{"id":"221a455b-341c-4f08-9395-66f7bf50deee","arxiv_id":"1908.02760","paper_version":2,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"DoFun 3.0 extends the Mathematica package DoFun with automatic derivation of correlation functions of composite operators, plus workflow tools and a public GitHub repository.","lead":"This paper describes version 3.0 of DoFun, a Mathematica package that automatically derives Dyson-Schwinger and functional renormalization group equations for quantum field theories. The new version adds the ability to derive correlation functions of composite operators, such as the energy-momentum tensor, which are needed for transport coefficient calculations.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Diagram identification limitation threatens the correctness of the composite-operator example","rationale":"The central claim of the paper is that DoFun 3.0 can derive functional equations, including new composite-operator correlations. The only concrete support for the new feature is the Sec. 3.4 example. That example uses identifyGraphs and get1PI to simplify a two-loop expression, and the paper says diagram identification is limited to two loops and can fail for mixed propagators. Since the example is precisely at the two-loop boundary and uses only pure gluons, it does not probe the known failure mode. The assertion in Appendix C that results are correct despite these limitations is an unsupported promise. This is load-bearing because a wrong diagram sum would invalidate the demonstration. The test of reproducing the example and running a mixed-propagator check would settle whether the limitation actually corrupts results. Given that the code is public and the paper is a software release, acceptance should be conditional on this validation; therefore, we propose CONDITIONAL rather than outright ACCEPT. No ad hominem is intended; the authors are appropriately transparent about limitations. The concern is about the gap between the transparency and the blanket correctness assertion.","tokens_in":13654,"tokens_out":9560,"duration_ms":103678,"concrete_test":"Install DoFun 3.0 (git) in Mathematica, run the notebook for Sec. 3.4, and verify that the intermediate counts (72 diagrams, 63 connected) and the final 1PI diagram set in Fig. 2 are reproduced exactly, with the stated symmetry factors. Then repeat the same doCO+identifyGraphs pipeline on a two-loop mixed-propagator theory (e.g., a real scalar coupled to a complex scalar via a cubic interaction) and compare against a manual enumeration of the diagrams; if any diagram is merged incorrectly or dropped, the blanket correctness claim fails.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"Appendix C concedes that diagram identification (identifyGraphs) works only up to two loops and can fail for mixed propagators, yet the paper's headline new feature—composite-operator correlation functions—is demonstrated by the two-loop Yang-Mills example in Sec. 3.4, which relies on identifyGraphs and get1PI to obtain the final result (Figs. 1–2). The blanket assertion 'The symbolic and algebraic results, though, are correct' is not backed by an independent check. If identifyGraphs silently merges two distinct diagrams (giving a wrong symmetry factor) or get1PI drops a nonvanishing diagram, Eq. (26) and the plotted result would be incorrect, undermining the central demonstration. The pure-gluon example does not exercise the documented failure mode of mixed propagators, and the code is not executed in the paper, so the correctness of the new feature remains unverified at exactly the point where the documentation admits fragility.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents version 3.0 of DoFun, a Mathematica package for deriving Dyson-Schwinger equations, functional renormalization group equations, and—new in this version—correlation functions of composite operators. The authors describe installation and basic workflow, the explicit field-type handling introduced in this version, the derivation algorithms based on the standard master equations (the DSE master equation, the Wetterich equation, and the replacement identity Eq. (21)), and a set of new tools such as diagram identification, connected/1PI extraction, and canonical ordering. The main new-feature demonstration is the two-loop correlation function of the spatial, traceless energy-momentum tensor in Yang-Mills theory, Eq. (26), obtained through doCO, getConnected, identifyGraphs, get1PI, and getAE, with diagrammatic results in Figs. 1–2. Appendices list changes from DoFun 2 and document known limitations of diagram identification and plotting.","tokens_in":13802,"tokens_out":9848,"duration_ms":116675,"significance":"If the implementation is correct, the new composite-operator functionality extends a widely used, publicly available tool (GPLv3, with a public git repository) and provides a nontrivial worked example relevant to transport calculations. The algorithms are parameter-free implementations of established functional identities, so there is no circularity or fitting. However, the paper does not provide an independent check of the new feature's output: no algebraic result is displayed, no test suite or verification notebook is referenced, and Appendix C concedes that diagram identification is reliable only up to two loops and can fail for mixed propagators. This makes the unverified two-loop example the main risk to the paper's central claim.","major_comments":[{"comment":"The two-loop composite-operator result, which is the advertised new feature of DoFun 3.0, is presented only as a symbolic diagrammatic expression, with the algebraic translation described only schematically around In[19]–In[20]. Appendix C states that identifyGraphs works only up to two loops and can fail for mixed propagators, yet the paper asserts without further evidence that “the symbolic and algebraic results, though, are correct.” This assertion is load-bearing: if identifyGraphs merges distinct diagrams or misassigns symmetry factors, or if get1PI drops a nonvanishing diagram, then Eq. (26) and Figs. 1–2 are wrong. Please add a reproducibility artifact—for example, a notebook that runs the full pipeline of Sec. 3.4 and checks the number of diagrams, their symmetry factors, and the 1PI truncation—or provide a low-order algebraic expression verified against an independent manual derivation. Please also state explicitly that the two-loop example lies within the reliability regime of identifyGraphs and clarify whether get1PI has any analogous limitation.","section":"§3.4, Figs. 1–2 and Appendix C"},{"comment":"The example uses the Yang-Mills action without ghost fields, stating that ghosts “do not contribute in this case.” This is not obvious: even though the composite operator πij depends only on the gluon field, ghost loops can enter connected multi-loop diagrams through ghost-gluon vertices, and no color or BRST argument is given for their vanishing at this order. If ghost diagrams were nonvanishing, the displayed result would be incomplete. Please provide the missing justification or repeat the example with ghosts included to demonstrate that doCO treats them correctly.","section":"§3.4, In[8] and Eq. (29)"}],"minor_comments":[{"comment":"The typeset code samples for setFields and the action contain brace structures that are easy to misread and may have unbalanced delimiters when copied verbatim; please check that the displayed input matches the code in the repository.","section":"§2, In[3]–In[4]"},{"comment":"The sentence “Of the originally 72 diagrams, many of which are identical, though, now 63 remain” is grammatically confusing; clarify whether the 63 are before or after summing identical diagrams.","section":"§3.4, In[14]"},{"comment":"The limitation section would be more useful if it stated explicitly which functions are affected by the two-loop and mixed-propagator restrictions, and whether getConnected and get1PI are free of the same restrictions.","section":"Appendix C"}],"recommendation":"major_revision","confidential_remarks":"For the editor: this is a solid software paper whose algorithms follow from standard identities and whose code is publicly available. I am not recommending rejection; my main concern is that the headline new feature lacks a verifiable artifact precisely where the paper's own Appendix C admits fragility. A reproducible notebook or a small verified algebraic result would resolve the issue. The ghost-omission point should also be addressed, since the current statement is unsupported. After these additions, the paper would be acceptable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"DoFun 3.0 is a solid, incremental update to a package that already had a user base. The genuinely new piece is automatic derivation of correlation functions of composite operators, built on the identity in Eq. (21) and the auxiliary-field trick that treats the operator as a vertex. The two-loop Yang-Mills example for the energy-momentum tensor correlation function is a reasonable demonstration, and the authors are careful to state what they dropped and why. The code is public, GPLv3, with documentation and a bug tracker, which is exactly what a software paper should ship.\n\nThe math is standard: master equations from Wetterich and the DSE integral, no free parameters, no fitting. The citation pattern is appropriate—prior DoFun versions are cited as the base, the composite-operator identity points to Ref. [8], and the example draws on standard Yang-Mills results. No self-citation load-bearing.\n\nThe soft spot is verification. The correctness of the final expression Eq. (26) depends on the internal functions identifyGraphs and get1PI. Appendix C discloses that diagram identification works only up to two loops and can fail for mixed propagators. The example stays within the two-loop limit and uses only gluons, so the disclosed failure modes are not directly exercised. Still, the paper shows no algebraic output and references no test suite, and the blanket assertion in Appendix C that 'the symbolic and algebraic results, though, are correct' is not backed by an independent check. That is a real gap, but it is a moderate one. The authors do provide some manual reasoning for why the non-1PI diagrams vanish, which mitigates the get1PI worry.\n\nWho is this for? Practitioners in non-perturbative QFT who already use or plan to use DoFun and need composite-operator correlation functions for transport or spectral-function calculations. It won't change the conceptual landscape, but it automates a genuinely tedious derivational step.\n\nI'd send this to peer review. The editor should ask for a small reproducibility addition: e.g., a script that verifies Eq. (26) against a hand-computed diagram, or at least a pointer to a published or online algebraic result from this example. With that, it's clearly publishable. Without, the correctness claim is more a matter of trust than proof, though the public code and honest limitations still make it acceptable to a specialized referee.","headline":"A solid, honest software update whose composite-operator feature is demonstrated within its documented limits; the main weakness is the lack of independent verification of the worked example.","tokens_in":14301,"tokens_out":3922,"would_cite":true,"duration_ms":43763,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["11.10.-z","03.70.+k","11.15.Tk"],"model":"deepseek-v4-flash","headline":"DoFun 3.0 now derives composite-operator correlation equations in Mathematica.","keywords":["Dyson-Schwinger equations","functional renormalization group equations","correlation functions","composite operators","quantum field theory","Feynman diagrams","Mathematica package","symbolic derivation"],"falsifier":"Take a two-loop DSE or composite-operator equation in a theory with mixed boson-fermion propagators, derive it by hand, and run DoFun's identifyGraphs: if a mixed-propagator diagram is not recognized as identical to its hand-derived counterpart or is dropped after 1PI extraction, the stated limitation is confirmed.","tokens_in":1484,"feed_emoji":"📐","tokens_out":1752,"duration_ms":57350,"temperature":0.7,"pith_summary":"This paper presents version 3.0 of DoFun, a Mathematica package that derives Dyson-Schwinger equations, functional renormalization group flow equations, and, newly in this version, correlation functions of composite operators. The central claim is that all three types of equations can be obtained from a user-supplied action and field list in symbolic Feynman-diagram form, then converted to algebraic expressions for further computation. The new composite-operator feature rests on the identity that any full correlation function can be expressed by acting with the operator on fields shifted by propagator times a field derivative, $\\langle F(\\varphi)\\rangle = F(\\Phi_i + D_{ij}^J \\, \\delta/\\delta\\Phi_j)$. A worked example derives the two-point function of the gluonic energy-momentum tensor up to two loops, including connected and one-particle-irreducible (1PI) extraction.","feed_headline":"One package now derives composite-operator equations","feed_subtitle":"The DoFun 3.0 update automates DSEs, flow equations, and operator correlation functions in Mathematica.","key_machinery":"The central mechanism is the replacement identity $\\langle F(\\varphi)\\rangle = F(\\Phi_i + D_{ij}^J \\, \\delta/\\delta\\Phi_j)$, which turns a full correlation function of any operator into a sequence of functional derivatives acting on dressed propagators and vertices. The package represents a composite operator as an auxiliary contracted object $C$ that behaves like a vertex, so the same differentiation and diagram-generation code used for DSEs and flow equations handles operator correlation functions. Three derivative rules, including $\\delta/\\delta\\Phi_i\\, D_{jk}^J = -\\epsilon^i_{jm}\\, D_{jm}^J\\, \\Gamma_{imn}^J\\, D_{nk}^J$, carry all propagator and vertex derivatives, with the sign function $\\epsilon$ encoding Grassmann field anticommutation.","core_discovery":"DoFun 3.0 claims to automate the derivation of DSEs, functional RGEs, and composite-operator correlation functions from a symbolic action, producing output that can be plotted as Feynman diagrams and translated into algebraic expressions. The composite-operator derivation writes the operator as a contracted vertex-like object and then applies the replacement identity of Eq. (21), with the number of loops in the final correlation function ranging up to $n-2$ for an $n$-field operator. In the energy-momentum-tensor example, the package generates 72 diagrams, reduces them by symmetry, keeps connected diagrams, and extracts 1PI diagrams, yielding a compact two-loop expression. The authors state that the symbolic and algebraic results are correct, while the automated identification of identical diagrams is known to work reliably only up to two loops and can fail for mixed propagators.","pith_inferences":["The same auxiliary-vertex trick likely extends to composite operators with more than two fields, but the two-loop limit on graph identification is the practical bottleneck for higher-loop operator equations.","Applying the method to fermionic bound-state operators would require carefully rechecking the Grassmann sign conventions, a task the paper's left-derivative setup makes tractable.","If the graph-isomorphism step were made more robust, the package could handle three-loop operator equations and theories with mixed propagators without manual diagram identification."],"forward_implications":["Users can derive DSEs and flow equations from a symbolic action without enumerating Feynman diagrams by hand.","Composite-operator correlation functions, such as those of the energy-momentum tensor, become accessible through the same automated pipeline.","The symbolic output can be converted to algebraic expressions suitable for trace evaluation or numerical computation.","Explicit field typing removes ambiguity for complex scalar fields and improves sign handling with left-derivatives.","New diagram-classification tools let users select by loop number, connectedness, 1PI property, or named diagram type."],"supporting_citations":[{"why":"Supplies the identity Eq. (21) that expresses any full correlation function through shifted fields and propagator derivatives.","marker":"[8]"},{"why":"Provides the original graphical derivation of DSEs that DoFun generalizes.","marker":"[18]"},{"why":"Documents DoFun 2.0, the previous implementation of DSE and RGE derivations that this version extends.","marker":"[20]"},{"why":"Describes the DoDSE algorithm underlying the DSE derivation routine.","marker":"[71]"},{"why":"Defines the Wetterich equation, the master flow equation implemented by the RGE derivation.","marker":"[72]"},{"why":"Establishes the physical motivation for the energy-momentum tensor correlator via a linear-response transport relation.","marker":"[73]"},{"why":"Identifies the color contractions that make certain non-1PI diagrams vanish in the example.","marker":"[74]"}],"fun_headline_variants":["DoFun 3.0 adds composite-operator derivations","Mathematica package automates operator equations","DoFun 3.0: New tools for functional equations","From action to diagrams: DoFun 3.0 composite ops"],"cache_read_input_tokens":16640,"weakest_assumption_plain":"The automated recognition and classification of Feynman diagrams must correctly identify all generated diagrams, but the paper itself states that this identification only works reliably up to two loops and can fail when mixed propagators appear.","fun_headline_variants_meta":{"raw":{"variants":["DoFun 3.0 adds composite-operator derivations","Mathematica package automates operator equations","DoFun 3.0: New tools for functional equations","From action to diagrams: DoFun 3.0 composite ops"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000202,"raw_usage":{"total_tokens":1294,"prompt_tokens":767,"completion_tokens":527,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":383,"completion_tokens_details":{"reasoning_tokens":460}},"tokens_in":383,"tokens_out":527,"duration_ms":5962,"temperature":1.0,"reasoning_tokens":460,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:34:36.146916+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a two-loop DSE or composite-operator equation in a theory with mixed boson-fermion propagators, derive it by hand, and run DoFun's identifyGraphs: if a mixed-propagator diagram is not recognized as identical to its hand-derived counterpart or is dropped after 1PI extraction, the stated limitation is confirmed.","supporting_citations":[{"cited_title":"Haas, Spectral functions in finite temperature SU(3) gauge theory and appli- cations to transport phenomena, 2014","cited_arxiv_id":null,"evidence_quote":"Identifies the color contractions that make certain non-1PI diagrams vanish in the example."}],"review_version":1}