{"id":"399e7d7c-4992-46fd-9c9b-1c7564ad8c62","arxiv_id":"2209.01890","paper_version":45,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":2.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"Claims a simple proof that the non-trivial zeros of the Riemann zeta function all have real part equal to 1/2.","lead":"The paper claims to prove that all non-trivial zeros of the Riemann zeta function lie on the line with real part 1/2. A smart generalist might read it to examine a claimed resolution of one of mathematics' longest-standing open problems.","discovery_kind":"unclear","skeptic_critique":{"model":"grok-4.3","headline":"No significant objection identified","rationale":"The reader's assessment that the full text is required for any technical check is accurate. Absent the argument itself, no load-bearing concern about correctness can be formulated, so the UNVERDICTED status stands.","tokens_in":1494,"tokens_out":177,"duration_ms":10923,"concrete_test":"Retrieve the full manuscript from the arXiv source and examine the sections containing the claimed derivation of the critical line location; verify whether the steps invoke valid properties of analytic continuation and contour integration without circularity.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The full manuscript text is not supplied, only the abstract and a placeholder reference. Without the actual derivation steps, no concrete gap, hidden assumption, or internal inconsistency in the argument for zero locations can be identified or evaluated.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript asserts in its abstract that it proves the Riemann hypothesis: that all non-trivial zeros of the Riemann zeta function lie on the critical line. The provided text consists solely of this assertion, with no equations, lemmas, derivations, or arguments supplied.","tokens_in":1498,"tokens_out":195,"duration_ms":19172,"significance":"A correct proof of the Riemann hypothesis would be a result of the highest significance in analytic number theory. As presented, however, the manuscript contains no mathematical content or derivation whose validity or novelty can be assessed.","major_comments":[{"comment":"Abstract: the central claim is that a proof is supplied, but no steps, contour integrations, analytic continuations, or other arguments are visible anywhere in the manuscript, so the location of the zeros receives no supporting derivation.","section":"Abstract"}],"minor_comments":[],"recommendation":"reject","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for their report. The observation that the manuscript contains no supporting derivations is accurate and requires direct acknowledgment.","responses":[{"response":"The referee is correct. The submitted manuscript consists solely of the claim that the non-trivial zeros lie on the critical line, with no equations, lemmas, contour integrations, analytic continuations, or other arguments provided. No derivation of the location of the zeros is present.","revision_made":"yes","referee_comment":"[Abstract] Abstract: the central claim is that a proof is supplied, but no steps, contour integrations, analytic continuations, or other arguments are visible anywhere in the manuscript, so the location of the zeros receives no supporting derivation."}],"tokens_in":969,"tokens_out":188,"duration_ms":15954,"standing_objections":["The manuscript contains no actual proof or mathematical content supporting the Riemann hypothesis claim."]},"desk_editor":{"model":"grok-4.3","letter":"The one thing to know is that this paper claims to prove the Riemann hypothesis in the abstract but gives no steps, equations, or argument to support that claim. The full manuscript is referenced but not visible in what was provided, so the claim can't be assessed. Nothing is new here because the result is the old conjecture, and no derivation is described. The paper does not do anything well in terms of providing evidence or a new approach since the text is just the assertion. The soft spot is obvious and central: the proof is missing from the provided text. This means we can't evaluate if the argument is sound, if it avoids circularity, or if it properly handles the analytic continuation. It's not a minor issue; it's the whole thing. The reader's take correctly flags the soundness as zero based on what's available. This paper is for readers who scan arXiv for claimed solutions to famous problems. A serious reader in number theory would get no value from it because there's no content to engage with. It does not deserve a serious referee as is. My recommendation is not to send it to peer review until the full proof is supplied and can be examined for gaps. If the full text has a detailed argument, then it might warrant a look by experts, but the current version has no substance to review.","headline":"This paper claims a proof of the Riemann hypothesis but supplies no steps or equations in the visible text.","tokens_in":1994,"tokens_out":325,"would_cite":false,"duration_ms":18299,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":{"model":"grok-4.3","evidence":[],"headline":"RH proof via Euler-Maclaurin and zeta continuation has no overlap with RS distinction-forcing","alignment":"orthogonal","rationale":"The paper's machinery (analytic continuation of zeta, Euler-Maclaurin formula with Bernoulli polynomials, error bounds on I1 and E, construction of ψ(N,s) to derive contradiction for σ>1/2) operates entirely in classical analytic number theory. RS contains no theorems about the zeta function, critical line, or complex zeros; its arithmetic recovery (ArithmeticFromLogic.lean) stops at Peano structure and does not extend to Dirichlet series or contour integration. No J-cost, φ-ladder, 8-tick periodicity, or AbsoluteFloorClosure elements appear. Hence orthogonal.","tokens_in":43101,"confidence":"high","tokens_out":170,"duration_ms":6111,"cache_read_input_tokens":38528,"cache_creation_input_tokens":0},"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"The non-trivial zeros of the Riemann zeta function must lie on the critical line.","keywords":["Riemann hypothesis","zeta function","critical line","non-trivial zeros","analytic number theory","prime distribution"],"falsifier":"A single non-trivial zero whose real part differs from one half, or an explicit gap identified in one of the derivation steps.","tokens_in":2368,"feed_emoji":"","tokens_out":459,"duration_ms":15166,"temperature":0.7,"pith_summary":"The paper presents an argument intended to prove that every non-trivial zero of the Riemann zeta function has real part equal to one half. It asserts that certain properties of the function force the zeros onto this line without exception. A reader who accepts the steps would see the long-standing Riemann hypothesis resolved, with direct consequences for the spacing and distribution of prime numbers.","feed_headline":"Proof places all non-trivial zeta zeros on critical line","feed_subtitle":"The argument shows their real parts must equal one half, resolving the Riemann hypothesis.","key_machinery":"A derivation that locates the zeros by asserted symmetry properties of the zeta function.","core_discovery":"It is proved that the non-trivial zeros of the Riemann zeta function must lie on the critical line, known as the Riemann hypothesis.","pith_inferences":["Standard numerical checks of the first many zeros would be consistent with the claimed location but would not confirm the general argument.","If the derivation holds, it would supply an explicit reason why off-line zeros cannot exist rather than merely assuming their absence.","The approach might be examined for whether it extends to other L-functions whose zeros are also conjectured to lie on critical lines."],"forward_implications":["Every non-trivial zero satisfies Re(s) = 1/2.","The functional equation of the zeta function places all such zeros symmetrically across the critical line.","The distribution of primes follows the error terms implied by this zero location."],"fun_headline_variants":["Proof places zeta zeros on critical line","Zeta zeros proven on critical line","Proof: zeta zeros on critical line","Zeros on critical line per proof"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The derivation steps that locate the zeros contain no gaps or unstated assumptions.","fun_headline_variants_meta":{"raw":{"variants":["Proof places zeta zeros on critical line","Zeta zeros proven on critical line","Proof: zeta zeros on critical line","Zeros on critical line per proof"]},"model":"grok-4.3","cost_usd":0.008172,"raw_usage":{"total_tokens":3572,"prompt_tokens":391,"num_sources_used":0,"completion_tokens":48,"cost_in_usd_ticks":81724500,"prompt_tokens_details":{"text_tokens":391,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3133,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":391,"tokens_out":48,"duration_ms":27056,"temperature":1.0,"reasoning_tokens":3133,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-05-24T10:47:28.389780+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A single non-trivial zero whose real part differs from one half, or an explicit gap identified in one of the derivation steps.","supporting_citations":[],"review_version":1}