{"id":"50fef5a1-dd3a-43ef-bc01-460d5299c066","arxiv_id":"2508.00060","paper_version":2,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"In a Brownian SYK chain at strong coupling, information from an injected qudit spreads inside a sharp light-cone at the butterfly velocity because the governing dynamics reduce to FKPP domain walls.","lead":"The paper calculates the spread of information from an injected qudit in a one-dimensional Brownian SYK chain at infinite temperature. At strong coupling the information stays localized inside a sharp light-cone whose speed is the butterfly velocity, emerging from domain-wall solutions of the FKPP equation.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"FKPP domain-wall sharpness depends on an uncontrolled continuum limit of the microscopic operator growth rates in the Brownian SYK chain.","rationale":"The reader's weakest_assumption correctly isolates the FKPP step. Because the review was abstract-only, the full derivation (presumably in the body) must be checked for the size of the truncation error; the proposed test directly quantifies whether that error preserves the discontinuity.","tokens_in":1781,"tokens_out":356,"duration_ms":24209,"concrete_test":"Starting from the microscopic master equation for the Brownian SYK chain, derive the closed equation for the spatially resolved OTOC or information density up to next-to-leading order in the gradient expansion; numerically integrate the resulting PDE on a lattice of size L=128 for coupling strength J=10 and compare the front width to the pure FKPP prediction. If the width remains O(1) rather than vanishing as 1/J, the sharp light-cone is an artifact of the truncation.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim requires that the late-time, strong-coupling dynamics reduce exactly to the FKPP equation whose traveling-wave solutions have a sharp front at speed v_B. The paper invokes general properties of chaotic operator growth to justify this reduction. However, the explicit mapping from the Brownian SYK Lindblad dynamics (or the corresponding Schwinger-Dyson equations for the out-of-time-order correlators) to the FKPP form necessarily involves a gradient expansion and truncation of higher-order nonlinearities. If those neglected terms remain O(1) near the front, they can produce a finite-width smoothing of the domain wall, eliminating the claimed sharp transition in the information content at ℓ ∼ v_B T.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper examines the spread of quantum information in a one-dimensional Brownian SYK chain using quantum error correction tools. A qudit is injected at a point p in an infinite-temperature state at t=0, and the information content of this qudit within a centered interval of length 2ℓ is computed at later time T. At strong coupling the quantity exhibits a sharp transition from near-zero to near-maximal correlation at ℓ ∼ v_B T, with the sharpness attributed to domain-wall solutions of the FKPP equation that emerge from the model's operator-growth dynamics.","tokens_in":1965,"tokens_out":481,"duration_ms":20637,"significance":"If the reduction to the FKPP equation and the resulting sharp fronts are rigorously established, the work supplies a concrete, analytically tractable demonstration of emergent locality in a chaotic quantum system. This directly supports the link between microscopic operator growth, sharp light-cones, and the Ryu-Takayanagi formula in holographic settings. The use of QEC diagnostics to quantify information spread is a methodological strength.","major_comments":[{"comment":"Abstract and subsequent discussion of the FKPP reduction: the claim that an explicit calculation yields a sharp transition at ℓ ∼ v_B T is not accompanied by the derivation steps that map the Brownian SYK Lindblad (or Schwinger-Dyson) equations onto the FKPP form, nor by error estimates or finite-size checks. Because this mapping is load-bearing for the quantitative location of the transition, the support for the central claim remains only moderate.","section":"Abstract / FKPP section"},{"comment":"The justification for the FKPP domain-wall sharpness invokes general properties of chaotic operator growth, but the gradient expansion and truncation of higher-order nonlinearities are not shown to be controlled near the front. If the neglected terms remain O(1), they can produce a finite-width smoothing that would eliminate the claimed sharp transition in the information content.","section":"Discussion of late-time dynamics"}],"minor_comments":[{"comment":"Notation for the interval length 2ℓ and the time T should be introduced with a clear figure or equation reference to avoid ambiguity when comparing to the butterfly velocity v_B.","section":"Introduction"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their careful reading of our manuscript and for the constructive comments. The feedback highlights the need for greater detail on the FKPP reduction and the control of approximations near the domain wall. We have revised the manuscript to address these points and respond to each major comment below.","responses":[{"response":"We agree that the mapping from the microscopic equations to the FKPP form was insufficiently detailed in the original submission. In the revised manuscript we have added a new subsection that explicitly derives the reduction from the Schwinger-Dyson equations of the Brownian SYK chain to the FKPP equation, including the strong-coupling limit and the truncation steps. We also include error estimates that show corrections are suppressed by inverse powers of the coupling and present finite-size numerical checks on small chains that confirm the location and sharpness of the transition at ℓ ∼ v_B T. These additions directly strengthen the quantitative support for the central claim.","revision_made":"yes","referee_comment":"[Abstract / FKPP section] Abstract and subsequent discussion of the FKPP reduction: the claim that an explicit calculation yields a sharp transition at ℓ ∼ v_B T is not accompanied by the derivation steps that map the Brownian SYK Lindblad (or Schwinger-Dyson) equations onto the FKPP form, nor by error estimates or finite-size checks. Because this mapping is load-bearing for the quantitative location of the transition, the support for the central claim remains only moderate."},{"response":"We thank the referee for raising this important point about the validity of the truncation near the front. In the revision we have expanded the discussion of late-time dynamics to include a scaling argument showing that, in the strong-coupling regime, the front is controlled by the linear instability of the operator growth, with nonlinear corrections entering only perturbatively. We argue that this keeps the domain wall sharp on the scales relevant to the information measure. A fully non-perturbative demonstration that all higher-order terms remain negligible would require additional techniques and lies beyond the scope of the present work.","revision_made":"partial","referee_comment":"[Discussion of late-time dynamics] The justification for the FKPP domain-wall sharpness invokes general properties of chaotic operator growth, but the gradient expansion and truncation of higher-order nonlinearities are not shown to be controlled near the front. If the neglected terms remain O(1), they can produce a finite-width smoothing that would eliminate the claimed sharp transition in the information content."}],"tokens_in":1483,"tokens_out":526,"duration_ms":20865,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"This paper computes how much information from a qudit injected at one site in a Brownian SYK chain ends up inside a finite interval at later time T. At strong coupling the recoverable fraction shows a sharp rise once the interval length reaches roughly v_B T. The authors link this to the FKPP equation whose domain-wall solutions produce a clean front, and they trace the front back to general features of operator growth in chaotic systems. That supplies a solvable example where emergent locality for information follows from the microscopic rules rather than from an assumed bulk geometry.","headline":"The Brownian SYK chain gives a direct microscopic calculation of recoverable information that jumps sharply at the butterfly velocity via FKPP domain walls.","tokens_in":2449,"tokens_out":180,"would_cite":false,"duration_ms":18867,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":{"model":"grok-4.3","evidence":[{"relation":"unclear","rs_module":"IndisputableMonolith/Foundation/RealityFromDistinction.lean","rs_theorem":"reality_from_one_distinction","paper_passage":"Underlying the emergence of this sharp light-cone is a non-linear generalization of the diffusion equation called the FKPP equation, which admits sharp domain wall solutions at late times and strong coupling."}],"headline":"SYK-chain FKPP domain walls produce sharp light-cone; RS derives light-cones from distinction but no shared machinery","alignment":"orthogonal","rationale":"Paper's core is saddle-point analysis of Brownian SYK Schwinger-Dyson equations yielding FKPP traveling waves (section 3.2, eq. 3.26) whose domain-wall solutions enforce the sharp ℓ ∼ v_B T transition in mutual information. This is a model-specific chaotic-dynamics calculation with no reference to J-cost, φ-ladders, 8-tick periodicity, or parameter-free constant derivations. RS modules (AbsoluteFloorClosure, AlexanderDuality for D=3, AlphaCoordinateFixation, reality_from_one_distinction) force spacetime and constants from a single distinction; the paper neither invokes nor contradicts those theorems.","tokens_in":64461,"confidence":"moderate","tokens_out":277,"duration_ms":16034,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"In a Brownian SYK chain at strong coupling, information from an injected qudit spreads inside a sharp light-cone bounded by the butterfly velocity.","keywords":["Brownian SYK chain","entanglement spreading","emergent locality","butterfly velocity","FKPP equation","quantum error correction","information light-cone"],"falsifier":"A direct computation or simulation of the recoverable information fraction versus interval length at late times and strong coupling, testing whether the rise from near-zero to near-maximal remains abrupt and centered at ℓ = v_B T.","tokens_in":2700,"feed_emoji":"⚛️","tokens_out":711,"duration_ms":27004,"temperature":0.7,"pith_summary":"The paper studies the spread of quantum information in a solvable one-dimensional model of chaotic dynamics consisting of a chain of Brownian SYK sites. It injects a qudit into an infinite-temperature state at a single point and computes the fraction of that qudit's information that is recoverable from a centered interval of length 2ℓ after a fixed time T. At strong coupling this fraction remains near zero for small ℓ and jumps to near its maximum value once ℓ exceeds v_B T, where v_B is the butterfly velocity. The transition arises because the late-time operator growth obeys the FKPP equation, whose domain-wall solutions enforce an emergent light-cone structure.","feed_headline":"Information in SYK chain jumps sharply at butterfly-velocity scale","feed_subtitle":"At strong coupling the recoverable qudit information in a centered interval rises from near zero to near maximal once the interval length is","key_machinery":"The FKPP equation, a nonlinear generalization of the diffusion equation whose domain-wall solutions at late times and strong coupling produce the observed sharp light-cone.","core_discovery":"At strong coupling the amount of information of the injected qudit contained in an interval of length 2ℓ shows a sharp transition as a function of ℓ from near zero to near maximal correlation, with the transition located at ℓ ∼ v_B T. This sharp light-cone is produced by the domain-wall solutions of the FKPP equation that governs the late-time, strong-coupling dynamics of the model.","pith_inferences":["The same sharp transition should appear in any chaotic many-body system whose scrambling dynamics reduce to an FKPP-like equation at late times.","Finite-size or finite-coupling corrections would round the step; their scaling with system size or coupling strength could be measured numerically.","Direct comparison of the information content with out-of-time-order correlators in the same model would test whether both quantities are controlled by the same domain-wall profile."],"forward_implications":["Quantum information spreads ballistically inside the butterfly-velocity light-cone rather than diffusively.","The sharp transition supplies an explicit realization of the emergent locality required by an RT-like formula for entanglement entropy.","Tools from quantum error correction can be used to track information content explicitly in this solvable chaotic model.","The same FKPP mechanism links operator growth in chaotic systems to the appearance of geometric bulk duals."],"fun_headline_variants":["Sharp light cone in SYK entanglement at butterfly velocity","FKPP domain walls drive emergent locality in SYK chains","Qudit recovery sharpens at butterfly velocity in SYK chain","Emergent locality appears via sharp transition in SYK model"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The late-time strong-coupling dynamics of the Brownian SYK chain are governed by the FKPP equation whose domain-wall solutions produce the sharp light-cone, justified from general properties of operator growth in chaotic systems.","fun_headline_variants_meta":{"raw":{"variants":["Sharp light cone in SYK entanglement at butterfly velocity","FKPP domain walls drive emergent locality in SYK chains","Qudit recovery sharpens at butterfly velocity in SYK chain","Emergent locality appears via sharp transition in SYK model"]},"model":"grok-4.3","cost_usd":0.009296,"raw_usage":{"total_tokens":4193,"prompt_tokens":734,"num_sources_used":0,"completion_tokens":65,"cost_in_usd_ticks":92962000,"prompt_tokens_details":{"text_tokens":734,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3394,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":734,"tokens_out":65,"duration_ms":21415,"temperature":1.0,"reasoning_tokens":3394,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-19T01:34:01.344304+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A direct computation or simulation of the recoverable information fraction versus interval length at late times and strong coupling, testing whether the rise from near-zero to near-maximal remains abrupt and centered at ℓ = v_B T.","supporting_citations":[],"review_version":1}