{"id":"e6f6d258-c71e-48e1-a0e9-bbed767bddb6","arxiv_id":"2508.14404","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":4.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"An algorithmic procedure, with code promised, for computing tangle Khovanov homology from the authors' own TQFT construction.","lead":"This paper presents an algorithm and code guide for computing Khovanov homology of tangles, the version of a knot invariant for objects with open strands. The computation inherits its mathematics from the same authors' earlier TQFT construction, so the tool's value depends on that construction and on released code.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Corrupted full text and unstated prior TQFT make the algorithm's correctness untestable; central claim is unsupported until a clean version is available.","rationale":"The reader's weakest_assumption correctly identified the dependence on the prior TQFT, which is indeed load-bearing for the computed tables. My review additionally stresses that the full text supplied is corrupted to the point of unreadability and includes a cross-contaminating arXiv ID, so even the algorithm's own details cannot be audited. This makes the paper unverifiable, not because of a specific mathematical error found, but because the necessary content is missing or garbled. The proposed test—retrieving a clean document and running a concrete tangle-to-Hopf-link comparison—would settle whether the pipeline works. Since no such verification is currently possible, I agree with the reader's UNVERDICTED verdict and would not change it. I do not move to REJECT because the mathematical claims might be valid once a clean version is available; the issue is evidentiary, not proof of falsehood.","tokens_in":14732,"tokens_out":6095,"duration_ms":75557,"concrete_test":"Obtain a clean, correctly compiled copy of this manuscript and the authors' companion TQFT paper from arXiv. Implement the described algorithm for the 2-strand tangle T(2,2), close it to form the Hopf link, and compare the resulting Khovanov homology groups with the known homology of the Hopf link (Z in degrees (0,0) and (1,2)). If the match is exact and the prior TQFT is independently shown to be invariant under Reidemeister moves, the central claim is provisionally confirmed; otherwise it fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the paper supplies a complete, implementable algorithm for computing Khovanov homology of tangles. Two load-bearing conditions must hold: (1) the algorithm is actually described in sufficient detail, and (2) the TQFT construction from the authors' prior work is a genuine invariant. The supplied full text is mojibake—mostly unreadable—and even contains an embedded arXiv ID for an unrelated cs.CV paper (arXiv:2508.14405v1), indicating the document is corrupted. Thus condition (1) cannot be verified. Moreover, condition (2) is not established in this paper: the abstract references 'our recent work' without proof or citation, and the omitted construction cannot be checked against the unreadable body. Any error in that TQFT—e.g., failure under Reidemeister moves—propagates directly into every computed table. Since no code artifact is provided, the promised 'practical guide' is also vacuous. Therefore the paper's primary contribution—a reliable computation procedure—is currently unsupported.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This manuscript (arXiv:2508.14404) purports to give a practical algorithm for computing Khovanov homology of tangles, building on a TQFT construction the authors say they introduced in recent work. The abstract states that the paper provides a 'detailed computation procedure' and 'a practical guide for implementing algorithms through codes.' The supplied full text, however, is not readable: it consists largely of mojibake, contains an embedded arXiv identifier for an unrelated cs.CV paper (arXiv:2508.14405v1), and does not expose any pseudocode, worked example, theorem statement, or validation table in intelligible form. I therefore could not verify the existence or correctness of the claimed algorithm, its implementation, or its agreement with known Khovanov homology computations. The paper's central claim—that this is a comprehensive, implementable computational method—is currently unsupported by the submitted text.","tokens_in":14813,"tokens_out":4829,"duration_ms":45971,"significance":"If the algorithm and the underlying TQFT construction are correct, this would be a useful contribution: tangle Khovanov homology is much less developed computationally than the knot/link case, and a concrete procedure with code would open applications in biology and chemistry. The stated goal is valuable and timely. However, as submitted, the paper delivers no checkable content: no explicit algorithm description, no reproducible code, no comparison with the standard Khovanov homology for closed knots/links, and no reference or proof establishing that the prior TQFT is invariant under Reidemeister moves. The contribution therefore cannot currently be used by readers, and its significance cannot be assessed. I would welcome a clean resubmission in which the algorithm, the TQFT foundations, the code, and validation are verifiable.","major_comments":[{"comment":"The supplied text is corrupted and unreadable; it includes the unrelated line 'arXiv:2508.14405v1 [cs.CV] 20 Aug 2025' and otherwise consists largely of mojibake. No pseudocode, worked example, or theorem/proof can be extracted. This blocks verification of the claimed 'detailed computation procedure'; condition (1) of the abstract's central claim is unsupported.","section":"Full text (entire manuscript)"},{"comment":"The computed object is defined by 'our recent work'—a TQFT construction that is neither cited nor reproduced here. The present paper therefore does not establish that the algorithm computes a well-defined invariant: any failure of Reidemeister invariance or functoriality in the prior construction propagates into every output. The paper is not self-contained against an external standard (e.g., agreement with standard Khovanov homology for closed links), so the computations cannot be validated from the submitted text.","section":"Abstract, first paragraph"},{"comment":"The abstract promises 'a practical guide for implementing algorithms through codes,' but the supplied text contains no code, no runnable examples, and no output tables. Thus the claimed practical computational contribution is not testable. I could not confirm even a single sample computation against known values.","section":"Abstract and conclusion"},{"comment":"No validation against standard Khovanov homology is visible in the corrupted text. Since tangle invariants specialize to knot/link invariants by closing the tangle, a few closed tangle examples compared with known knot/link Khovanov homology would be a decisive check. As submitted, this check is absent (or unreadable), leaving the correctness of the algorithm unestablished.","section":"Validation"}],"minor_comments":[{"comment":"The embedded unrelated arXiv identifier must be removed; it is evidence of file corruption. A clean resubmission should ensure correct font encoding so that all mathematical symbols and diagrams are readable.","section":"File encoding/header"},{"comment":"The 'recent work' containing the TQFT construction should be cited explicitly in the abstract and introduction, or summarized in an appendix, so that the dependency is transparent.","section":"References"},{"comment":"Because of the corrupted text, notation and examples could not be checked. A resubmission should include a clear statement of the smoothing calculus, edge assignment, and differential, each illustrated on a small tangle.","section":"Notation and examples"}],"recommendation":"major_revision","confidential_remarks":"This manuscript was not in a reviewable state: the full text is corrupt and the prior TQFT is not cited. I recommend returning it to the authors for a clean, complete resubmission. If a clean version still omits the TQFT construction and code, or contains no validation against standard Khovanov homology, it should not be considered further."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"The honest bottom line: I can't review this paper, and neither can a referee. The supplied full text is corrupted mojibake with a different arXiv ID embedded, so the algorithm, its pseudocode, worked examples, and any validation tables are unreadable. Judging only from the abstract, the claimed contribution is a practical computation procedure and code guide for tangle Khovanov homology built on the authors' own TQFT construction. That is a reasonable thing to want: tangle invariants matter for DNA/protein topology and physics, and a usable implementation would be a service to that community. The abstract is also honest in framing this as a companion to the prior TQFT paper, not as a new invariant.\n\nThe soft spots are load-bearing but mostly not ones I can check. First, the correctness of every computed table depends on the prior TQFT construction, which is only referenced as 'our recent work' with no citation detail, no proof summary, and no verification here. That is circular if the reader is expected to take the tables as evidence for the construction. A companion paper can get away with this if the base paper is published and the code is checkable; neither condition is met. Second, the abstract says tangle Khovanov computation is 'largely unexplored,' which oversells the situation—there is existing literature on functor-valued tangle invariants. Third, the paper promises code but provides no artifact; without code or detailed reproducible examples, 'practical guide' is not yet a deliverable. I am not claiming the mathematics is wrong. I cannot tell. But the central claim—that a researcher can implement and verify the procedure from this paper—is unsupported by the supplied text.\n\nRecommendation: desk-reject the current version, not because the idea is bad, but because the submission is unreadable and missing its key artifact. Ask the authors to resubmit with a clean PDF, a precise citation to the TQFT construction, the code repository, and validation of their outputs against known Khovanov homology for closures or small knotted tangles. If they supply those, I'd take another look.","headline":"Unreadable full text and no code make the algorithm impossible to assess; a clean version with validation could be a useful computational companion, but the current submission is not refereeable.","tokens_in":15410,"tokens_out":2133,"would_cite":false,"duration_ms":24780,"reading_group":"no","serious_thinker":"unclear","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["57K18","57K10","57R56"],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper gives a direct, code-backed procedure for computing Khovanov homology of tangles from a diagram.","keywords":["Khovanov homology","tangles","TQFT","knot invariants","computational topology","chain complex","algorithm"],"falsifier":"Run the algorithm on two diagrams of the same tangle that differ by a Reidemeister move; if the resulting homology groups differ, the claimed invariant fails. Alternatively, close a tangle into a knot and compare the computed groups with the standard Khovanov homology of that closure computed by established software; a mismatch in any rank or grading would refute the construction.","tokens_in":14495,"feed_emoji":"🧵","tokens_out":3813,"duration_ms":44197,"temperature":0.7,"pith_summary":"Khovanov homology is a powerful invariant of knots and links, but until now its computation has been largely limited to closed knots and links. Tangles, which are knot-like diagrams whose strands may have open ends, are more flexible and appear naturally in biology, chemistry, and quantum physics. The paper claims that a recent topological quantum field theory (TQFT) construction for tangle Khovanov homology can be turned into a concrete, step-by-step algorithm. It also provides implementation code, so that a researcher can in principle compute the Khovanov homology of a tangle directly from its diagram. If the procedure is correct, it extends a standard tool of knot theory to a much broader class of objects.","feed_headline":"Tangle Khovanov homology gets an algorithm","feed_subtitle":"A TQFT-based procedure computes the invariant directly from a diagram and ships with code.","key_machinery":"The load-bearing object is the TQFT construction that assigns a chain complex to a tangle with free endpoints on its boundary. It makes the computation local: the algorithm decomposes the tangle diagram into pieces, applies the TQFT's maps piece by piece, and assembles the results into a single chain complex. The code is the practical implementation of that assembly.","core_discovery":"The paper's central claim is that the authors' earlier TQFT construction for Khovanov homology of tangles can be made algorithmic. Given a tangle diagram, the procedure produces homology groups by following the TQFT's local rules, assembling a chain complex whose homology is the tangle invariant. The paper describes the computation in detail and supplies code to carry it out. For closed knots and links, the construction is designed to reproduce the standard Khovanov homology, so the tangle computation is an extension of the familiar invariant rather than a replacement.","pith_inferences":["A natural next step is to benchmark the code against the closure test: closing a tangle into a knot or link should recover ordinary Khovanov homology up to a grading shift, providing an independent check of the implementation.","The same algorithmic skeleton should transfer to other Khovanov-type theories, such as sl(3) or annular Khovanov homology, wherever a TQFT description exists; the paper itself only claims the Khovanov case.","The practical ceiling will likely mirror that of knot Khovanov homology: exponential growth in the number of crossings. The paper's code provides a platform for measuring that growth on concrete tangles."],"forward_implications":["Anyone with a tangle diagram can in principle compute its Khovanov homology mechanically, without designing a bespoke spectral sequence.","The procedure turns tangle Khovanov homology into a computational tool for studying protein, DNA, and other molecular structures naturally modeled by tangles.","Automated computation makes it feasible to generate tables of tangle homology, which can be mined for patterns and conjectures.","Because the construction is a TQFT, the same code can be extended to compute maps induced by tangle cobordisms, not just the homology groups."],"supporting_citations":[],"fun_headline_variants":["Algorithm computes tangle Khovanov homology","Tangle Khovanov homology: now computable","New code for tangle Khovanov homology","Compute Khovanov homology for tangles directly","Tangle Khovanov homology gets concrete algorithm"],"cache_read_input_tokens":2688,"weakest_assumption_plain":"The algorithm's outputs count as tangle Khovanov homology only if the earlier TQFT construction is a true invariant—independent of how the tangle is drawn—and agrees with ordinary Khovanov homology once the open ends are closed up. The present paper supplies the computation procedure, not the proof of that foundation.","fun_headline_variants_meta":{"raw":{"variants":["Algorithm computes tangle Khovanov homology","Tangle Khovanov homology: now computable","New code for tangle Khovanov homology","Compute Khovanov homology for tangles directly","Tangle Khovanov homology gets concrete algorithm"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000137,"raw_usage":{"total_tokens":936,"prompt_tokens":644,"completion_tokens":292,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":388,"completion_tokens_details":{"reasoning_tokens":221}},"tokens_in":388,"tokens_out":292,"duration_ms":3731,"temperature":1.0,"reasoning_tokens":221,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-05T18:33:53.645584+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the algorithm on two diagrams of the same tangle that differ by a Reidemeister move; if the resulting homology groups differ, the claimed invariant fails. Alternatively, close a tangle into a knot and compare the computed groups with the standard Khovanov homology of that closure computed by established software; a mismatch in any rank or grading would refute the construction.","supporting_citations":[],"review_version":1}