{"id":"b04e67c3-db0b-49b1-8ff0-8a062465424f","arxiv_id":"2607.26880","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":4,"one_line_summary":"Calibrated physical-pressure derivatives (propagated plus receiver-calibration terms) make Schrödingerised acoustic propagation yield consistent Born, adjoint, and Gauss–Newton actions for local FWI, verified on discrete checks and a nine-qubit hybrid demo.","lead":"The paper builds a pressure-consistent Born/adjoint/Gauss–Newton interface so Schrödingerised wave propagation can feed a local full-waveform inversion update. It shows that omitting the receiver-calibration term in p=cπ leaves an order-one Born error and can wreck the update direction, and demonstrates a tiny hybrid quantum–classical inversion on ideal nine-qubit circuits.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"Auxiliary-recovery rates for the tangent/Born map are assumed, not established; that is the soft link in the consistency chain.","rationale":"The reader correctly flags conditional consistency hypotheses and ideal toy-scale hybrid as the reason for CONDITIONAL. The sharpest load-bearing piece inside that cluster is specifically the unproven auxiliary-recovery rates on the tangent/Born map (Prop. 3.1, 4.2 and the empirical-only N_p row), not a flaw in the product-rule calibration term or the discrete operator algebra—those are well supported by Prop. 2.1, independent RK4/autodiff/Jacobian checks, and the O(1) ablation. No internal contradiction was found. Code-not-public and four-parameter ideal-circuit scope already justify CONDITIONAL; the proposed N_p sweep would only tighten or loosen confidence in the Schrödingerised consistency link, not flip the verdict by itself. Hence UNCHANGED and agreement with the reader.","tokens_in":30915,"tokens_out":644,"duration_ms":42722,"concrete_test":"In the smooth periodic setting of Table 6.3 / Prop. 4.2, fix a fine spatial grid (e.g. 96² or 192²) and refine N_p over {3,5,7,9,11,15,21} against a high-N_p reference; report separate errors for background pressure and for the full calibrated Born action (and the calibration-only term). If Born error stagnates or decays slower than the assumed Δp²+e^{-αL_p} trend while spatial error is held negligible, the conditional consistency link to Schrödingerised propagation is weaker than claimed.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim needs Prop. 3.1 and Prop. 4.1–4.2 to transfer auxiliary-recovery error into calibrated pressure Born rows (hence adjoint and GN actions) under hypothesized bounds ε_R, CΔp², and Ce^{-αL_p}. Spatial refinement in Table 6.3 shows clear second-order behavior for the complete Born action; the auxiliary row only reports a 3.3× reduction from N_p=3 to 11 as an “empirical trend,” with no fitted order and no separate background-vs-tangent breakdown. Prop. 4.2 explicitly assumes those auxiliary rates rather than deriving them for the recovery map R_pa acting on Duhamel tangent states. If R_pa fails to meet the assumed rates on δψ (while still looking acceptable on background ψ_0), the discrete finite-dimensional map can remain internally consistent (as the FD/autodiff/Jacobian checks confirm) while the Schrödingerised-to-physical Born interface retains an uncontrolled consistency gap. The nine-qubit hybrid does not stress this: it freezes a tiny auxiliary grid and compares circuit outputs to the same discrete midpoint operator, not to a refined continuous or high-N_p reference.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper constructs a pressure-consistent Born, adjoint, and Gauss–Newton interface for constant-density acoustic FWI from Schrödingerised first-order dynamics. Because physical pressure is p=cπ rather than the energy variable π, the directional derivative retains both a propagated term c0 δπ and a direct receiver-calibration term δc π0; both are kept in the Duhamel Born map and its adjoint/normal actions. The authors give a conditional consistency budget (Props. 4.1–4.2), a component-wise resource model, multi-method discrete verification (FD, independent RK4 tangent/adjoint, autodiff JVP/VJP, explicit Jacobians), second-order periodic spatial refinement when calibration is retained versus an O(1) plateau when it is omitted, assembled-matrix statevector checks, and a nine-qubit compiled midpoint Born circuit whose ideal-circuit Bernoulli samples drive a four-parameter hybrid VQLS update in which all ten predeclared seeds reduce model error.","tokens_in":31296,"tokens_out":1642,"duration_ms":59890,"significance":"If the construction holds under the stated hypotheses, the paper supplies a concrete and previously under-specified operator-and-readout bridge between Schrödingerised wave propagation and the matrix-free actions a local FWI step actually needs. The strongest contribution is not a complexity claim but the calibrated pressure derivative itself: the ablation (order-one Born FD error; regularized GN step relative error 1.296 and correlation 0.068 when calibration is dropped) is falsifiable and load-bearing, and the discrete chain is checked by independent tangent/reverse codes, autodiff, and explicit Jacobians rather than by construction. The resource table separating access, preparation, LCU normalization, quadrature, and selected-output measurement is a useful accounting template. The hybrid demo and resource model are toy-scale and ideal-circuit, so significance for quantum advantage remains prospective; significance for correct pressure-observable differentiation in Schrödingerised FWI interfaces is real and well evidenced at the finite-dimensional level.","major_comments":[{"comment":"Props. 3.1 and 4.1–4.2 transfer auxiliary-recovery error into calibrated pressure Born rows under hypothesized bounds ε_R, CΔp², and Ce^{-αL_p}. Prop. 4.2 explicitly assumes those auxiliary rates for background and tangent states rather than deriving them for R_pa acting on Duhamel tangent fields. Table 6.3 shows clear second-order spatial behavior for the complete Born action, but the auxiliary row only reports a 3.3× reduction (N_p=3→11) as an “empirical trend,” with no fitted order and no separate ψ0 vs δψ breakdown. This is the soft link in the Schrödingerised-to-physical claim: internal discrete consistency (FD/autodiff/Jacobians) can hold while the continuous/semi-discrete Born interface retains an uncontrolled gap on tangent recovery. Please either (i) prove or numerically establish auxiliary rates for the tangent/Born map under the same norms as Prop. 4.2, or (ii) restate the mai","section":"§4.1–4.2, Prop. 4.2, Table 6.3"},{"comment":"The compiled nine-qubit instance and hybrid inversion sample Bernoulli outcomes from ideal-circuit probabilities (unrestricted connectivity, classically precomputed Pauli coefficients, no device noise). Normal-system assembly, regularization, line search, and model refresh are classical; VQLS acts on a 4×4 normalized system. This is a legitimate measurement-chain prototype, but the abstract, title, and conclusion language (“quantum-assisted waveform inversion,” “connect Schrödingerised propagation to a local FWI update”) can be read as claiming a demonstrated quantum FWI pathway beyond what §5–6 and the Discussion actually show. Please calibrate claims to the evidence: ideal finite-shot selected-output interface at toy scale, with scalable oracles and hardware noise deferred. In particular, state explicitly that no asymptotic advantage or noise-robust update is claimed.","section":"Abstract; §5.2; §6.2; §8"},{"comment":"The finite-dimensional diagnostics use a coefficient-independent first-order source-state convention (3.10), while the continuous fixed-physical-forcing map (2.3) contributes an extra (δc f_s, 0) term. Supplement Table S10 shows O(1) Born error when that source derivative is omitted from the fixed-physical-forcing map—an important audit—but the main text’s primary operator chain and the compiled circuit follow the fixed-state convention. For the central “physical-pressure derivative” claim, please state in the main narrative (not only the supplement) which convention the reported J, J^T, J^T J and the hybrid update implement, and that a fixed-physical-forcing realization must retain the source term analogously to receiver calibration. Otherwise readers may export the calibrated receiver construction while silently dropping a parallel O(1) source contribution.","section":"§2.1; §3.1 (Source convention); §6; Supplement S6 Table S10"}],"minor_comments":[{"comment":"The running header and title page show spaced/broken tokens (“CALIBRA TED”, “OBSER V ABLE”, “W A VEFORM”). Clean typography in the production version.","section":"Title page / header"},{"comment":"Figure 6.1 right panel and the omitted-calibration GN diagnostics are central; ensure the singular-spectrum comparison and the step-correlation/line-search rejection numbers (relative error 1.296, correlation 0.068) appear with explicit pointers in the main text near the figure, not only in the supplement.","section":"§6.1, Fig. 6.1"},{"comment":"Table 4.1 is helpful accounting but mixes asymptotic oracle language with “evidence in this paper” that is dense/statevector/compiled. A one-line caption note that the compiled instance precomputes Paulis (no sparse oracle) would avoid over-reading the table as an implemented block-encoding.","section":"§4.4, Table 4.1"},{"comment":"Notation: L, L_ac_Sch, J, and bL appear for closely related maps; a small notation paragraph listing continuous vs discrete vs computed vs sketched objects would reduce load in §§3–4.","section":"§3–4"},{"comment":"Related-work pointers to classical adjoint-state and GN FWI are adequate; a brief sentence contrasting the present pressure-row derivative with frozen-observable or π-only readouts in prior Schrödingerisation PDE circuits would sharpen novelty without expanding scope.","section":"§1"}],"recommendation":"minor_revision","confidential_remarks":"The paper sits between computational inverse problems and quantum algorithms. Its durable contribution is the calibrated pressure derivative and the unusually thorough discrete-operator audit; the quantum circuit is a small ideal-shot prototype. That is still publishable in quant-ph if claims stay matched to evidence, but editors may also consider a computational-mathematics venue if the quantum framing is judged secondary. I do not see circularity or misconduct issues; the inverse-crime toy inversion is disclosed. The auxiliary-recovery gap is the one technical point I would watch in revision."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The thing worth knowing is simple: if you Schrödingerise constant-density acoustics with energy variables, physical pressure is p=cπ, so the Born row must keep both c0 δπ and the direct δc π0 term. Drop the second and you are differentiating a different observable. They show that cleanly—O(1) FD error, GN step relative error ~1.3 and correlation ~0.07 versus the calibrated direction, line search rejects the bad step—and the full map passes independent RK4 tangent/adjoint, autodiff, explicit Jacobians, and second-order periodic spatial refinement.\n\nWhat is actually new is not Schrödingerisation itself (Jin et al. are cited) or hybrid FWI slogans. It is the pressure-consistent operator-and-readout interface: Duhamel plus receiver-row derivative through Born, adjoint, and GN normal action; a conditional consistency budget; a resource split that treats selected-output/sketched measurements as the sensible target rather than full gathers; and a compiled nine-qubit midpoint Born with separate propagated and calibration interferometers driving a four-parameter finite-shot VQLS update. The discrete-operator work is careful and multi-checked. The ablation is the strongest single result.\n\nSoft spots in proportion: Prop. 4.1–4.2 transfer auxiliary-recovery error under hypothesized εR, Δp², and exponential truncation; the auxiliary row is only an empirical 3.3× trend, not a fitted order on tangent states. So the finite-dimensional map can be internally correct while the continuous Schrödingerised-to-physical link stays conditional. The hybrid is ideal-circuit Bernoulli sampling, four parameters, classical assembly—prototype, not hardware or field-scale evidence. Code is not public yet. None of that breaks the central discrete claim.\n\nThis is for people building quantum or hybrid PDE-constrained inverse machinery who need the observable and measurement target specified correctly. Not for exploration seismologists expecting a production FWI solver. Math and citations look honest; no load-bearing contradiction. I would send it to referees. Engage if you work on this interface; skim the ablation and resource table if you only need the punchline.","headline":"Solid methods paper: the receiver-calibration term in D(cπ) is the real contribution, and the discrete checks back it hard; the Schrödingerised-to-physical consistency chain still leans on assumed auxiliary rates and a toy ideal-circuit demo.","tokens_in":31909,"tokens_out":565,"would_cite":true,"duration_ms":16887,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["65M32","65M12","65M06","81P68","35L05","65F22"],"pacs":[],"model":"grok-4.5","headline":"Physical pressure in Schrödingerised acoustics has a two-term derivative; both terms are required for correct Born, adjoint, and Gauss–Newton FWI updates.","keywords":["full-waveform inversion","Born modelling","Schrödingerisation","quantum algorithms","inverse scattering","Hessian action","pressure calibration","selected-output measurement"],"falsifier":"On the paper’s smooth periodic tests, drop the receiver-calibration term and check whether the Born finite-difference error stays order one and the regularized Gauss–Newton step keeps relative error near 1.3 and correlation near 0.07 against the calibrated step; if those failures disappear without the term, the central claim is wrong.","tokens_in":31769,"feed_emoji":"🌊","tokens_out":952,"duration_ms":19083,"temperature":0.7,"pith_summary":"Full-waveform inversion recovers wavespeed from measured pressure by repeatedly applying Born, adjoint, and Gauss–Newton actions. This paper shows how to build those actions from Schrödingerised wave propagation so that the physical pressure observable stays consistent. Energy variables give a Hamiltonian, but pressure equals wavespeed times one of those variables, so its derivative always has two pieces: a propagated wavefield sensitivity and a direct receiver-calibration term. Keeping both yields compatible discrete operators; dropping the calibration term leaves an order-one Born error and can send the regularized update in the wrong direction. The authors prove a conditional consistency estimate, cost the preparation and selected-output measurements, compile a nine-qubit Born circuit, and drive a four-parameter hybrid inversion in which all ten predeclared finite-shot runs cut the initial model error. The point is practical: Hamiltonian wave evolution alone does not define a local FWI step until the physical-pressure derivative and the measured update observables are specified.","feed_headline":"Both terms in the pressure derivative are required for FWI","feed_subtitle":"Dropping receiver calibration leaves order-one Born error and can reverse the Gauss–Newton step","key_machinery":"The calibrated pressure Born row: Duhamel differentiation of the Schrödingerised state plus the explicit receiver-row derivative ℓj(δc π0), assembled into matrix-free actions Jv, J⊤r, and J⊤Jv under the chosen data and model inner products.","core_discovery":"Differentiating physical pressure p = cπ at background c0 produces D(cπ)[c0](δc) = c0 δπ + δc π0. Retaining both the propagated term and the receiver-calibration term in the Born map, its adjoint, and the Gauss–Newton normal action gives pressure-consistent operators for Schrödingerised constant-density acoustics; omitting calibration differentiates a different observable and substantially changes the local update.","pith_inferences":["The same product-rule gap will appear in any coefficient-dependent observable built on top of an energy-scaled or impedance-scaled Hamiltonian, not only acoustic pressure.","Once variable density, PML auxiliaries, or transducer models enter the generator, each adds its own explicit derivative rows that must be costed like the receiver-calibration term.","Selected-output measurement plus classical normal-system assembly suggests near-term hybrid loops may be limited more by how many Born columns and shots a local update needs than by full-gather tomography."],"forward_implications":["Quantum or hybrid FWI pipelines that simulate energy variables must still measure calibrated physical-pressure rows, not raw π amplitudes.","Selected sketches of receiver–time functionals can replace full-gather readout when the goal is a local gradient or Hessian-action direction.","Resource counts must bill receiver preparation, LCU normalization, and calibration-term estimation separately from Hamiltonian simulation.","Omitting the calibration block can make a line search reject the update even when the omitted-term solver is internally consistent."],"fun_headline_variants":["Both pressure-derivative terms needed for consistent Schrödingerised FWI","Omitting receiver calibration leaves order-one Born error in FWI","Pressure-consistent Born and Gauss–Newton need the full D(cπ) term","Drop calibration and the Gauss–Newton direction can reverse","Retaining c0δπ + δc π0 keeps Schrödingerised FWI operators consistent"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"The link from Schrödingerised propagation to a correct local update holds only under stated stability and auxiliary-recovery error budgets, and the hybrid demonstration uses ideal-circuit probabilities at four model parameters rather than noisy hardware at field scale.","fun_headline_variants_meta":{"raw":{"variants":["Both pressure-derivative terms needed for consistent Schrödingerised FWI","Omitting receiver calibration leaves order-one Born error in FWI","Pressure-consistent Born and Gauss–Newton need the full D(cπ) term","Drop calibration and the Gauss–Newton direction can reverse","Retaining c0δπ + δc π0 keeps Schrödingerised FWI operators consistent"]},"model":"grok-4.5","effort":"low","cost_usd":0.004995,"raw_usage":{"total_tokens":1517,"prompt_tokens":918,"num_sources_used":0,"completion_tokens":98,"cost_in_usd_ticks":49948000,"prompt_tokens_details":{"text_tokens":918,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":501,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":918,"tokens_out":98,"duration_ms":7871,"temperature":1.0,"reasoning_tokens":501,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-30T18:15:57.965171+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"On the paper’s smooth periodic tests, drop the receiver-calibration term and check whether the Born finite-difference error stays order one and the regularized Gauss–Newton step keeps relative error near 1.3 and correlation near 0.07 against the calibrated step; if those failures disappear without the term, the central claim is wrong.","supporting_citations":[],"review_version":1}