{"id":"f406cf02-9a57-4ce5-ad42-d88f7b75b6d4","arxiv_id":"2508.05798","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":3.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper previews an upcoming axiomatization in which probabilistic and quantum algorithms are modeled as basic sequential algorithms with oracles, extending the classical abstract state machine thesis.","lead":"This short paper previews a planned axiomatization of 'basic interactive algorithms', arguing that nondeterministic, probabilistic, and quantum algorithms can all be seen as basic algorithms with suitable oracles. A reader in computing theory might care because it could unify several algorithm classes under one formal framework and clarify the 'physical thesis' about what a physical computer can compute.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Quantum algorithm unification claim is unverifiable in this preview because the oracle model is unspecified; risk of either vacuous or insufficient representation.","rationale":"The reader identified the oracle mechanism's adequacy for quantum non-sequential features as the weakest assumption. I agree and further specify that the concern is twofold: adequacy and non-vacuity. The preview gives no formal definitions, so the claim is genuinely unverifiable from the provided text; hence the reader's UNVERDICTED verdict is appropriate. My concrete test would become executable once the full formal framework is available. Because the paper is explicitly a preview of future work, the lack of proof or definitions does not by itself refute the claim—it only makes verification impossible now. Thus the verdict should remain UNCHANGED. The stress-test does not require manufacturing a flaw; here the identified concern is a legitimate prerequisite for the central claim, and the concrete test provides a way to decide it in the future.","tokens_in":41398,"tokens_out":6791,"duration_ms":74351,"concrete_test":"Examine the promised full axiomatization (upcoming paper or later sections of this manuscript) containing the formal definitions of 'basic interactive algorithm' and 'oracle.' Use the minimal quantum circuit as a test case: one qubit initially |0>, apply a Hadamard gate, measure in the computational basis, and condition the subsequent output on the measurement outcome. Attempt to instantiate this circuit under the paper's definitions as an interactive ASM with oracles. Check two things: (1) Does the model satisfy the stated axioms (e.g., bounded exploration, sequential time) without resorting to treating the entire quantum state as a monolithic atomic term that only the oracle can modify? (2) Are oracles constrained to be physically realizable (e.g., implementable by quantum circuits of polynomial size) or may they be arbitrary functions? If arbitrary oracles are allowed, the unification","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that nondeterministic, probabilistic, and quantum circuit algorithms can all be viewed as basic algorithms with appropriate oracles. For this claim to be substantive, the oracle mechanism must be constrained so that the reduction is non-vacuous and faithful to the sequential-time, discrete-step nature of basic algorithms. The preview, however, provides no formal definition of 'oracle' or 'basic interactive algorithm,' and the abstract only asserts that quantum circuit algorithms fit. The weakest spot is precisely the adequacy and non-triviality of the oracle abstraction. Two failure modes are plausible: (i) if oracles are arbitrary, unrestricted functions, then any quantum circuit becomes trivially a basic algorithm that makes a single oracle call implementing the whole circuit; the purported unification is then vacuous and provides no insight into the nature of quantum algorithms. (ii) If oracles are required to be classical computable functions (to preserve effectivity), then quantum superpositions and intermediate measurements cannot be represented without exponential blow-up or loss of the quantum features, so the claim would be false. The preview does not state which constraints on oracles are intended. This is not an objection to the eventual program, but it is the load-bearing assumption that must be validated before the central claim can be accepted.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This short preview/dialog note recalls the 1990s ASM axiomatization of sequential algorithms, which the author now calls 'basic algorithms,' and distinguishes the original Church-Turing thesis from the stronger 'physical thesis.' It claims that nondeterministic and probabilistic algorithms can be viewed as basic algorithms with appropriate oracles, and that the same view applies to quantum circuit algorithms and other classes. No formal definitions or proofs appear in the abstract, and the full text as submitted is almost entirely unreadable due to encoding corruption, so the concrete technical content cannot be verified.","tokens_in":41681,"tokens_out":4684,"duration_ms":51341,"significance":"If the advertised program were carried out, a unified behavioral axiomatization covering nondeterministic, probabilistic, and quantum circuit algorithms would be a substantial contribution to the theory of algorithms and would sharpen the physical Church-Turing thesis. The paper's historical framing and its reliance on the independently established ASM axiomatization are genuine strengths. However, as it stands the central claim is only asserted. The oracle mechanism is unspecified, so the quantum claim is vulnerable to vacuous or unfaithful formalization; no proof or even precise statement is recoverable from the submitted text.","major_comments":[{"comment":"The claim that 'the same view applies to quantum circuit algorithms' is load-bearing but unsupported: there is no formal definition of 'oracle' or 'basic interactive algorithm' in the recoverable text. The oracle notion must be constrained so that the reduction is neither vacuous (an arbitrary oracle implementing the whole circuit in one step) nor ineffective (a classical oracle too weak to represent superposition and measurement). The author needs to state the oracle axioms and give at least a precise version of the quantum reduction before this claim can be assessed.","section":"Abstract, last sentence"},{"comment":"The body of the paper is mojibake; no definition, theorem, equation, or proof is recoverable. Thus the abstract's assertion that the paper 'illustrates' the oracle view for nondeterministic and probabilistic algorithms cannot be checked. A readable source file is a precondition for any further evaluation and should be supplied in a revision.","section":"Full text (as submitted)"},{"comment":"The paper self-describes as a 'preview' offering a 'foretaste of an upcoming work.' This explicitly defers the axiomatization to a future paper, yet the abstract makes concrete present-tense claims about nondeterministic, probabilistic, and quantum algorithms. The scope needs to be clarified: either restrict the paper to historical/terminological exposition, or include the promised technical core. Currently the assertions outrun the demonstrated content.","section":"Abstract, first paragraph"}],"minor_comments":[{"comment":"The new name 'basic algorithms' for 'sequential algorithms' or 'classical algorithms' should be tied to the prior literature (e.g., Gurevich's ASM axiomatization) to avoid terminological confusion.","section":"Terminology"},{"comment":"The 'physical thesis' is invoked without citations; references to Gandy, Deutsch, or related papers on the physical Church-Turing thesis would be helpful.","section":"References"},{"comment":"The submission contains an extraneous arXiv identifier and math.AP header line, apparently an artifact of text extraction; the source should be cleaned.","section":"Metadata"},{"comment":"If the paper is intended as a preview, it would benefit from an explicit statement of which results are established here and which are deferred to the full paper, possibly as a bulleted list.","section":"Structure"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is not in a reviewable form because the full text is corrupted. The oracle-adequacy issue raised in the reader's report is real and land central: without constraints on oracles, the quantum unification claim is either trivial or unproven. If the full paper contains the formal development, the authors should be encouraged to submit that work rather than a preview; a revision of the present text would need to include the formal definitions or be reframed as purely historical."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a preview in the literal sense—there is no new theorem, proof, or data here. The abstract is a well-written advertisement for Gurevich's forthcoming axiomatization of basic interactive algorithms. The genuinely useful bit is the sharp separation of the logician's Church-Turing thesis from the physical thesis; that distinction is often blurred and worth restating.\n\nWhat's new is the claim that nondeterminism, probability, and quantum circuits can all be seen as 'basic algorithms with appropriate oracles.' I can't verify that from this submission. The stress-test note is correct: without a precise definition of the oracle class, the claim risks being vacuous (a single oracle call for the whole circuit) or false (classical computable oracles can't handle superposition without exponential blow-up). The abstract asserts, not demonstrates. That's fine for a preview, provided the full paper delivers the constraints.\n\nI should note I'm evaluating the abstract only—the supplied full text came through as corrupted/encoded garble. That's not the authors' fault, but it limits what I can honestly say about the historical and methodological sections.\n\nThe citation pattern is self-referential but not objectionable: the ASM axiomatization is established, verified work, and Gurevich is building on it. The preview's reliance on that foundation is legitimate.\n\nBottom line: if the upcoming paper provides a non-vacuous oracle model that faithfully captures quantum and probabilistic computation while preserving the sequential, discrete-step character of basic algorithms, that's a substantial result. This preview, however, is a promise, not a payoff. It deserves a light editorial or commentary venue, but not full peer review as a research contribution—there's nothing to referee technically yet.","headline":"A clearly-written preview with no new results; the oracle-based unification claim is the load-bearing promise, but unverified and unspecified here.","tokens_in":42096,"tokens_out":3278,"would_cite":false,"duration_ms":35470,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This preview argues that nondeterministic, probabilistic, and quantum algorithms can be recast as basic algorithms with appropriate oracles, pointing toward a unified axiomatization of basic interactive algorithms.","keywords":["basic algorithms","abstract state machines","oracles","nondeterministic algorithms","probabilistic algorithms","quantum algorithms","interactive algorithms","Church–Turing thesis"],"falsifier":"Find a concrete quantum circuit algorithm whose observable input–output behavior provably cannot be matched by any basic algorithm with an oracle that answers only discrete queries between finitely many steps—for example, a circuit whose output must reflect the full amplitude vector of a superposition rather than any finite transcript of oracle answers. Such a circuit would refute the preview's central claim.","tokens_in":41316,"feed_emoji":"⚛️","tokens_out":6609,"duration_ms":67588,"temperature":0.7,"pith_summary":"Classical algorithms were axiomatized decades ago as basic algorithms, with every basic algorithm shown behaviorally equivalent to an abstract state machine. This dialog preview argues that the expanded algorithmic landscape—nondeterministic, probabilistic, quantum circuit, and other interactive algorithms—can be brought under the same roof: each can be viewed as a basic algorithm equipped with appropriate oracles. If the promised axiomatization of basic interactive algorithms succeeds, one set of principles would cover many algorithm families and sharpen the distinction between the logician's Church–Turing thesis and the broader physical thesis. The preview itself is a foretaste; the axiomatization and proofs are deferred to the upcoming work.","feed_headline":"Oracles fold quantum algorithms into basic-algorithm theory","feed_subtitle":"Preview argues one axiomatization of interactive algorithms can cover classical, random, and quantum computation.","key_machinery":"The central machinery is the paired notions of a basic algorithm and an oracle. A basic algorithm is the sequential, step-by-step computation already captured by the classical axiomatization; an oracle is an external agent that answers queries between steps, supplying nondeterministic choices, random bits, or quantum measurement outcomes. The classical result that every basic algorithm is behaviorally equivalent to an abstract state machine provides the yardstick for the reduction. In this preview, the oracle does the work of absorbing everything non-sequential or non-deterministic about an algorithm, leaving a shared discrete-step computational core that the upcoming axiomatization of basic","core_discovery":"The paper's central claim is that the quarter-century-old axiomatization of sequential algorithms is not left behind by newer algorithm paradigms. Nondeterministic and probabilistic algorithms are illustrated as basic algorithms whose oracles supply the missing choices or random bits, and the author asserts that quantum circuit algorithms and many other classes fit the same pattern. The underlying mechanism is the oracle: a way to import the non-classical or non-deterministic part of a computation into the environment while the algorithm itself remains a basic, step-by-step, sequential-time process. The paper also draws a sharp line between the Church–Turing thesis as logicians use it—a thes","pith_inferences":["An implication left implicit is that this framing relocates the novelty of probabilistic and quantum computation from the algorithm to the environment: the computational engine stays classical and sequential, and the oracle is where randomness or quantumness enters. That would make 'quantum advantage' a property of the environment plus interaction protocol, not of a new kind of step.","A testable extension: apply the same oracle construction to other proposed algorithm families—analog, adiabatic, or continuous-time models—and check whether their input–output behavior can be reproduced by a basic algorithm with a suitable oracle. The preview's claim predicts yes as long as the computation can be organized into discrete steps.","The paper's sharp separation of the two theses suggests that an experiment showing a physical process that cannot be simulated by a Turing machine would refute the physical thesis while leaving the logician's Church–Turing thesis untouched; this distinction is often blurred in popular debate.","The likely pressure point is time: if a genuinely continuous-time oracle is needed, the discrete-step postulate of basic algorithms may have to be relaxed, which would change the shape of the axiomatization rather than merely adding an oracle."],"forward_implications":["If the oracle reduction is right, nondeterministic and probabilistic algorithms inherit the behavioral equivalence result: each has an abstract state machine with an oracle that matches its behavior.","Quantum circuit algorithms would fall inside the interactive basic-algorithm framework, so the axiomatization of basic interactive algorithms would supply a common semantic foundation for quantum and classical computation.","The distinction between the Church–Turing thesis and the physical thesis becomes a formal boundary: the first is about basic algorithms, while the second is a much stronger claim about physical systems that no axiomatization of algorithms alone can settle.","The upcoming axiomatization would give a precise sense in which 'algorithm' has expanded since the 1960s without changing the underlying sequential computational core."],"supporting_citations":[],"fun_headline_variants":["Oracles extend basic-algorithm theory to quantum","Unified algorithm view via oracles for random and quantum","Sequential algorithms plus oracles cover probabilistic and quantum","Classic axiomatization absorbs quantum via oracles","Oracle mechanism fits quantum into basic-algorithm framework"],"cache_read_input_tokens":2816,"weakest_assumption_plain":"The load-bearing premise is that an oracle can absorb the genuinely non-sequential features of quantum and interactive computation—superposition, measurement, and continuous interaction—while the algorithm itself still advances in discrete sequential steps.","fun_headline_variants_meta":{"raw":{"variants":["Oracles extend basic-algorithm theory to quantum","Unified algorithm view via oracles for random and quantum","Sequential algorithms plus oracles cover probabilistic and quantum","Classic axiomatization absorbs quantum via oracles","Oracle mechanism fits quantum into basic-algorithm framework"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000152,"raw_usage":{"total_tokens":1018,"prompt_tokens":702,"completion_tokens":316,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":446,"completion_tokens_details":{"reasoning_tokens":254}},"tokens_in":446,"tokens_out":316,"duration_ms":3973,"temperature":1.0,"reasoning_tokens":254,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T23:09:13.853593+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Find a concrete quantum circuit algorithm whose observable input–output behavior provably cannot be matched by any basic algorithm with an oracle that answers only discrete queries between finitely many steps—for example, a circuit whose output must reflect the full amplitude vector of a superposition rather than any finite transcript of oracle answers. Such a circuit would refute the preview's central claim.","supporting_citations":[],"review_version":1}