycled, but the electrode matching, the layer functions YE and TE, and the three-regime map are derived and checked here. They solve the layer equation numerically, give closed-form bulk solutions with modified Bessel functions, and overlay direct kinetic-equation numerics; the error stays under 9 % even at ke = 0.1. That is solid kinetic theory.\n\nThe soft spot is the usual one: the collision operator is a fixed-rate even/odd model (p = 0 or 4) taken from exact diagonalization. It is assumed to hold inside the far-from-equilibrium curved layers. They mitigate it by showing the leading conductance is model-independent and by validating the profiles against the full kinetic equation for p = 0. The experimental link remains qualitative—no quantitative fit to the Zeng data—but the geometric knob (inner radius) and the non-monotonic alpha(B) are falsifiable. Citation pattern is normal; they build on their own prior asymptotics and cite the relevant hydro and tomography literature.\n\nThis is for people working on electron hydrodynamics or Corbino magnetotransport. The math is transparent and the predictions are sharp enough that I would bring it to reading group and cite the three-regime structure. A serious editor should send it to referees; the central claim holds up.","headline":"Clean asymptotic theory for electrode-driven tomographic flow in Corbino disks that produces a curvature-tunable magnetoresistance enhancement and three clear B-field regimes.","tokens_in":14948,"tokens_out":559,"would_cite":true,"duration_ms":10795,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Tomographic electrons in a Corbino disk create an extended electrode boundary layer that superballistically injects current and enhances magnetoresistance, with a curvature-tunable slip that may explain anomalous viscosity scaling.","keywords":["tomographic transport","Corbino disk","electron hydrodynamics","magnetoresistance","boundary layers","odd-parity modes","superballistic conductance","Fermi liquid"],"falsifier":"Measure the quadratic magnetoresistance coefficient versus magnetic field in a Corbino disk of known radii: if the coefficient first drops when the cyclotron radius becomes comparable to the expected odd-mode mean free path and later rises when it reaches the even-mode mean free path, and if the size of the low-field enhancement scales with the inverse of the inner electrode radius, the central claim is confirmed; absence of either signature falsifies it.","tokens_in":15025,"feed_emoji":"🧲","tokens_out":1034,"duration_ms":7839,"temperature":0.7,"pith_summary":"In clean two-dimensional electron gases, Pauli blocking makes odd-parity deformations of the Fermi surface live much longer than even-parity ones. The resulting “tomographic” transport cannot be captured by ordinary hydrodynamics. This paper solves the kinetic equation for such electrons flowing between concentric electrodes in a Corbino disk. Near each electrode an extended non-equilibrium boundary layer forms; inside it the electrode conductance reaches twice the Sharvin value (superballistic injection) and the azimuthal velocity acquires an anomalously large slip that grows with electrode curvature. The enhanced slip produces a parametric boost of the quadratic magnetoresistance coefficient. As magnetic field is raised the coefficient passes through three successive regimes—tomographic, hydrodynamic, then Ohmic—separated by the two mean free paths. The weak-field tomographic corrections carry temperature and density scalings opposite to Fermi-liquid viscosity, offering a possible account of the anomalous viscosity reported in recent Corbino experiments.","feed_headline":"Tomographic electrons boost Corbino magnetoresistance","feed_subtitle":"Extended electrode layers give superballistic injection and a curvature-tunable slip that may explain anomalous viscosity","key_machinery":"Matched asymptotic expansion of the linearized Fermi-liquid kinetic equation in the even-mode Knudsen number ke ≪ 1. The expansion yields bulk Stokes–Ohm equations corrected by long-lived odd modes, together with tomographic boundary-layer solutions that enforce both the superballistic electrode condition and the curvature-dependent slip law used to compute the magnetoresistance.","core_discovery":"Tomographic flow in a Corbino disk generates an extended boundary layer of thickness set by the geometric mean of the short even-mode and long odd-mode mean free paths. Inside that layer current is injected superballistically (electrode conductance saturating twice the Sharvin value) and the azimuthal velocity obeys a curvature-dependent slip condition. The resulting enhancement of the quadratic magnetoresistance coefficient is therefore geometry-tunable and is rapidly suppressed once the cyclotron radius falls below the odd-mode mean free path, producing three distinct magnetic-field regimes whose weak-field scaling can mimic anomalous viscosity.","pith_inferences":["Because the slip condition depends explicitly on electrode curvature, a series of Corbino disks with systematically varied inner radii should map out the tomographic contribution independently of bulk scattering rates.","The same matched-expansion machinery should apply to other electrode-driven geometries (e.g., multi-terminal Hall bars), predicting analogous superballistic contact resistances whenever long-lived odd modes are present.","If the odd-mode mean free path can be extracted from the first crossover field, its measured density and temperature dependence would furnish a direct experimental test of the p = 4 Pauli-blocking prediction."],"forward_implications":["The strength of the tomographic correction can be dialed by changing only the inner electrode radius, giving experimental control over the anomalous scaling.","Moderate magnetic fields that suppress the odd-mode layer recover ordinary hydrodynamic viscosity, allowing a cleaner extraction of the Fermi-liquid viscosity from the same device.","The non-monotonic field dependence of the magnetoresistance coefficient itself becomes a diagnostic of the two distinct mean free paths.","Weak-field temperature and density scalings opposite to Fermi-liquid theory appear naturally once electrode boundary layers are treated, offering a route to reconcile existing viscosity data."],"fun_headline_variants":["Tomographic flow builds superballistic layers in Corbino disks","Curvature sets slip that enhances Corbino magnetoresistance","Odd-mode layers drive three magnetoresistance regimes","Extended boundary layers boost quadratic magnetoresistance","Tomographic slip velocity tunes Corbino magnetotransport"],"cache_read_input_tokens":128,"weakest_assumption_plain":"The collision integral is replaced by a simple fixed-rate model that assigns one short lifetime to every even mode and one long lifetime (with power-law angular dependence) to every odd mode; this model is assumed to stay accurate inside the curved electrode layers where the distribution is far from local equilibrium.","fun_headline_variants_meta":{"raw":{"variants":["Tomographic flow builds superballistic layers in Corbino disks","Curvature sets slip that enhances Corbino magnetoresistance","Odd-mode layers drive three magnetoresistance regimes","Extended boundary layers boost quadratic magnetoresistance","Tomographic slip velocity tunes Corbino magnetotransport"]},"model":"grok-4.5","effort":"low","cost_usd":0.005044,"raw_usage":{"total_tokens":1368,"prompt_tokens":791,"num_sources_used":0,"completion_tokens":62,"cost_in_usd_ticks":50440000,"prompt_tokens_details":{"text_tokens":791,"audio_tokens":0,"image_tokens":0,"cached_tokens":0},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":515,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":791,"tokens_out":62,"duration_ms":3924,"temperature":1.0,"reasoning_tokens":515,"cache_read_input_tokens":0,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-11T06:05:57.750198+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Measure the quadratic magnetoresistance coefficient versus magnetic field in a Corbino disk of known radii: if the coefficient first drops when the cyclotron radius becomes comparable to the expected odd-mode mean free path and later rises when it reaches the even-mode mean free path, and if the size of the low-field enhancement scales with the inverse of the inner electrode radius, the central claim is confirmed; absence of either signature falsifies it.","supporting_citations":[],"review_version":1}