{"id":"d326cc20-d517-436b-921d-396cc78e71d3","arxiv_id":"2603.15290","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.5,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Raw maximal amplitudes at the open IQH transition factor as gain times intrinsic extreme, with parabolic extreme-moment scaling driven largely by near-log-normal gain.","lead":"At the integer quantum Hall transition in an open network model, the largest wave-function amplitude factors into a sample-wide gain times an intrinsic extreme piece. Separating them shows that raw extremes look nearly log-normal while the intrinsic piece does not follow ordinary extreme-value collapse, giving a new probe of open critical states.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection beyond the finite-size caveat already flagged by the reader.","rationale":"The reader’s weakest_assumption already isolates the load-bearing limitation: the accessible window may still be gain-dominated, so raw near-parabolicity need not be the asymptotic extreme sector. The manuscript itself flags this after Eq. (4) and in Appendix C. The gain decomposition is partly definitional yet the measured reorganization of τ̃_max(q) and the failure of GEV collapse for |ψ̃|_max are nontrivial numerical facts inside that window. No stronger technical objection (e.g., inconsistency with known IQH multifractality, misuse of Legendre transforms, or definitional circularity) lands. Therefore the CONDITIONAL verdict with high confidence is appropriate and needs no adjustment.","tokens_in":11415,"tokens_out":485,"duration_ms":4767,"concrete_test":"Re-extract ν and γ from E[ln|ψ|_max] and the Jensen gap at L = 4096 (or larger) with ensembles ≳ 10^6; if the parabolic coefficients remain stable within the quoted errors and the α_0 − ν residual shrinks below ~0.002, the finite-size caveat weakens; if they drift or the residual grows, the asymptotic status of raw parabolicity is still open.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is a finite-size numerical phenomenology of the open CC network: |ψ|_max = A |ψ̃|_max, raw τ_max(q) ≈ −γ q² + ν q over |q| ≲ 1 with near-Gaussian bulk of ln|ψ|_max, and qualitative reorganization after gain normalization without single-parameter GEV collapse. That claim is internally consistent with the reported data (L ≤ 2048, large ensembles, Appendices C–E). The only soft spot is precisely the one the authors and the reader already mark: whether the raw parabolicity and near-log-normality survive as L → ∞ or remain a gain-dominated window (explicitly left open after Eq. (4); α_q extrapolations still mismatch ν, γ by ~0.005). No additional hidden inconsistency, circularity, or unstated assumption is required for the Letter’s stated conclusions.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript studies extreme wave-function amplitudes at the integer quantum Hall transition in the open Chalker–Coddington network. It reports that the maximal link amplitude factorizes as |ψ|_max = A |ψ̃|_max, with A a sample-dependent global gain (total intensity excluding the contact). Extreme-moment scaling E[(|ψ|_max)^{2q}] ∼ L^{-d τ_max(q)} is introduced; over |q| ≲ 1 the raw exponent is approximately parabolic, τ_max(q) ≈ -γ q^{2} + ν q (ν ≈ -0.430, γ ≈ 0.137), and the bulk of ln|ψ|_max is near-Gaussian. After gain normalization the exponent reorganizes (dominated by a linear term with small asymmetric nonlinear corrections) and |ψ̃|_max does not support single-parameter GEV collapse under standard centering/scaling in the accessible window L ≤ 2048. Appendices supply the open-network construction, adjusted R^{2} diagnostics, Legendre extrapolation of α_q, a full-state multifractal benchmark, and gain/normalized PDFs.","tokens_in":11693,"tokens_out":1256,"duration_ms":9301,"significance":"If the reported finite-size phenomenology holds, the work supplies a concrete extreme-value multifractality framework for open critical systems and isolates a gain-versus-intrinsic decomposition that is absent from conventional self-normalized multifractal analyses. The large ensembles (O(10^6)–O(10^7)), high adjusted R^{2} for the parabolic fits, and consistency of the full-state Δ_q benchmark with established IQH literature strengthen the numerical claims inside the studied window. Extreme observables are positioned as a complementary probe of correlated criticality beyond bulk inverse-participation-ratio moments, which is a useful and falsifiable direction for localization transitions in open geometries.","major_comments":[{"comment":"After Eq. (4) and in Appendix C the authors correctly leave open whether the raw parabolic τ_max(q) and near-Gaussian bulk of ln|ψ|_max persist asymptotically. The residual mismatch between Legendre-extrapolated α_0, α_{1/2} and the logarithmic-moment estimates of ν, γ (∼0.005) is of the same order as the quoted uncertainties and indicates that irrelevant corrections remain non-negligible at L = 2048. For the central claim that raw extremes are gain-dominated and reorganize under normalization, this is acceptable as finite-size phenomenology, but the abstract and conclusions should state more explicitly that the asymptotic status of the raw parabola (and of the absence of GEV collapse for |ψ̃|_max) is not established beyond the accessible window.","section":"Eq. (4); Appendix C; abstract/conclusions"},{"comment":"The statement that |ψ̃|_max “does not support a single-parameter generalized extreme-value collapse under standard centering/scaling” (main text and Appendix E) is load-bearing for the claim of a distinct intrinsic extreme sector. The supporting evidence is the lack of collapse of standardized PDF(ln|ψ̃|_max) and a qualitative compound (Gumbel-like + Gaussian-tail) shape. A more quantitative diagnostic—e.g., Kolmogorov–Smirnov or Anderson–Darling distances to the three GEV families after maximum-likelihood location/scale fits, or a two-parameter GEV attempt—would make the rejection of GEV universality sharper and less protocol-dependent within the same size window.","section":"Gain normalization paragraph; Appendix E / Fig. E2"}],"minor_comments":[{"comment":"Notation for the normalized maximum switches between |ψ̃|_max and |˜ψ|_max in the abstract versus the body; a single consistent tilde convention would help.","section":"Abstract vs. Eq. (12)"},{"comment":"Figure 2 caption and panel (b) refer to “shifted variable” p without restating p := L^{ν d/2} |ψ|_max in the caption; a one-line reminder would improve readability.","section":"Fig. 2"},{"comment":"Appendix D’s continuum argument that Δ_q = Δ¯_q + 1 is standard but could briefly note the regime of validity (large-distance dominance) already used in the open-geometry literature.","section":"Appendix D"},{"comment":"A short explicit comparison of the measured ν, γ with any known delay-time or integrated-intensity exponents (Ref. [26]) would clarify how much of the raw parabola is expected from the gain alone.","section":"Gain discussion; Ref. [26]"}],"recommendation":"minor_revision","confidential_remarks":"The Letter is a solid numerical phenomenology paper for a specialized but active community (IQH multifractality / open networks). The finite-size caveat is already flagged by the authors; I do not see a hidden inconsistency that would justify major revision or rejection. Fit for a short-format journal is good if the asymptotic language is tightened."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The one thing worth knowing is the factorization |ψ|_max = A |ψ̃|_max in the open Chalker–Coddington network, together with the measured contrast: raw extreme moments give an approximately parabolic τ_max(q) ≈ -γq^{2} + νq over |q| ≲ 1 (ν ≈ -0.43, γ ≈ 0.137) and a near-Gaussian bulk for ln|ψ|_max, while after dividing out the sample gain A the exponent reorganizes (mostly linear plus small asymmetric corrections) and the normalized maximum does not collapse to a single-parameter GEV form in the L ≤ 2048 window.\n\nWhat is new is not the general idea of extreme-value multifractality or log-correlated freezing—those are already in the literature they cite—but the concrete gain decomposition for open-network extremes, the definition of extreme-moment scaling for the maximum, and the clean demonstration that the raw near-log-normality is largely controlled by A. The numerics are careful: ensembles of order 10^6–10^7, high adjusted R^{2} on the parabolic fits, a consistent full-state multifractal benchmark in Appendix D, and transparent Legendre/α_q extrapolations in Appendix C. The appendices on gain statistics and the compound PDF of the normalized maximum are useful and honest.\n\nThe soft spot is exactly the one the authors already flag: everything is inside L ≤ 2048 and |q| ≲ 1. Parabolicity of τ_max and the ultimate extreme-value class after gain removal are left open; the α_q extrapolations still sit ~0.005 off ν and γ. That is a finite-size caveat, not a hidden contradiction. Circularity is low: A is defined from total intensity, so the product form is partly by construction, but the independent scaling of A, of the raw moments, and of the normalized moments is measured, not forced. No code or data release, so reproducibility is only moderate.\n\nThis is for people who work on IQH multifractality, open critical systems, or extreme-value diagnostics beyond i.i.d. GEV. It is a serious numerical Letter, not a theory paper. I would send it to referees; the claims are clear, the data support the finite-size phenomenology, and the open questions are stated as such. Worth engaging if you care about rare-event probes of open quantum criticality.","headline":"Solid finite-size Letter: open-CC maxima factor as gain times intrinsic extreme, raw τ_max(q) looks parabolic and near-log-normal, and gain removal reorganizes both the exponent and the PDF away from ordinary GEV.","tokens_in":12316,"tokens_out":697,"would_cite":true,"duration_ms":5613,"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":"At the integer quantum Hall transition, the largest wave-function amplitude splits into a sample-wide gain times an intrinsic extreme.","keywords":["integer quantum Hall transition","Chalker–Coddington network","extreme-value statistics","multifractality","gain decomposition","open quantum systems","wave-function maxima"],"falsifier":"Push the same extreme-moment analysis and standardized-density collapse to substantially larger L (or wider |q|) after gain normalization: if a single-parameter GEV collapse appears or the residual ˜τ_max(q) becomes purely linear, the claim that the intrinsic extreme sector is non-GEV and correlation-dominated fails; if the reorganization persists, the claim holds.","tokens_in":12254,"feed_emoji":"📉","tokens_out":621,"duration_ms":6922,"temperature":0.7,"pith_summary":"This paper asks what the largest amplitude of a critical quantum Hall wave function does when the system is open and driven by a point contact. In the open Chalker–Coddington network the maximum factors as a global gain A times an intrinsic extreme component. The raw maxima have approximately parabolic extreme-moment exponents and a near-Gaussian bulk for the log-amplitude over the sizes studied; those features are largely controlled by the near-log-normal gain. Once the gain is divided out, the exponent function changes character and the normalized maximum no longer collapses to a single-parameter extreme-value form under ordinary centering and scaling. Extreme observables therefore isolate a correlation-dominated rare-event sector that ordinary bulk multifractal moments miss, and they offer a practical probe of open quantum criticality.","feed_headline":"Max wave amplitude splits into gain times intrinsic extreme","feed_subtitle":"At the open quantum Hall critical point, raw extremes look near-log-normal; removing the gain exposes a distinct rare-event sector.","key_machinery":"Gain decomposition |ψ|_max = A |ψ̃|_max, with A the square root of the total stationary intensity excluding the contact; it separates collective amplification from the intrinsic extreme sector whose moments and densities are then measured separately.","core_discovery":"In the open Chalker–Coddington network at the integer quantum Hall critical point the maximal link amplitude factorizes as |ψ|_max = A |ψ̃|_max, where A is the sample-dependent global gain. Extreme-moment scaling of the raw maximum yields an approximately parabolic exponent τ_max(q) ≈ −γ q² + ν q over moderate q, while ln|ψ|_max has an almost Gaussian bulk; after gain normalization the exponent reorganizes and the intrinsic maximum does not support single-parameter GEV collapse in the accessible size window.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Max |ψ| factors as gain A times intrinsic extreme","Extreme moments give parabolic τ before gain removal","Gain strip reorganizes extreme stats at IQH point","Intrinsic max lacks single-param GEV collapse","Global gain largely controls raw wavefunction extremes"],"cache_read_input_tokens":128,"weakest_assumption_plain":"That the near-parabolic and near-Gaussian behaviour seen for system sizes up to a few thousand and moderate moments already describes the true asymptotic extreme sector, rather than a finite-size window still shaped by the gain and corrections.","fun_headline_variants_meta":{"raw":{"variants":["Max |ψ| factors as gain A times intrinsic extreme","Extreme moments give parabolic τ before gain removal","Gain strip reorganizes extreme stats at IQH point","Intrinsic max lacks single-param GEV collapse","Global gain largely controls raw wavefunction extremes"]},"model":"grok-4.5","effort":"low","cost_usd":0.006672,"raw_usage":{"total_tokens":1694,"prompt_tokens":777,"num_sources_used":0,"completion_tokens":60,"cost_in_usd_ticks":66720000,"prompt_tokens_details":{"text_tokens":777,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":857,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":777,"tokens_out":60,"duration_ms":7399,"temperature":1.0,"reasoning_tokens":857,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T20:29:22.043855+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Push the same extreme-moment analysis and standardized-density collapse to substantially larger L (or wider |q|) after gain normalization: if a single-parameter GEV collapse appears or the residual ˜τ_max(q) becomes purely linear, the claim that the intrinsic extreme sector is non-GEV and correlation-dominated fails; if the reorganization persists, the claim holds.","supporting_citations":[],"review_version":1}