{"id":"fea5c501-6f9c-41b3-b75c-c457a26666bd","arxiv_id":"2607.14583","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Common fixed points of nonselective measurement channels erase all marginal evidence of invasiveness while preserving branch-level violations of Leggett-Garg inequalities.","lead":"The paper shows that exact no-signaling-in-time (NSIT) can hold even when a measurement disturbs each outcome branch, so silent marginals do not imply a classical temporal history. It provides an analytic qutrit example in which every pairwise NSIT test is exactly zero while a Leggett-Garg inequality is violated, clarifying what NSIT actually certifies.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"No significant objection identified","rationale":"The reader's weakest assumption is the exhaustiveness of Theorem 2. I verified it analytically and found it correct; the proof sketch, though terse, is sufficient. The central claim does not depend on exhaustiveness. The only other issue is a rhetorical overstatement about branch displacement 'governing' the violation, which is not a correctness issue. Hence no load-bearing concern; the paper's core result is sound and the reader's CONDITIONAL verdict is reasonable if minor presentation issues are addressed.","tokens_in":7417,"tokens_out":18881,"duration_ms":166411,"concrete_test":"Symbolically expand M_τ(ρ)=ρ for a general 3×3 density matrix to second order in τ and verify that the unique solutions are exactly ρ*(λ) of Eq. (16). Additionally, simulate the qutrit at λ=2/3, Ωt=π/9 to confirm K1−1=8/27 and η_NSIT=0 numerically.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central counterexample – a qutrit CFP family with exact pairwise NSIT and an LGI violation – is analytically correct. The reader's concern about the converse of Theorem 2 is real but not load-bearing: the forward direction (CFP ⇒ NSIT) plus the explicit LGI calculation already prove the paper's main message. Moreover, the converse can be verified by a second-order Taylor expansion: M_0(ρ)=ρ kills a–(b,c) coherences, and the τ² term forces p_a=p_b, leaving exactly Eq. (16). Even if the manifold were not exhaustive, the claimed counterexample stands. The 'governed by branch displacement' phrase is an overstatement, since K1,max−1 ∝ λ while B_λ=λ(2−λ)/2, but this does not affect the core result.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript introduces common fixed points (CFPs) of nonselective measurement–evolution channels as a mechanism by which exact no-signaling-in-time (NSIT) can coexist with invasive branch disturbance. For a qutrit ring with a local degenerate Lüders measurement, it constructs the one-parameter family Eq. (16), proves that these states satisfy η_NSIT = 0 in every pairwise context (Theorem 1), and derives the closed-form LGI correlation K1(t) and maximum margin K1,max = 1 + 4λ/9 (Eqs. (20)–(22)). Additional hidden-variable, entropic, protocol-landscape, depolarizing-noise, and finite-shot analyses are reported. The paper concludes that exact pairwise NSIT certifies only the absence of marginal signals after outcome erasure, not branch-level non-disturbance or temporal classicality.","tokens_in":7609,"tokens_out":7436,"duration_ms":70782,"significance":"If accepted, the paper provides a sharp, analytically explicit counterexample to the common inference from NSIT to macrorealist noninvasiveness. The central construction is self-contained: the CFP condition, the NSIT argument, and the LGI violation are derived in closed form without free parameters, and the maximally mixed state is included, which strengthens the conceptual point. The central counterexample appears correct. The main weaknesses are that the converse/exhaustiveness part of Theorem 2 is only sketched with algebra deferred to the Supplemental Material, and the numerical sections are not verifiable from the provided text. These gaps do not undermine the forward direction, which already proves the headline separation, but they do affect the 'full manifold' and robustness claims.","major_comments":[{"comment":"The proof of the converse direction of Theorem 2 is only sketched: 'Expanding M_τ(ρ)=ρ near τ=0 forces equal a,b populations and removes the remaining b–c coherence,' with the full algebra in the Supplemental Material. Since the abstract and Section 'Qutrit ring and full CFP manifold' claim that Eq. (16) is the full global CFP manifold, this exhaustiveness statement is load-bearing for the 'full manifold' headline. Please provide the complete expansion in the main text or make the Supplemental Material available and explicit. The forward direction alone suffices for the central counterexample, so this is a completeness issue rather than an error.","section":"Theorem 2, Eq. (16)"},{"comment":"The numerical results summarized in Figs. 2 and 3 and in Eq. (30) — the 1201×801 LP scan, the Jensen–Shannon completion, the depolarizing-noise thresholds, and the finite-shot Monte Carlo — are all deferred to the Supplemental Material, which is not included in the manuscript. As presented, these claims are not checkable. Either include the SM or clearly state that these are supplementary to the analytic result. The main result can stand without them, but the paper should not present unverifiable numbers as part of the central evidence.","section":"Hidden-variable reconstruction / Protocol landscape and robustness"}],"minor_comments":[{"comment":"The phrase 'The violation is governed by finite branch displacement' is an overstatement. From Eqs. (22) and (24), K1,max − 1 = 4λ/9 is linear in λ, while Bλ = λ(2−λ)/2 is quadratic; the two are not proportional. Suggest softening 'governed by' to 'accompanied by' or specifying a precise functional relation if one is intended.","section":"Abstract and Section 'Exact NSIT but analytic LGI violation'"},{"comment":"The notation P(ij)(q) is ambiguous: q appears both as a label for the probability and as an outcome variable. Consider writing P(ij)(q_i, q_j) or similar throughout to distinguish marginals from joint probabilities.","section":"Eq. (4)"},{"comment":"The color scale for the hidden-variable negativity NHV in Fig. 2(a) is not defined in the caption. Please state that it is the LP minimum of Eq. (25), or otherwise indicate the units.","section":"Fig. 2"}],"recommendation":"major_revision","confidential_remarks":"The central analytic result is correct and conceptually valuable. The main issues are the missing proof of the converse in Theorem 2 and the absence of the Supplemental Material. If the SM is already complete and the algebra is straightforward, I would accept after those are included; in the current form, the 'full manifold' claim is not independently verifiable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Bottom line: the central counterexample is correct and clean. The authors construct a qutrit family on which exact pairwise NSIT holds identically, yet every non-trivial member violates a Leggett–Garg inequality, including the maximally mixed state. The new piece is the mechanism — common fixed points of the nonselective measurement–evolution channel — and the full analytic manifold. This goes beyond the earlier logical observation that pairwise NSIT is insufficient for macrorealism: here you have a complete family, not a single example.\n\nWhat the paper does well: Theorem 1 (CFP ⇒ exact pairwise NSIT) is simple and self-contained; the LGI computation is explicit, with K1,max = 1 + 4λ/9; and the branch displacement Bλ = λ(2−λ)/2 gives a quantitative sense of the hidden disturbance. The numerical scans (hidden-variable reconstruction, entropic witness, noise, finite shots) are supportive and honestly presented. No free parameters are fitted; the construction is direct.\n\nSoft spots: The converse of Theorem 2 — that Eq. (16) is the full global CFP manifold — is only sketched, with the algebra deferred to the Supplemental Material. That is a genuine gap if you care about the claim of completeness. It is not load-bearing for the paper’s main message, since the forward direction plus the explicit LGI calculation already proves the separation. The stress-test note is right that a second-order Taylor expansion verifies the converse. Minor: the phrase “the violation is governed by finite branch displacement” overstates the relation; K1,max−1 is linear in λ while Bλ is quadratic, so they are not simply proportional. And the numerics aren’t independently reproducible from the main text, but they are secondary.\n\nThe citation pattern looks healthy; Clemente–Kofler is credited for the known logical insufficiency, and the references to earlier NSIT–LGI work are on point. The paper is an honest, useful contribution. It deserves a serious referee, and the gap in Theorem 2 is addressable without touching the core result. If you work on macrorealism or temporal correlations, this is worth citing and worth discussing.","headline":"A clean analytic counterexample showing exact pairwise NSIT can coexist with LGI violation; the core result is solid, the full-manifold claim is slightly over-extended.","tokens_in":8021,"tokens_out":2486,"would_cite":true,"duration_ms":24025,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["81P15","81P16"],"pacs":[],"model":"deepseek-v4-flash","headline":"Exact no-signaling in time does not imply temporal classicality: a qutrit common-fixed-point manifold has zero NSIT yet violates a Leggett–Garg inequality.","keywords":["no-signaling in time","Leggett-Garg inequalities","common fixed points","nonselective measurement","temporal classicality","qutrit ring","measurement disturbance"],"falsifier":"Find any global fixed point of Mτ outside the one-parameter family (16) by direct numerical search over Hermitian ρ for a dense grid of τ near 0; if one exists, the exhaustiveness claim fails. More directly, in a qutrit prepared in ρ*(2/3), measuring K1 at Ωt = π/9 with η_NSIT = 0 should give K1 = 35/27; observing K1 ≤ 1 with independently demonstrated zero signaling would contradict the paper's prediction.","tokens_in":7350,"feed_emoji":"⚛️","tokens_out":6135,"duration_ms":60791,"temperature":0.7,"pith_summary":"The paper tests whether exact no-signaling in time (NSIT)—the complete absence of a marginal trace of an earlier measurement—is enough to certify that the measurement was noninvasive and the process has a classical temporal history. It answers no, by constructing an exact mechanism, common fixed points (CFPs), where the outcome-erased channel restores the ensemble state while the selective branches are disturbed. For a qutrit ring with a degenerate Lüders measurement, every state on the analytically solved CFP manifold has exact pairwise NSIT, yet every nontrivial member, including the maximally mixed state, violates a Leggett–Garg inequality with margin up to 4λ/9. The violation is controlled by the branch displacement B=λ(2−λ)/2, not by residual signaling. The upshot: NSIT is a certificate of marginal silence after outcome erasure, not of branch-level non-disturbance or temporal classicality.","feed_headline":"Zero signaling in time still fails a Leggett-Garg test","feed_subtitle":"On a qutrit ring, exact no-signaling-in-time hides branch disturbance that violates the classical bound.","key_machinery":"Common fixed point (CFP): a state σ such that Mτ(σ) = D(Uτ σ Uτ†) = σ for all intervals τ; because the zero-time dephasing D also fixes σ, summing over the earlier outcome reproduces the unconditioned marginal, forcing NSIT. The qutrit ring Hamiltonian and the degenerate projective readout of site 0 make the ab sector invariant and c a dark eigenstate, so the manifold is one-dimensional and solvable; the same structure supplies the branch states |a⟩ and (λ|b⟩⟨b| + 2(1−λ)|c⟩⟨c|)/(2−λ), whose difference from the average is the resource B.","core_discovery":"The paper's central claim is that an exactly silent marginal is compatible with invasive branch dynamics. It proves this by Theorem 1: if a state is a common fixed point of the nonselective sequential channel Mτ = D∘Uτ, then every pairwise NSIT condition holds with η_NSIT = 0. The paper then solves the global CFP manifold for a single excitation on a three-site ring under the measurement \"is the excitation at site 0?\", obtaining ρ*(λ) = λ/2 Π_ab + (1−λ)|c⟩⟨c|. For every λ > 0, including the maximally mixed λ = 2/3, exact pairwise NSIT holds but the Leggett–Garg correlator K1 reaches 1 + 4λ/9, violating the classical bound. Hidden-variable reconstruction and an entropic witness independently","pith_inferences":["A natural next step is to use CFP engineering in reverse: prepare a state that is a fixed point of the discarded-register channel and use the surviving LGI violation as a witness of hidden branch disturbance, potentially as a metrological resource.","The construction likely generalizes beyond the qutrit: any system with an invariant subspace and a dark state under a degenerate measurement could host a similar fixed-point manifold, so exact NSIT with LGI violation may be a generic phenomenon.","The paper leaves open whether complete NSIT (all possible pairs and contexts) rather than pairwise NSIT also admits such exact separation; if it does, the operational value of NSIT as a macrorealism witness would be further weakened.","A finite-shot prediction (already present in the paper) is that about 200 shots per context at λ = 2/3, p = 0.1 suffice to clear the classical bound; this could be translated directly into an experimental falsification protocol."],"forward_implications":["Any experiment that uses exact pairwise NSIT as its sole witness for noninvasiveness can be fooled by a CFP state; additional witnesses such as LGI, entropic margins, or hidden-variable reconstruction are needed.","The maximally mixed qutrit state, with K1,max = 35/27, is a concrete zero-signaling, non-classical state that can be tested with current qutrit setups.","The violation region is not fine-tuned: the two-interval landscape has a finite island, and optimized depolarizing noise allows p up to ~0.27 for λ = 2/3 before the LGI bound is restored.","Branch displacement B = λ(2−λ)/2, not residual signaling, scales with the LGI margin; this links the magnitude of hidden disturbance to the observable temporal contextuality."],"fun_headline_variants":["Exact NSIT still violates Leggett-Garg on qutrit ring","Silent marginals, invasive branches: qutrit ring beats LGI","No-signaling in time does not imply classical memory","Maximally mixed qutrit ring: exact NSIT, yet LGI violation","Exact no-signaling hides branch disturbance that violates LGI"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The proof that Eq. (16) is the full global CFP manifold is sketched rather than fully derived in the main text; if the reverse direction of Theorem 2 fails, the 'full manifold' headline weakens, although the existence of one CFP with exact NSIT and LGI violation already carries the paper's main point.","fun_headline_variants_meta":{"raw":{"variants":["Exact NSIT still violates Leggett-Garg on qutrit ring","Silent marginals, invasive branches: qutrit ring beats LGI","No-signaling in time does not imply classical memory","Maximally mixed qutrit ring: exact NSIT, yet LGI violation","Exact no-signaling hides branch disturbance that violates LGI"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000801,"raw_usage":{"total_tokens":3353,"prompt_tokens":733,"completion_tokens":2620,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":477,"completion_tokens_details":{"reasoning_tokens":2525}},"tokens_in":477,"tokens_out":2620,"duration_ms":18753,"temperature":1.0,"reasoning_tokens":2525,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-02T01:40:36.091867+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Find any global fixed point of Mτ outside the one-parameter family (16) by direct numerical search over Hermitian ρ for a dense grid of τ near 0; if one exists, the exhaustiveness claim fails. More directly, in a qutrit prepared in ρ*(2/3), measuring K1 at Ωt = π/9 with η_NSIT = 0 should give K1 = 35/27; observing K1 ≤ 1 with independently demonstrated zero signaling would contradict the paper's prediction.","supporting_citations":[],"review_version":1}