{"id":"5526d0b8-a051-42c2-b5ec-394ea7fb33e4","arxiv_id":"2607.12644","paper_version":1,"verdict":"CONDITIONAL","confidence":"LOW","novelty_score":5.5,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Off-shell quantum equivalence is defined via Vilkovisky–DeWitt effective-action scalars built from configuration-space tensors and admissible probes, distinguishing local, branchwise and global equivalence under field redefinitions and auxiliary extensions.","lead":"The paper proposes an operational criterion for off-shell equivalence of quantum field theories using the Vilkovisky–DeWitt effective action and scalar observables. It matters because gravity, cosmology and non-equilibrium QFT routinely need stronger-than-on-shell notions of when two formulations describe the same quantum physics.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified beyond the abstract-only limitation already flagged by the Reader.","rationale":"The abstract states a clear operational criterion and applies it to a standard pair of formulations (metric f(R) versus its auxiliary and scalar–tensor versions). The Reader’s weakest-assumption diagnosis is exactly the point at which the argument could fail: if the VD-plus-probes arena is incomplete or probe-class dependent in a physically relevant way, the claimed distinctions do not settle the physical question. No stronger, more concrete flaw is extractable from the abstract alone. The recommended concrete test simply operationalizes that same concern once the full text appears. Consequently the Reader’s CONDITIONAL / LOW-confidence verdict stands without adjustment.","tokens_in":2099,"tokens_out":421,"duration_ms":4103,"concrete_test":"Obtain the full manuscript and verify that the admissible-probe class is defined independently of the f(R) example (e.g., by an explicit functional characterization or by a short list of axioms that do not presuppose the auxiliary constraint). If the probe class is only illustrated by the same examples used to draw the local/global distinctions, the operational criterion is circular and the central claim weakens.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The Reader correctly isolates the load-bearing assumption: that the Vilkovisky–DeWitt effective action plus a class of admissible probes supplies a complete operational arena for deciding off-shell equivalence. With only the abstract available, that assumption cannot be stress-tested further; no internal inconsistency, missing step, or concrete technical gap is visible in the stated claim. The distinctions drawn for metric f(R) (constraint-enforced auxiliary reformulation versus independent scalar–tensor integration) follow directly once the criterion is granted, and the abstract presents them as consequences rather than additional postulates. Because the full derivations, probe definitions and explicit calculations are absent, the concern remains precisely the one the Reader already recorded; manufacturing a sharper attack would be unfaithful to the available text.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The manuscript proposes an operational criterion for off-shell equivalence of quantum field theories (including gravity) based on the Vilkovisky–DeWitt effective action. Equivalence is to be decided on scalar observables obtained by pairing configuration-space tensors with a class of admissible probes, thereby distinguishing ordinary on-shell equivalence from stronger off-shell notions relevant to gravity, cosmology and non-equilibrium QFT. Metric f(R) gravity and a scalar-field prototype are used to illustrate local, branchwise and global equivalence: the paper claims that metric f(R) and its auxiliary-field reformulation define the same quantum theory when the auxiliary constraint is enforced in the path integral, whereas treating the metric and scalar as independent integration variables in the corresponding scalar–tensor action defines a different quantum theory. Apparent quantum inequivalences are attributed to comparisons of inequivalent quantum objects rather than to failures of genuine equivalence.","tokens_in":2237,"tokens_out":911,"duration_ms":11913,"significance":"If the criterion is correctly formulated and the prototype calculations hold, the work would supply a precise, probe-sensitive language for off-shell equivalence under field redefinitions and auxiliary extensions—an issue that is load-bearing in quantum gravity and modified-gravity model building. Explicit credit is due for framing the problem inside the existing Vilkovisky–DeWitt framework rather than inventing an ad-hoc effective action, and for separating constraint-enforced auxiliary reformulations from independent scalar–tensor quantizations. The claimed distinction for metric f(R) would clarify a recurring source of confusion in the literature. Because only the abstract is available, these strengths remain conditional on the missing derivations, measure choices and probe constructions.","major_comments":[{"comment":"Only the abstract is available for review. The central claim—that scalar observables built from configuration-space tensors and admissible probes via the Vilkovisky–DeWitt effective action correctly decide off-shell equivalence—cannot be verified without the explicit definition of the admissible-probe class, the path-integral measure, and the concrete constructions for metric f(R) and the scalar prototype. Until those appear, the load-bearing criterion remains unassessable.","section":null},{"comment":"Abstract claim that metric f(R) and its auxiliary-field reformulation yield the same quantum theory when the auxiliary constraint is enforced in the path integral, while independent metric-plus-scalar integration defines a different theory: this distinction is the paper’s main physical payoff, yet no equation, measure factor or probe pairing is supplied. A major revision (or full-text review) must exhibit the constrained versus unconstrained path integrals side by side and show that the scalar observables coincide in one case and differ in the other.","section":null},{"comment":"The operational arena is declared to be the Vilkovisky–DeWitt effective action together with a chosen class of admissible probes. The abstract does not indicate whether that class is fixed by a general principle or selected case-by-case. If the latter, the local/global distinctions drawn for f(R) risk being probe-class dependent; the manuscript must either prove probe-independence for the observables of interest or state the dependence as part of the criterion.","section":null}],"minor_comments":[{"comment":"The abstract is clear and well structured, but the phrases “local, branchwise and genuinely global equivalence” are introduced without even a one-sentence definition; a brief parenthetical would help non-specialist readers.","section":null},{"comment":"Once the full text is supplied, standard presentation items (notation for the Vilkovisky connection, explicit form of the probes, and a short comparison table of the three f(R) quantizations) should be checked for consistency with the abstract’s claims.","section":null}],"recommendation":"uncertain","confidential_remarks":"This is an abstract-only review. I cannot responsibly recommend accept, minor_revision, major_revision or reject without the full manuscript. The Reader’s and Skeptic’s assessments correctly flag that the sole load-bearing assumption is the completeness of the Vilkovisky–DeWitt-plus-admissible-probes arena; nothing in the abstract contradicts itself, but nothing can be checked either. Please supply the full text for a proper report. Scope appears suitable for hep-th if the technical content matches the abstract."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The one thing to know is that this is an abstract-only hep-th note proposing an operational criterion for off-shell equivalence via Vilkovisky–DeWitt scalar observables (configuration-space tensors paired with admissible probes). The concrete claim is that metric f(R) and its auxiliary reformulation define the same quantum theory when the auxiliary constraint is enforced in the path integral, while treating metric and scalar as independent integration variables does not. That distinction is the load-bearing result.\n\nWhat looks new is the insistence on testing equivalence on that class of scalar observables, plus the local/branchwise/global taxonomy applied to field redefinitions and auxiliary extensions. The abstract is clear and well-motivated: the ordinary on-shell theorem is insufficient for gravity, cosmology and non-equilibrium QFT, and they give a precise place to look instead. Credit where due—the framing is clean, the f(R) prototype is the right test case, and they correctly separate “different quantum objects” from genuine inequivalence. No free parameters or invented entities show up in the abstract; the criterion sits on existing VD machinery rather than circular fitting.\n\nSoft spots are exactly the ones the reader flagged and no worse. We have no derivations, no explicit probe constructions, no path-integral measures, and no calculations. The weakest assumption is that VD plus a chosen probe class is the complete arena for deciding off-shell equivalence; if that class is under-specified or incomplete, the local/global distinctions do not settle the physics. That is a real but proportionate concern for an abstract-only read—not a manufactured flaw. The stress-test found nothing sharper, and I agree: manufacturing a deeper attack would be unfaithful to the available text. Soundness cannot be scored higher than provisional.\n\nThis is for people who already work with the Vilkovisky–DeWitt effective action, field redefinitions in gravity, or the quantum status of f(R)/scalar–tensor pairs. A serious referee should see the full paper; the claim is important enough inside that subfield and formally grounded enough in existing machinery to deserve referee time rather than a desk reject. I would not cite it yet (no body), and I would not bring an abstract-only piece to reading group, but I would accept it for peer review if the manuscript arrives with the missing technical content.","headline":"Abstract-only conceptual paper proposing a VD-based operational criterion for off-shell equivalence; plausible and useful framing for f(R)/auxiliary cases, but unverifiable without the body.","tokens_in":2840,"tokens_out":561,"would_cite":false,"duration_ms":4717,"reading_group":"no","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"Off-shell quantum equivalence is decided by scalar observables built from the Vilkovisky–DeWitt effective action and admissible probes, not by classical field redefinitions.","keywords":["off-shell equivalence","Vilkovisky–DeWitt effective action","field redefinitions","metric f(R) gravity","auxiliary fields","scalar–tensor theory","quantum field theory","configuration-space tensors"],"falsifier":"Compute the Vilkovisky–DeWitt effective action (or a concrete scalar observable built from it) for metric f(R) gravity with the auxiliary constraint enforced and for the same theory quantized with independent metric and scalar variables; if the resulting scalar observables coincide for all admissible probes, the claimed distinction collapses.","tokens_in":2962,"feed_emoji":"⚛️","tokens_out":664,"duration_ms":5689,"temperature":0.7,"pith_summary":"Field redefinitions that leave classical physics unchanged do not automatically leave the quantum theory unchanged once one goes off shell, where the usual equivalence theorem no longer applies. This paper supplies an operational test for that stronger notion of equivalence: two quantum descriptions are equivalent precisely when they produce the same scalar observables obtained by pairing configuration-space tensors with a chosen class of admissible probes inside the Vilkovisky–DeWitt effective action. The criterion is deliberately sensitive to the observable class under consideration, so it can separate ordinary on-shell equivalence from the stricter local, branchwise, and global off-shell notions required in gravity, cosmology, and non-equilibrium field theory. Applied to metric f(R) gravity, the test shows that the pure metric theory and its auxiliary-field reformulation define the same quantum theory once the auxiliary constraint is enforced in the path integral; by contrast, treating the corresponding scalar–tensor action with independent metric and scalar integration variables yields a genuinely different quantum theory. Apparent quantum inequivalences are thereby traced to comparisons of different objects rather than to a failure of the underlying equivalence.","feed_headline":"Off-shell quantum equivalence fixed by Vilkovisky–DeWitt probes","feed_subtitle":"Metric f(R) and its constrained auxiliary form match; free scalar–tensor quantization does not.","key_machinery":"The Vilkovisky–DeWitt effective action, used as the arena in which configuration-space tensors are paired with admissible probes to produce gauge- and parametrization-independent scalar observables that serve as the operational test of off-shell equivalence.","core_discovery":"Equivalence of quantum descriptions off shell is settled by comparing scalar observables built from the Vilkovisky–DeWitt effective action and admissible probes. Under that criterion, metric f(R) gravity and its auxiliary-field reformulation are the same quantum theory when the auxiliary constraint is imposed in the path integral, while independent quantization of the scalar–tensor variables defines a different theory.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Vilkovisky–DeWitt probes settle off-shell quantum equivalence","Metric f(R) matches constrained auxiliary form as one quantum theory","Scalar probes on Vilkovisky–DeWitt action fix off-shell equivalence","Auxiliary constraint enforces quantum match for metric f(R)","Free scalar–tensor quantization differs from constrained f(R) form"],"cache_read_input_tokens":128,"weakest_assumption_plain":"That the Vilkovisky–DeWitt effective action together with a chosen class of admissible probes is the complete and correct arena in which off-shell equivalence must be decided.","fun_headline_variants_meta":{"raw":{"variants":["Vilkovisky–DeWitt probes settle off-shell quantum equivalence","Metric f(R) matches constrained auxiliary form as one quantum theory","Scalar probes on Vilkovisky–DeWitt action fix off-shell equivalence","Auxiliary constraint enforces quantum match for metric f(R)","Free scalar–tensor quantization differs from constrained f(R) form"]},"model":"grok-4.5","effort":"low","cost_usd":0.003766,"raw_usage":{"total_tokens":1187,"prompt_tokens":791,"num_sources_used":0,"completion_tokens":94,"cost_in_usd_ticks":37660000,"prompt_tokens_details":{"text_tokens":791,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":302,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":791,"tokens_out":94,"duration_ms":3183,"temperature":1.0,"reasoning_tokens":302,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-15T04:28:05.595874+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"Compute the Vilkovisky–DeWitt effective action (or a concrete scalar observable built from it) for metric f(R) gravity with the auxiliary constraint enforced and for the same theory quantized with independent metric and scalar variables; if the resulting scalar observables coincide for all admissible probes, the claimed distinction collapses.","supporting_citations":[],"review_version":1}