Toward Auto-Research: Mining Falsifiable Research Ideas from Paper Knowledge Graphs with Categorical Structure

# Mining Falsifiable Research Ideas from Paper Knowledge Graphs with Categorical Structure
Source: [https://arxiv.org/html/2608.20361](https://arxiv.org/html/2608.20361)
Yuchen WangFirst author and corresponding author\.wangyuchen21@buaa\.edu\.cnSino\-German Joint Software Institute, Beihang University, Beijing, ChinaZhongzhi LuanCorresponding author\.rick710055@263\.netSino\-German Joint Software Institute, Beihang University, Beijing, China

###### Abstract

Automated research\-idea generation systems built on large language models \(LLMs\) share a structural weakness: they reduce ideation to free\-text recombination, random paper pairing, or embedding\-similarity retrieval\. The three approaches fail in the same way – each treats a paper as a flat object, a string or a vector, and so quotients away the typed problem\-method\-metric\-claim arrows a researcher actually uses when reasoning about a cross\-domain analogy\. We recover the missing structure with the minimal piece of category theory that a typed graph alone does not provide: composition, together with identity arrows, which makes it possible to ask whether a proposed analogy preserves relation chains\. Concretely, each paperppis modelled as a small category𝒞p\\mathcal\{C\}\_\{p\}whose objects are extracted typed research entities and whose morphisms are the relations the paper asserts; a cross\-domain analogy frompptoqqis then a partial functor candidateF:𝒞p⇀𝒞qF\\colon\\mathcal\{C\}\_\{p\}\\rightharpoonup\\mathcal\{C\}\_\{q\}that preserves object kinds and covered relation classes, and the failure modes of the three baselines specialise cleanly to “loses arrows,” “does not checkFF,” and “assembles diagrams that need not commute\.” We instantiate the model as a three\-layer algorithm – categorical signature clustering, a functor\-preservation gate, and a six\-axis LLM plausibility judge whose axes locally answer whether the resulting diagram commutes or whether the apparent match is a homonymy artefact\. Evaluated on a corpus of tens of thousands of full\-text\-parsed papers under four ablation conditions, the categorical gate filters cross\-domain candidates at roughly a 17:1 ratio while the quantitative\-falsifier rate of accepted ideas stays above 83% throughout; every rejected candidate is retained with its per\-axis rationale, so the gate doubles as a logging layer rather than a silent filter\.

*Keywords*research idea generation⋅\\cdotknowledge graph⋅\\cdotcategorical clustering⋅\\cdotcross\-domain analogy⋅\\cdotLLM plausibility judge⋅\\cdotfalsifier hypothesis

![Refer to caption](https://arxiv.org/html/2608.20361v1/figs/grsai_user_outputs/fig1_teaser_simplified_01.png)Figure 1:Overview of the proposed categorical front end for research idea generation\.*Left:*flat ideation baselines operate on text, vectors, or untyped node pairs and therefore lose the typed arrows that make an analogy checkable\.*Center:*the proposed front end treats each paper as a small categorical structure and screens candidate cross\-domain bridges with a partial\-functor / commutativity\-style gate\.*Right:*surviving bridges are converted into falsifiable idea families with explicit evaluator\-facing tests\.## 1Introduction

A growing class of “AI scientist” systems automate the full research loop – literature review, ideation, code, experiments, and write\-up – using large language models \(LLMs\) as the active component\[[18](https://arxiv.org/html/2608.20361#bib.bib18),[8](https://arxiv.org/html/2608.20361#bib.bib8),[13](https://arxiv.org/html/2608.20361#bib.bib13),[15](https://arxiv.org/html/2608.20361#bib.bib15)\]\. A weakness shared by these systems is the*idea\-generation*front end: the search for promising research directions is typically reduced to free\-text prompting, LLM\-as\-judge novelty scoring, or retrieval over a flat embedding of paper abstracts\. Empirical evaluations are unkind to this design\. A 100\-author human study reports that LLM\-generated ideas are rated*more*novel than expert ones but*less*feasible\[[7](https://arxiv.org/html/2608.20361#bib.bib7)\]; SoundnessBench\[[21](https://arxiv.org/html/2608.20361#bib.bib21)\]concludes that “current LLMs are not yet reliable as stand\-alone first\-gate evaluators for scientific rigor\.”

We argue in this paper that the failure is not a tuning problem – it is a*representational*one\. LLM\-only recombination, random paper pairing, and embedding\-similarity retrieval all share a single weakness: they treat each paper as a flat object \(a text blob or a single vector\) and therefore cannot represent the internal structure that makes a paper a*paper*: a problem, a method, a metric, a dataset, a claim, and the arrows asserting which method solves which problem and which metric quantifies which claim\. When a researcher looks for a real cross\-domain analogy, the move is not “find a paper whose abstract is nearby in some embedding”; it is “find a paper whose internal arrows can be mapped, one\-to\-one, onto the arrows of mine, so that the diagram still commutes\.” The first three approaches cannot ask this question – they have no arrows to map\.

#### From bridge requirements to categorical constraints\.

A valid cross\-paper bridge is useful only when its structural commitments are explicit and checkable\. The task itself imposes three requirements on such a bridge\. First, the bridge must preserve*typed units*: a method should map to a method, a metric to a metric, and a problem to a problem\. Second, it must preserve*typed relations*: if the source paper asserts that a method solves a problem or that a metric quantifies a claim, the target side must contain the corresponding relation rather than merely the same vocabulary\. Third, these preserved relations must be coherent when chained: transferring “method solves problem” and “metric evaluates method” should still yield a target\-side mechanism that can be checked\. These are exactly the minimal ingredients of a small category – objects, morphisms, composition, identity arrows, and maps that preserve this structure\. Thus a candidate cross\-domain idea becomes a partial structure\-preserving map, and the algorithm in §[6](https://arxiv.org/html/2608.20361#S6)implements only the checks needed for that map: signature matching, arrow\-preservation filtering, and a six\-axis judge that asks whether the local square closes\.

#### What this paper contributes\.

The paper has*algorithmic*contributions, not infrastructural ones\.

1. 1\.A formal model of paper\-level structure as a category and of research\-idea generation, including cross\-domain bridges, as a partial\-functor search problem \(§[2](https://arxiv.org/html/2608.20361#S2)–[3](https://arxiv.org/html/2608.20361#S3)\)\.
2. 2\.A concrete algorithm that operationalises the model in three layers: \(i\) a*categorical signature*schema that lifts typed*object×\\timesmetric*pairs to typed morphisms with a de\-boilerplate gate against universally\-frequent signatures; \(ii\) a sparse paper×\\timespaper graph clustered into 216 intra\-discipline communities; \(iii\) a functor\-preservation gate plus a six\-axis LLM*plausibility judge*that operationalises the commutativity question with explicit per\-axis rationales \(§[6](https://arxiv.org/html/2608.20361#S6)\)\.
3. 3\.An evaluation under four experimental conditions – within×\\timescross×\\timesdump×\\timescomplete – that ablate the contribution of each algorithm layer \(§[7](https://arxiv.org/html/2608.20361#S7)–[8](https://arxiv.org/html/2608.20361#S8)\)\.

The categorical KG we use as substrate is built by our prior work, PARNESS\[[1](https://arxiv.org/html/2608.20361#bib.bib1)\], which provides full\-text PDF parsing, typed\-entity extraction, and the underlying knowledge\-graph storage\. The data layer is not a contribution of this paper; the algorithm that runs on top of it is\.

#### Position vs the sheaf\-obstruction wave\.

Applied category theory has produced a recognisable 2025–2026 wave that uses sheaf cohomological obstruction as a coherence detector for distributed AI beliefs: HOLOGRAPH\[[31](https://arxiv.org/html/2608.20361#bib.bib31)\]reads non\-vanishingH1H^\{1\}of LLM\-prior presheaves as obstruction to global causal structure; Sheaf\-Laplacian Obstruction\[[32](https://arxiv.org/html/2608.20361#bib.bib32)\]formalises cross\-modal alignment hardness; Olivieri–Hernández detect AI\-agent theory\-shift by checking transport and gluing failure on a finite sheaf\[[30](https://arxiv.org/html/2608.20361#bib.bib30)\]\. None of these targets idea generation\. We adopt the gate\-level intuition – “is this analogy a real morphism or a homonymy artefact?” – and apply it at the cross\-paper level, with the LLM operationalising commutativity instead ofH1H^\{1\}\.

## 2Why Existing Approaches Are Insufficient

Before describing our algorithm we explain why three standard approaches to research idea generation do not solve the problem we care about\. The three are: \(B1\) LLM\-only ideation; \(B2\) random pairing over an existing paper KG; and \(B3\) embedding\-similarity retrieval\. We treat them as*baselines for the representational question*: each makes a different assumption about how to represent a paper, and each fails for a corresponding reason\.

#### B1: LLM\-only recombination\.

A modern LLM prompted with “generateNNcross\-disciplinary research ideas” produces fluent, surface\-novel text\. Three failure modes are documented in the literature and observed in our own pilots\. First, the LLM hallucinates citations: an idea typically arrives with “inspired by Smith et al\. 2022” that does not exist or does not say what it is claimed to say\[[18](https://arxiv.org/html/2608.20361#bib.bib18),[21](https://arxiv.org/html/2608.20361#bib.bib21)\]\. Second, the LLM has no notion of a*morphism*: an idea of the form “applyXXfromAAtoBB” is generated by string substitution, without checking thatXX’s domain inAAeven type\-checks inBB\. Third, the LLM’s distribution of mechanisms collapses –*mode collapse*– toward a handful of fashionable techniques \(diffusion, attention, contrastive learning\), regardless of source paper\[[34](https://arxiv.org/html/2608.20361#bib.bib34)\]\.

#### B2: Random paper pairing on a KG\.

Given a paper KG, one could pick two papers uniformly at random and ask an LLM to ideate a bridge\. This is what an unconstrained “pair\-and\-prompt” baseline does\. The combinatorial space is too large to be useful: on our corpus of 17,650 full\-text\-parsed papers \(§[5](https://arxiv.org/html/2608.20361#S5)\),\(176502\)≈1\.56×108\\binom\{17650\}\{2\}\\approx 1\.56\\\!\\times\\\!10^\{8\}pairs are available; the overwhelming majority of randomly selected pairs share no plausible mechanism, and the LLM’s output is forced to either refuse or fabricate one\. There is no signal to filter on – random pairing assumes that a functor between the two papers exists rather than checking\.

#### B3: Embedding\-similarity retrieval\.

The most common research\-aware approach is to embed each paper’s abstract \(or its typed entities\) in a dense vector space and retrieve nearest neighbours\[[10](https://arxiv.org/html/2608.20361#bib.bib10),[35](https://arxiv.org/html/2608.20361#bib.bib35)\]\. This is strictly stronger than B1/B2 but suffers from a specific failure mode that we observed repeatedly in our judge rationales:*homonymy collapse*\. Two papers with high embedding similarity often share*vocabulary*without sharing*structure*: the word “mechanism” in a circuit netlist \(DE\-HNN\) means a solver step, and in equivariant image registration \(CARL\) means an equivariant feature transformation – two completely different morphisms with the same surface token\. A cosine distance cannot tell these apart\. More generally, an embedding is a function𝒞p→ℝd\\mathcal\{C\}\_\{p\}\\to\\mathbb\{R\}^\{d\}that flattens the entire internal structure of paperppinto a single vector; the morphisms of𝒞p\\mathcal\{C\}\_\{p\}are quotiented out\. What embedding similarity surfaces is exactly the set of pairs for which this quotient agrees – which is necessary but far from sufficient for a genuine cross\-domain analogy\.

#### The shared failure\.

The three baselines fail for one reason: they represent each paper as a flat object \(string, vector, or KG node without typed internal arrows\)\. A researcher looking for a real cross\-domain analogy does not work this way\. Table[1](https://arxiv.org/html/2608.20361#S2.T1)summarises the contrast: different surface implementations, same structural loss\. The next section makes that argument precise\.

Table 1:Why flat ideation baselines fail, and what the categorical front end restores\. The point is representational: without typed arrows, composition, and a bridge\-existence check, a generator can produce fluent ideas but cannot tell whether the proposed analogy is structurally valid\.

## 3A Categorical Model of Research\-Paper Structure

This section formalises the structural requirements identified above\. The presentation follows the checks a cross\-paper idea must pass and then introduces the categorical vocabulary needed to state those checks precisely\. The correspondence to concrete system components appears in Table[2](https://arxiv.org/html/2608.20361#S3.T2)\.

#### What a valid bridge must preserve\.

Suppose paperppcontributes a methodMpM\_\{p\}that solves problemPpP\_\{p\}under metricmpm\_\{p\}, and we want to transfer that mechanism into a target paperqq\. A valid bridge cannot be only a nearby abstract, a shared keyword, or a plausible sentence\. It must answer three concrete questions:

1. 1\.Are the units well typed?The image of a method should be a method\-like unit inqq, not a dataset or a generic theme\.
2. 2\.Are the relations preserved?IfppassertsMp→solvesPpM\_\{p\}\\xrightarrow\{\\mathrm\{solves\}\}P\_\{p\}, the proposed image inqqmust assert the analogous typed relation, not merely share a word such as “mechanism” or “alignment\.”
3. 3\.Do relation chains remain coherent?When relations are composed – for example a method is evaluated by a metric that quantifies a claim – the transferred chain should still describe a target\-side mechanism that can be checked\.

A typed KG can express the first two questions\. The third requires a notion of composition, and the bridge must preserve that composition\. That is the precise point at which the model becomes categorical\.

#### The minimal formal object\.

We use only the elementary vocabulary of category theory\. A*category*𝒞\\mathcal\{C\}consists of objects, morphisms between objects, identities, and an associative composition operation

∘:Mor\(B,C\)×Mor\(A,B\)⟶Mor\(A,C\)\.\\circ\\colon\\ \\mathrm\{Mor\}\(B,C\)\\times\\mathrm\{Mor\}\(A,B\)\\ \\longrightarrow\\ \\mathrm\{Mor\}\(A,C\)\.\(1\)A*functor*F:𝒞→𝒟F\\colon\\mathcal\{C\}\\to\\mathcal\{D\}maps objects and morphisms while preserving identities and composition:

F​\(g∘f\)=F​\(g\)∘F​\(f\),F​\(idA\)=idF​\(A\)\.F\(g\\circ f\)\\;=\\;F\(g\)\\circ F\(f\),\\qquad F\(\\mathrm\{id\}\_\{A\}\)\\;=\\;\\mathrm\{id\}\_\{F\(A\)\}\.\(2\)A*partial functor*F:𝒞⇀𝒟F\\colon\\mathcal\{C\}\\rightharpoonup\\mathcal\{D\}is the same structure\-preserving map but defined only on a subcategory; this is the right object for research ideation because an analogy usually transfers only a mechanism, not an entire paper\. A diagram commutes when two directed paths with the same endpoints compose to the same morphism\. For example, if one path fromAAtoBBhas arrowsf1,…,fkf\_\{1\},\\ldots,f\_\{k\}and the other has arrowsg1,…,grg\_\{1\},\\ldots,g\_\{r\}, then

fk∘⋯∘f1=gr∘⋯∘g1∈Mor\(A,B\)\.f\_\{k\}\\circ\\cdots\\circ f\_\{1\}\\;=\\;g\_\{r\}\\circ\\cdots\\circ g\_\{1\}\\quad\\in\\mathrm\{Mor\}\(A,B\)\.\(3\)For standard accounts see Mac Lane\[[2](https://arxiv.org/html/2608.20361#bib.bib2)\], Awodey\[[3](https://arxiv.org/html/2608.20361#bib.bib3)\], Spivak\[[4](https://arxiv.org/html/2608.20361#bib.bib4)\], and Fong–Spivak\[[6](https://arxiv.org/html/2608.20361#bib.bib6)\]\.

#### Paper structure as a small category\.

For each paperpp, we instantiate a small category𝒞p\\mathcal\{C\}\_\{p\}\. Its objects are the extracted entity instances in the paper, each with a kind map

τp:Ob​\(𝒞p\)⟶\{Problem,Method,Metric,Dataset,Claim,…\}\.\\tau\_\{p\}\\colon\\mathrm\{Ob\}\(\\mathcal\{C\}\_\{p\}\)\\longrightarrow\\bigl\\\{\\textsc\{Problem\},\\,\\textsc\{Method\},\\,\\textsc\{Metric\},\\,\\textsc\{Dataset\},\\,\\textsc\{Claim\},\\ldots\\bigr\\\}\.\(4\)Its morphisms are the typed relations asserted between those entity instances:

Method→solvesProblem,Metric→quantifiesClaim,Dataset→evaluatesMethod\.\\textsc\{Method\}\\xrightarrow\{\\;\\mathrm\{solves\}\\;\}\\textsc\{Problem\},\\quad\\textsc\{Metric\}\\xrightarrow\{\\;\\mathrm\{quantifies\}\\;\}\\textsc\{Claim\},\\quad\\textsc\{Dataset\}\\xrightarrow\{\\;\\mathrm\{evaluates\}\\;\}\\textsc\{Method\}\.\(5\)This follows the applied\-category\-theory view of scientific schemas as small categories, close to Spivak’s olog\-style modelling of typed concepts and asserted relationships\[[4](https://arxiv.org/html/2608.20361#bib.bib4)\]\.

#### The corpus\-scale proxy: categorical signatures\.

The full𝒞p\\mathcal\{C\}\_\{p\}is too large and noisy to compare exhaustively for every pair of papers\. The algorithm therefore manipulates a compact signature,

σp=\{\(ObjKind,MetricKind\)\}p,\\sigma\_\{p\}\\;=\\;\\bigl\\\{\\,\(\\textsc\{ObjKind\},\\,\\textsc\{MetricKind\}\)\\,\\bigr\\\}\_\{p\},\(6\)the family of typed object–metric signature atoms extracted from paperpp’s method entities after boilerplate demotion\. Each atom is a projection of one or more paper\-internal morphisms to their typed source/target\-and\-metric information, not an arbitrary keyword\. Shared signature elements retrieve paper pairs whose internal arrows have a candidate match, while the later gates decide whether that match is a real bridge or a homonymy artefact\.

#### A candidate idea as a partial structure\-preserving map\.

A cross\-domain bridge from paperppto paperqqis represented as a candidate partial functor

F:𝒞p⇀𝒞q\.F\\colon\\mathcal\{C\}\_\{p\}\\rightharpoonup\\mathcal\{C\}\_\{q\}\.\(7\)In system terms, this means a paper pair together with matched typed objects, matched signature elements, and evidence pointers for the source and target relations\. It must preserve object kinds, map covered source relations to target relations of the corresponding kind, and satisfy a local commutativity check\. The last condition is the formal version of “does the transferred mechanism still work?” Figure[2](https://arxiv.org/html/2608.20361#S3.F2)shows the smallest instance\.

MpM\_\{p\}PpP\_\{p\}solves𝒞p\\mathcal\{C\}\_\{p\}MqM\_\{q\}PqP\_\{q\}solves𝒞q\\mathcal\{C\}\_\{q\}FFFFsource relation maps totarget relationFigure 2:The commute condition the plausibility judge of this paper operationalises\. A partial functorF:𝒞p⇀𝒞qF\\colon\\mathcal\{C\}\_\{p\}\\rightharpoonup\\mathcal\{C\}\_\{q\}\(dashed blue\) is a valid local bridge when applyingFFto the source\-paper arrowmethod\-solves\-problemyields the corresponding target\-paper arrow\. The embedding\-similarity baseline \(B3 of the preceding section\) can match the four*objects*pairwise but cannot certify that the*square closes*\. Of the six axes the plausibility judge scores, the two highest\-weight ones –*type agreement*\(do the mathematical types of the source arrow and its image agree?\) and*vocabulary genuineness*\(is the matching vocabulary a real morphism rather than a homonymy artefact?\) – are exactly what asks whether the square closes\.
#### What is actually checked\.

The implementation does not enumerate all paths in𝒞p\\mathcal\{C\}\_\{p\}and does not run a theorem prover\. Instead, it uses a scalable local approximation to the functor and commutativity requirements\. Object\-kind agreement checks whetherFFis well typed\. Morphism\-class agreement and preservation rate check whether source arrows are mapped to target arrows of the same kind\. The six\-axis plausibility judge then asks whether the proposed transfer is a real mechanism rather than lexical coincidence:*type agreement*,*vocabulary genuineness*, and*mechanism specificity*are the direct local checks, with the remaining axes recording evidence quality, bridgeability, and novelty\. Thus every accepted idea has a categorical witness in the operational sense used here: a typed source arrow, a typed target arrow, and an explicit judged claim that the local square closes\.

#### Why this is more than a typed graph\.

A labelled KG supplies nodes and edges, so it can represent typed units and typed relations\. What it lacks by itself is the preservation question: when a bridge maps a source relation chain into a target relation chain, should the two paths be considered the same transferred mechanism? Category theory adds exactly the required language – composition, identity, functorial preservation, and commutativity – without requiring heavier machinery\. In this paper those notions act as an engineering specification: they determine the schema, the candidate miner, the preservation\-rate gate, and the judge rubric\.

#### Math\-to\-system correspondence\.

Table[2](https://arxiv.org/html/2608.20361#S3.T2)is the contract between the structural requirements and the implementation\. Each row names a mathematical role, the concrete artefact that carries it, and the component that implements or checks it\. The algorithm in §[6](https://arxiv.org/html/2608.20361#S6)is simply this contract made executable at corpus scale\.

Table 2:Math↔\\leftrightarrowsystem correspondence\. The categorical construction defined above is the specification; each row names which concrete component implements that piece, and where in the algorithm description and data layer it is realised\.

## 4Related Work

We position our work against four threads\. The first is the foundation on which the data substrate is built; the others are contemporary work in the same problem space\.

#### Foundation: PARNESS\.

The categorical paper KG used in this work is built by PARNESS\[[1](https://arxiv.org/html/2608.20361#bib.bib1)\], our prior work introducing a DAG\-kernel harness for end\-to\-end automated research\. PARNESS provides full\-text PDF parsing \(with graceful abstract\-only fallback for papers where legal full\-text access is unavailable\), a typed\-entity extractor for turning paper bodies into typed\-entity nodes, and the underlying knowledge\-graph storage\. The present paper sits one layer above: PARNESS supplies the typed\-entity graph; we contribute the categorical signature schema, the clustering algorithm, the functor\-preservation gate, and the plausibility judge that run on top\.

#### End\-to\-end AI scientists\.

Sakana v2\[[18](https://arxiv.org/html/2608.20361#bib.bib18)\]introduced agentic tree search and produced an entirely AI\-generated workshop paper\. Agent Laboratory\[[8](https://arxiv.org/html/2608.20361#bib.bib8)\]demonstrates that the literature/experiment/report loop runs at 84% lower cost than its predecessor\. Kosmos\[[13](https://arxiv.org/html/2608.20361#bib.bib13)\]extends the run length to∼\\sim12 hours of parallel data analysis, literature search, and hypothesis generation\. AI\-Researcher\[[15](https://arxiv.org/html/2608.20361#bib.bib15)\]stresses “systematic exploration beyond cognitive limitations\.” ResearchAgent\[[9](https://arxiv.org/html/2608.20361#bib.bib9)\]couples idea proposal with collaborative reviewing agents\. All of these systems accept an idea seed from the user or use free\-text LLM judgment to grade their own ideas\. Independent audits of the earlier Sakana system note that literature retrieval is weak and that “novelty often repeats existing work,” a problem that motivates our structural front end\.

#### Structured / KG\-grounded idea generation\.

SciMON\[[10](https://arxiv.org/html/2608.20361#bib.bib10)\]introduced literature\-grounded “inspirations” with an explicit novelty objective\. ResearchAgent and Chain\-of\-Ideas\[[11](https://arxiv.org/html/2608.20361#bib.bib11)\]organise the literature into linear research chains; VirSci\[[12](https://arxiv.org/html/2608.20361#bib.bib12)\]uses heterogeneous expert agents\. Scideator\[[24](https://arxiv.org/html/2608.20361#bib.bib24)\]extracts and recombines \(purpose, mechanism, evaluation\) facets; CHIMERA\[[20](https://arxiv.org/html/2608.20361#bib.bib20)\]mines recombination instances at scale as an IE task\. KG\-CoI\[[25](https://arxiv.org/html/2608.20361#bib.bib25)\]anchors reasoning in an external KG to reduce hallucination\. Knowledge graph\-assisted design\-by\-analogy\[[35](https://arxiv.org/html/2608.20361#bib.bib35)\]formalises function\-effect\-structure ontologies\. Nova\[[14](https://arxiv.org/html/2608.20361#bib.bib14)\]uses iterative planning and retrieval to boost diversity; IRIS\[[19](https://arxiv.org/html/2608.20361#bib.bib19)\]adds MCTS test\-time compute and human\-in\-the\-loop\. LacMaterial\[[39](https://arxiv.org/html/2608.20361#bib.bib39)\]makes the analogical move explicit \(“planet:sun :: electron:nucleus”\) in materials discovery\. Most of these systems use similarity\-based or LLM\-judge filters; none combines a categorical clustering of the paper KG with a multi\-axis structural gate\.

#### Categorical and sheaf\-theoretic gates\.

The sheaf\-on\-KG line begins with Knowledge Sheaves\[[26](https://arxiv.org/html/2608.20361#bib.bib26)\]\(KG embedding as approximate global section of a cellular sheaf\) and Sheaf Neural Networks\[[27](https://arxiv.org/html/2608.20361#bib.bib27),[28](https://arxiv.org/html/2608.20361#bib.bib28)\]\. Boudourides\[[38](https://arxiv.org/html/2608.20361#bib.bib38)\]extends this to a Grothendieck topology on the free category of a KG\.*Categorical Deep Learning*\[[29](https://arxiv.org/html/2608.20361#bib.bib29)\]argues for monads in 2\-categories of parametric maps as a unifying language for neural architectures\. A separate 2025–2026 wave applies sheaf*cohomology*as an obstruction detector for AI coherence: HOLOGRAPH\[[31](https://arxiv.org/html/2608.20361#bib.bib31)\]for causal discovery with LLM priors, Sheaf\-Laplacian Obstruction\[[32](https://arxiv.org/html/2608.20361#bib.bib32)\]for cross\-modal compatibility, Causal Abstraction Networks\[[33](https://arxiv.org/html/2608.20361#bib.bib33)\]for multi\-agent causal beliefs, and Olivieri–Hernández\[[30](https://arxiv.org/html/2608.20361#bib.bib30)\]for detecting agent theory\-shift via gluing failure\. None applies the obstruction\-as\-gate pattern to cross\-paper research idea generation grounded in a real paper KG\. Analogous recent work,*Unlocking LLM Creativity through Analogical Reasoning*\[[34](https://arxiv.org/html/2608.20361#bib.bib34)\], motivates the same goal – structural analogy as a brake on mode collapse – without category\-theoretic formalism\. The cognitive\-science roots of this move trace to Gentner’s structure\-mapping theory\[[36](https://arxiv.org/html/2608.20361#bib.bib36)\]\.

#### Evaluation\.

Si et al\.\[[7](https://arxiv.org/html/2608.20361#bib.bib7)\]run the first head\-to\-head human evaluation of LLM ideation\. IdeaBench\[[16](https://arxiv.org/html/2608.20361#bib.bib16)\]and AI Idea Bench 2025\[[17](https://arxiv.org/html/2608.20361#bib.bib17)\]provide standardised idea\-quality benchmarks\. MLR\-Bench\[[37](https://arxiv.org/html/2608.20361#bib.bib37)\]evaluates open\-ended ML research agents end\-to\-end\. SoundnessBench\[[21](https://arxiv.org/html/2608.20361#bib.bib21)\]specifically targets the first\-gate soundness question and concludes that LLMs are unreliable as the sole soundness grader – a finding that shapes our decision to operate the judge as advisory \(fail\-open\) rather than blocking\.

## 5Data and KG Construction

The corpus and KG that our algorithm runs on are produced by PARNESS\[[1](https://arxiv.org/html/2608.20361#bib.bib1)\]; we do not claim them as a contribution\. This section summarises only the aspects relevant to interpreting the experiments and to guiding the schema decisions that drive the categorical idea\-mining algorithm presented in §[6](https://arxiv.org/html/2608.20361#S6)\.

#### Corpus\.

The substrate this paper’s algorithm runs on is a curated set of17,650 full\-text\-parsed papers– PDF body, sections, figures, tables and formulas extracted by the PARNESS PDF pipeline into typed records – together with an additional9,081 abstract\-only papersfor which legal full\-text retrieval is unavailable\. The abstract\-only papers contribute metadata to the KG but no method\-step signatures, and are therefore invisible to the within\-domain miner of §[6](https://arxiv.org/html/2608.20361#S6)\. Both sets of paper IDs are released as static text files alongside the source repository so that other groups can replicate or compare against the same corpus without access to the parsed data itself – the full\-text list[kg\_papers\_full\_text\.txt](https://github.com/gtrhythm/PARNESS/blob/main/papers/categorical_kg_idea_mining/inputs/kg_papers_full_text.txt)and the abstract\-only list[kg\_papers\_abstract\_only\.txt](https://github.com/gtrhythm/PARNESS/blob/main/papers/categorical_kg_idea_mining/inputs/kg_papers_abstract_only.txt)\.

#### Generated\-idea artifacts\.

We also release the generated opportunity records, judge\-survivor list, proposal records, and five\-form hypothesis\-family outputs as static JSON/JSONL/CSV artifacts in the PARNESS repository:[papers/categorical\_kg\_idea\_mining/artifacts](https://github.com/gtrhythm/PARNESS/tree/main/papers/categorical_kg_idea_mining/artifacts)\. The artifact contains generated ideas and audit metadata only; it does not redistribute parsed full text or copyrighted paper contents\.

#### Parsing\.

Body sections, claims, methods, metrics and similar typed entities are extracted by a structured LLM\-call pipeline using*MiniMax\-M2\.7*as the extraction model\. The PARNESS layer is what turns each PDF into the typed\-entity records \(coveringMethod,Hypothesis,Observation,Contribution,Claim,Critique,Inquiry,Branch, and a dozen more typed kinds\) that this paper’s algorithm reads\.

#### Schema choices relevant to this paper\.

Three properties of the substrate matter for the algorithm in §[6](https://arxiv.org/html/2608.20361#S6)and would be missed if we treated the KG as “a generic property graph”\.

1. 1\.*Object–metric typing is required, not optional\.*EachMethodentity carries an explicit pair recording the*kind*of object the method targets and the*kind*of metric used to evaluate it\. These pairs are the smallest unit on which our*categorical signatures*\(§[3](https://arxiv.org/html/2608.20361#S3)\) can be defined; without typed extraction the morphism familyσp\\sigma\_\{p\}collapses into a bag of keywords and the homonymy problem of §[2](https://arxiv.org/html/2608.20361#S2)returns\.
2. 2\.*Section\-level provenance is retained\.*Every typed entity points back to the paragraph and section that produced it\. This is what makes the*evidence pointer*on a generated idea verifiable by a human reader, and is what allows the de\-boilerplate gate \(next item\) to be evaluated correctly\.
3. 3\.*Universally\-frequent signatures are demoted, not dropped at extraction time\.*Signatures with document frequency≥\\geq80% \(typically “release code,” “comprehensive evaluation,” and similar\) are flaggedboilerplate=truebut left in the record\. The algorithm in §[6](https://arxiv.org/html/2608.20361#S6)can then choose to ignore them at clustering time while still using them for completeness when answering an evidence query\.

None of these properties is specific to the underlying storage engine; we treat the KG as an abstract typed graph and do not depend on the storage details\. Figure[3](https://arxiv.org/html/2608.20361#S5.F3)makes the link between schema choices and algorithm operations explicit\.

Data\-layer schema choiceAlgorithm operation\(1\)typed*object\-kind*×\\times*metric\-kind*pairs on everyMethodentitymorphism familyσp\\sigma\_\{p\}for paperpp\(signature extraction\)\(2\)section\-level provenance pointer on every typed entityverifiable evidence pointer on each generated hypothesis \(direction proposer\)\(3\)boilerplate flag on universal\-frequency signatures \(df/N≥0\.80\\mathrm\{df\}/N\\geq 0\.80\)de\-boilerplate gate; clustering edge weight\|σp∩σq\|non\-bp\|\\sigma\_\{p\}\\cap\\sigma\_\{q\}\|\_\{\\text\{non\-bp\}\}Data\-layer schema choices are dictated by what the categorical idea\-mining algorithm needs to compute –not by storage convenience\. Each supports the local preservation checks of Fig\.[2](https://arxiv.org/html/2608.20361#S3.F2)at corpus scale\.Figure 3:Schema\-to\-algorithm mapping\. Each of the three data\-layer decisions described in the Data section is dictated by a specific operation the categorical idea\-mining algorithm of the next section needs to perform on the signature familyσp\\sigma\_\{p\}\. \(1\) Typed object×\\timesmetric pairs are the*atoms*ofσp\\sigma\_\{p\}, without which clustering would degenerate to bag\-of\-tokens\. \(2\) Section\-level provenance is what lets the evidence pointer attached to a generated hypothesis be human\-verifiable, closing the loop between an LLM proposal and the source paper\. \(3\) The boilerplate flag, demoted\-but\-retained, preserves completeness for retrieval while allowing the categorical clustering to use only signature atoms that carry IDF signal\.

## 6Method: The Categorical Idea\-Mining Algorithm

Conceptually, the algorithm has three structural layers: \(i\) a categorical signature schema that projects each paper’s typed relations into a compact signature family; \(ii\) a clustering step that turns the corpus into an intra\-discipline community structure; \(iii\) a mining\-and\-judging step that enumerates partial\-functor candidates between papers and screens them with local preservation and commutativity\-style checks\. Figure[4](https://arxiv.org/html/2608.20361#S6.F4)expands these layers for the full cross\-domain judged path \(C4\); the four ablation variants that remove or replace individual components are specified separately in §[7](https://arxiv.org/html/2608.20361#S7)\.

![Refer to caption](https://arxiv.org/html/2608.20361v1/figs/grsai_user_outputs/fig4_c4_pipeline_six_axes_grsai_02.png)Figure 4:Canonical cross\-domain complete path \(C4\)\. The top row shows opportunity discovery: the PARNESS KG supplies extracted paper entities and relation evidence; the categorical signature index projects each paper into non\-boilerplate typed signature atoms; the cross\-domain miner uses same\-kind nearest\-neighbour anchors to propose candidate bridges\. The bottom row shows validation and generation: the functor\-preservation gate computes a preservation\-rate signal, the six\-axis judge is applied only in the judged C4 path, triage ranks or rescues surviving opportunities, and generation runs proposer, reranker, and five\-form family expansion\. The other experimental conditions remove or replace pieces of this path as specified in Fig\.[6](https://arxiv.org/html/2608.20361#S7.F6); arrows here are system data\-flow arrows, not categorical morphisms\.To read Fig\.[4](https://arxiv.org/html/2608.20361#S6.F4), an*opportunity*is the record that moves through the pipeline: it starts as a candidate paper pair or within\-cluster micro\-paradigm, accumulates structural evidence and gate scores, and may end as generated hypotheses\. The*signature index*is the per\-paper familyσp\\sigma\_\{p\}of typed signature atoms defined in Eq\.[6](https://arxiv.org/html/2608.20361#S3.E6); the*cross miner*is the same\-kind nearest\-neighbour search that proposes candidate partial\-functor bridges; the*functor gate*computes the preservation\-rate signal; the*judge*is the six\-axis LLM plausibility scorer;*triage*ranks or rescues surviving opportunities; and*generation*denotes proposer, reranker and five\-form family expansion\. C4 is the full cross\-domain judged path shown in the figure\. C1/C3 replace the cross miner with the within\-domain miner, and C1/C2 omit parts of the complete judged path as detailed in Fig\.[6](https://arxiv.org/html/2608.20361#S7.F6)\.

Fig\.[4](https://arxiv.org/html/2608.20361#S6.F4)is the canonical path\. To make it concrete, Fig\.[5](https://arxiv.org/html/2608.20361#S6.F5)shows the corresponding discovery trace: the system first turns a large paper corpus into typed signatures, uses shared signature atoms to retrieve candidate cross\-domain paper pairs, and only then applies the categorical preservation gate, judge and hypothesis\-family generator\.

![Refer to caption](https://arxiv.org/html/2608.20361v1/figs/grsai_user_outputs/fig5_generic_pair_discovery_layout_grsai_03.png)Figure 5:Corpus\-to\-hypothesis walkthrough\. The left\-to\-right trace emphasizes that cross\-domain opportunities are not hand\-picked pairs: papers are first indexed by typed categorical signatures, candidate pairs are retrieved through shared structure, and the resulting bridge is then screened by a functor\-preservation gate and a plausibility judge before being expanded into falsifiable hypothesis families\. Thus the figure illustrates both selection \(*which two papers should be linked?*\) and validation \(*does the link preserve enough structure to be testable?*\)\.### 6\.1Categorical signatures and clustering

#### Signature extraction\.

For each paperppwe read itsMethodentities and emit the signature family \(cf\. Eq\.[6](https://arxiv.org/html/2608.20361#S3.E6)\)

σp=\{\(ObjKindi,MetricKindi\)\}i\.\\sigma\_\{p\}\\;=\\;\\bigl\\\{\\,\(\\textsc\{ObjKind\}\_\{i\},\\,\\textsc\{MetricKind\}\_\{i\}\)\\,\\bigr\\\}\_\{i\}\.\(8\)By the categorical model of §[3](https://arxiv.org/html/2608.20361#S3)each pair is a signature atom: a typed projection of one or more morphisms in𝒞p\\mathcal\{C\}\_\{p\}\. The family is a compact representation \(typically 1–6 elements per paper after de\-boilerplate\) of the paper’s internal arrow structure\.

#### Sparse paper×\\timespaper graph\.

We construct a sparse paper×\\timespaper graph whose edge weight betweenppandqqis the IDF\-weighted count of shared signature classes,

w​\(p,q\)=∑s∈σp∩σqidf​\(s\),idf​\(s\)=log⁡N1\+df​\(s\),w\(p,q\)\\;=\\;\\sum\_\{s\\,\\in\\,\\sigma\_\{p\}\\cap\\sigma\_\{q\}\}\\,\\mathrm\{idf\}\(s\),\\qquad\\mathrm\{idf\}\(s\)\\;=\\;\\log\\\!\\frac\{N\}\{1\+\\mathrm\{df\}\(s\)\},\(9\)whereNNis the corpus size anddf​\(s\)\\mathrm\{df\}\(s\)is the document frequency of signature classss\. Universally\-frequent signatures \(df​\(s\)/N≥0\.80\\mathrm\{df\}\(s\)/N\\geq 0\.80\) are dropped by the de\-boilerplate gate before the intersection is computed, and edges withw​\(p,q\)=0w\(p,q\)=0are absent\. Empirically the median non\-boilerplate signature count per paper is 1, so we set the edge condition to require at least one shared non\-boilerplate signature\.

#### Community detection\.

We cluster the paper graph by Leiden / CPM at resolutionγ=1\.0\\gamma=1\.0and merge sub\-minimum\-size communities into their strongest neighbour by inter\-community edge weight\. The output is a per\-paper cluster label\. On our corpus this yields 216 clusters; 76 of these participate in at least one cross\-cluster edge that survives the bridgeability prior of §[6\.2](https://arxiv.org/html/2608.20361#S6.SS2)\. Operationally, communities play the role of corpus\-level regions: a cross\-domain bridge connects two such regions and is witnessed by a partial\-functor candidate between two of their member papers\.

### 6\.2Mining: within\- and cross\-domain candidates

#### Within\-domain miner\.

For each cluster the within\-domain miner enumerates rare\-signature sub\-paradigms: tuples of signatures whose intra\-cluster cohesion is high but whose corpus\-wide IDF is also high\. Each surviving micro\-paradigm becomes an*opportunity*tagged as a within\-domain mechanism\-depth candidate, with a small set of evidence papers attached\.

#### Cross\-domain miner\.

The cross\-domain miner is what proposes candidate partial functors\. We embed each typed\-entity node into a dense space and issue akk\-nearest\-neighbour \(kNN\) query \(k=5k=5\) per anchor; we filter to same\-kind, different\-paper pairs and apply a bridgeability prior \(same\-cluster threshold 0\.82, cross\-cluster 0\.80\)\. For each surviving pair\(p,q\)\(p,q\)we compute the structural*preservation rate*: how many of the candidate relations on the source paper map \(under cosine≥\\geq0\.70\) into a relation of the same kind on the target paper\. This is the discrete local proxy for arrow preservation and the commutativity\-style check of §[3](https://arxiv.org/html/2608.20361#S3)\. Cross\-domain opportunities are tagged as shared\-mechanism candidates and carry a list of preserved method\-class signatures\.

### 6\.3Gates: from candidates to bridges

#### Functor\-preservation gate\.

The functor\-preservation gate reads cached preservation rates between cluster pairs fromFunctoredges in the KG and, per opportunity, aggregates over its parent domain pairs\. Aggregated rate below0\.300\.30demotes the opportunity \(score×0\.5\\times 0\.5\); it is operated as a demote, not a hard block, so the downstream judge can still see the candidate\.

#### Reasonability gate\.

The reasonability gate blends three feasibility components –*method overlap*\(centroid cosine on method embeddings, weight 0\.50\),*formalism overlap*\(Jaccard on the formal vocabulary, weight 0\.30\), and*institutional bridge*\(citation proximity, weight 0\.20\) – minus a distance penalty \(weight 0\.30\)\. Decisions are tiered:F≥0\.60F\\geq 0\.60accepted,0\.30≤F<0\.600\.30\\leq F<0\.60speculative,F<0\.30F<0\.30rejected\.

#### Six\-axis plausibility judge\.

The judge is the algorithm’s operationalisation of commutativity at the LLM level\. For each opportunity an LLM is prompted to score six axes in\[0,1\]\[0,1\]with explicit per\-axis rationales, listed here with their weights: \(i\)*type agreement*\(w=0\.30w=0\.30\): do the mathematical types of the source and target morphisms match? \(ii\)*vocabulary genuineness*\(w=0\.20w=0\.20\): is the matching vocabulary a real morphism rather than a homonymy artefact? \(iii\)*mechanism specificity*\(w=0\.15w=0\.15\): is the morphism named concretely, or only by an opaque label? \(iv\)*transferability realism*\(w=0\.15w=0\.15\): could the source\-side mechanism plausibly be instantiated in the target setting? \(v\)*falsifiability within 24 hours*\(w=0\.10w=0\.10\): can the resulting hypothesis be checked by a short, concrete experiment? \(vi\)*novelty value*\(w=0\.10w=0\.10\): does the bridge surface a direction not already pursued in the existing literature? The aggregate survival threshold is0\.300\.30\. The judge is operated*advisory*: null or unparseable LLM outputs are treated as pass \(fail\-open\), and every rejected opportunity is archived with its full per\-axis vector and rationale for offline re\-audit\. We discuss the SoundnessBench\[[21](https://arxiv.org/html/2608.20361#bib.bib21)\]\-driven rationale for the advisory choice in §[9\.1](https://arxiv.org/html/2608.20361#S9.SS1)\.

### 6\.4Triage and hypothesis\-family generation

#### Triage router\.

The triage router routes surviving opportunities by a weighted blend of judge score and structural score \(weights 0\.35, 0\.25, 0\.20, 0\.10, 0\.10 over preservation rate, raw rate, log\-saturated number of preserved signatures, bridgeability of physical objects, and novelty gap\)\. High\-judge candidates land in the proceed lane; high\-structure / low\-judge candidates are rescued\. A small exploration quota is reserved for under\-judged but structurally rich candidates\.

#### Direction proposer\.

A surviving opportunity is converted into anInquiry\+Branch\+Hypothesistriple by an LLM call that is given the canonical source/target members \(centrality\-filtered\) and the preserved method\-class signatures\. The prompt is identical across the four experimental conditions of §[7](https://arxiv.org/html/2608.20361#S7); what differs is*which opportunities reach it*\.

#### Hypothesis\-family expander\.

Each proposal is expanded into a five\-form falsifier family:

- •*strict:*\|mtarget−msource\|/msource≤ε\|m\_\{\\text\{target\}\}\-m\_\{\\text\{source\}\}\|/m\_\{\\text\{source\}\}\\leq\\varepsilon\.
- •*rank:*mmethod\>mbaselinem\_\{\\text\{method\}\}\>m\_\{\\text\{baseline\}\}on the target metric\.
- •*existence:*mmethod≥mrandom\+δm\_\{\\text\{method\}\}\\geq m\_\{\\text\{random\}\}\+\\delta\.
- •*baseline\_ratio:*mmethod/mbaseline≤ρm\_\{\\text\{method\}\}/m\_\{\\text\{baseline\}\}\\leq\\rho\.
- •*neg\_transfer:*mmethod<mrandom−δm\_\{\\text\{method\}\}<m\_\{\\text\{random\}\}\-\\delta\.

Thresholdsε,ρ,δ\\varepsilon,\\rho,\\deltaare filled by the LLM and validated against a known\-metric table; each form is paired with an explicit evaluator spec\.

## 7Experimental Conditions

We evaluate the algorithm of §[6](https://arxiv.org/html/2608.20361#S6)under four experimental conditions arranged on two binary axes:*within*vs*cross*domain \(which miner is used\) and*dump*vs*complete*\(which gates are active\)\. These four conditions are not separate contributions; they are an ablation that isolates the effect of the diversifier and the plausibility judge\.

Figure[6](https://arxiv.org/html/2608.20361#S7.F6)lays out the 2×\\times2 ablation\.

within domaincross domaindumpcompleteC1– within×\\timesdumpminer→\\togovernor \(annotate\)→\\totriageC2– cross×\\timesdumpcross\-miner→\\tofunctor gate→\\totriageC3– within×\\timescompleteC1\+\+*diversifier*\(MMR\)C4– cross×\\timescomplete\+\+judgeC2\+\+diversifier\+\+*plausibility judge*Figure 6:Experimental conditions as a 2×\\times2 ablation\. The two axes are the miner \(within vs cross domain\) and the gate configuration \(dump vs complete\)\. Moving*down*adds the diversifier; moving*down\-right*additionally adds the six\-axis plausibility judge\. C4 \(green outline\) is highlighted because it is the full cross\-domain complete setting: it keeps the cross\-domain functor gate from C2 and adds the diversifier plus the six\-axis plausibility judge\.All four conditions share the same proposer prompt, the same family expander, the same generation cap \(500 proposals and 500 families per shard, withK=4K=4shards\), the same sampling parameters \(temperature==0\.9,n\_samples==2\), and the same upstream KG corpus\. The LLM provider is MiniMax\-M2\.7; the entity embedder is qwen3\-embedding\-4b \(2560\-d\)\.

## 8Results

#### Funnel\.

Table[3](https://arxiv.org/html/2608.20361#S8.T3)and Figure[7](https://arxiv.org/html/2608.20361#S8.F7)summarise the per\-stage counts\. Condition C1 mines 13,951 within\-domain opportunities; C2 mines 163 cross\-domain pairs – a 86×\\timesasymmetry\. The number itself is not the headline;*the fact that the asymmetry exists at all*is\. Embedding\-similarity retrieval \(B3 of §[2](https://arxiv.org/html/2608.20361#S2)\) does not exhibit this gap: a nearest\-neighbour search over paper\-level embeddings returns roughly comparable counts of within\-domain and cross\-domain pairs above any fixed cosine threshold, because cosine cannot distinguish “shared vocabulary” from “shared structure”\. The 86×\\timesgap is what the categorical gate*produces*– it is direct evidence that the functor\-preservation requirement is filtering out the homonymy pseudo\-bridges that a flat retriever would pass through\. Thus the gap is not a recall failure but an expected sparsity signal: cross\-domain analogies are admitted only when typed morphism structure, not merely lexical proximity, is preserved\. The corresponding judge funnel in C4 – 154 of 163 candidates rejected, 9 surviving – looks aggressive but is computationally inexpensive: each LLM judgment costs roughly10310^\{3\}output tokens, so the entire judge pass costs about 1\.6×105\\times 10^\{5\}tokens, two orders of magnitude below the downstream proposer\-and\-family load\. The strictness of the gate*buys*the cost reduction observed later in the token economy panel of Fig\.[9](https://arxiv.org/html/2608.20361#S8.F9)\.

#### Budgeted expansion, not a capacity limit\.

The small final C4 count should not be read as the maximum number of ideas the system can produce\. It is a deliberately budgeted expansion: the judge threshold0\.300\.30turns 163 cross\-domain candidates into 9 survivors; the proposer then usesn\_samples=2\\texttt\{n\\\_samples\}=2, yielding 18 proposal\-level ideas; and the family expander emits five falsifier forms per expanded proposal, yielding 50 idea members in this run\. Raisingn\_samples, expanding every proposal, or lowering the judge threshold would produce more ideas, but with a predictable trade\-off: higher review load, higher token cost, and lower average plausibility\. The archive design below preserves the rejected judgments precisely so that a user can re\-open this budget later without re\-running the judge\.

Table 3:Per\-stage funnel under the four experimental conditions\. “Gate\-passed” is the last gate before triage \(functor / reasonability for C1–C3, judge for C4\)\.StageC1 \(W/dump\)C2 \(X/dump\)C3 \(W/compl\.\)C4 \(X/compl\.\+J\)Mined opportunities13,95116313,951163Gate\-passed13,95116313,9519LLM proposals2,8513052,86518Hypothesis families1,991210520∗10∼\\simidea members \(×5\\times 5\)9,9551,0502,60050∗C3 family count depressed by transient LLM\-provider quota contention\.![Refer to caption](https://arxiv.org/html/2608.20361v1/x1.png)Figure 7:Per\-stage counts across the four conditions \(log scale\)\. The within\-vs\-cross opportunity gap \(86×\\times, C1/C3 vs C2/C4\) and the C4 judge funnel \(17×\\times\) dominate the picture\.
#### Judge survivors\.

Table[4](https://arxiv.org/html/2608.20361#S8.T4)lists all nine C4 survivors\. Reading the table as a whole, the survivors fall into three interpretable tiers that mirror the categorical model rather than an arbitrary score cut\. The single high\-confidence bridge \(row 1, score 0\.753\) sits*within*the diffusion\-3D family: both papers explicitly name the same score function under SE\(3\) equivariance, so the partial\-functor candidate has clear images for the relevant objects and arrows, and the local preservation check is strongest\. The worth\-investigating tier \(rows 2–3, score 0\.42–0\.57\) crosses sub\-fields but preserves a concrete mathematical object – in row 2 it is the well\-mixed atmospheric lifetime parameterisation that survives both the climate\-model schema and the biogeochemistry\-coupling schema; in row 3 it is the DDIM inversion operator shared between video\-editing and preference\-aligned diffusion\. The speculative tier \(rows 4–9, score 0\.30–0\.42\) shares only a generic mechanism family \(optimisation, self\-supervision, planning, robust RL\) without a named common object; the judge has effectively flagged “the diagram*could*commute, but the specific morphism is not stated in either paper”\. This three\-tier pattern is what makes the threshold0\.300\.30meaningful: the categorical content of a bridge degrades smoothly with the score, so an aggregate threshold is*interpretable*as a cut on structural depth rather than a free hyperparameter\. A second observation: row 2 \(ICON→\\toCLIMBER\-X\) is a true cross\-disciplinary bridge that an embedding\-similarity baseline would not surface, because the two papers’ abstracts share little surface vocabulary; the judge nevertheless rates it second\-highest because the categorical structure of the well\-mixed assumption is shared verbatim across the schemas of the two systems\.

Table 4:The nine C4 judge survivors \(out of 163 cross\-domain candidates\)\.s→ts\\\!\\to\\\!tare KG cluster indices; the “score” column is the weighted six\-axis aggregate\. The high\-confidence threshold is 0\.70\.
#### Coverage\.

Within\-domain conditions touch all 216 KG clusters; cross\-domain conditions touch 76\. Gini coefficients on the per\-cluster opportunity counts are 0\.514 \(within\) and 0\.568 \(cross\)\. Two consequences follow\. First, the within\-domain Gini around0\.50\.5is well below the regime in which a single hot cluster dominates the corpus \(one mode would push Gini past0\.80\.8\): the categorical clustering is producing communities that broadly track the discipline structure of the corpus rather than collapsing into a few super\-clusters\. Second, the cross\-domain Gini is only slightly higher than the within\-domain one \(\+0\.054\+0\.054\)\. Were the cross\-bridges concentrated on a handful of well\-known interdisciplinary “corridors” \(image↔\\leftrightarrowlanguage, RL↔\\leftrightarrowtheory, etc\.\), we would expect a far larger gap\. The fact that the gap is small is what suggests the cross\-domain miner is finding genuinely diverse structural bridges across 76 of the 216 clusters \(the*bridgeable fraction*of the corpus is roughly35%35\\%\), rather than rediscovering the same cliches\. Figure[8](https://arxiv.org/html/2608.20361#S8.F8)shows the top\-10 cluster distributions\.

![Refer to caption](https://arxiv.org/html/2608.20361v1/x2.png)Figure 8:Top\-10 cluster coverage\. Within\-domain conditions spread opportunities over 216 clusters with Gini=0\.514; cross\-domain conditions hit 76 clusters with Gini=0\.568\.
#### Diversity\.

Branch\-frame uniqueness ratio is≥\\geq0\.993 in every condition, and the unique\-hypothesis\-first\-sentence ratio is100%100\\%\. The non\-trivial part is not the magnitude \(an LLM atT=0\.9T=0\.9rarely produces verbatim duplicates\) but that diversity is preserved*across*structurally similar opportunities\. In an LLM\-only baseline, opportunities sharing the same source cluster tend to collapse into a single “framing” \(reported as mode collapse by\[[34](https://arxiv.org/html/2608.20361#bib.bib34)\]\); in our pipeline, two opportunities that share the same cluster but differ in which signature atom they pick out produce distinct framings, because the proposer prompt is conditioned onσp\\sigma\_\{p\}rather than on the cluster label\. Structural diversity in the input thus propagates to lexical diversity in the output, rather than being washed out at the LLM step\.

#### Quality\.

Figure[9](https://arxiv.org/html/2608.20361#S8.F9)shows the share of proposals with a quantitative falsifier \(a numeric comparator such as≤\\leq,≥\\geq, or a literal threshold\) and the tokens\-per\-final\-idea cost\. Quantitative\-falsifier rate is 84\.5% \(C1\), 86\.6% \(C2\), 83\.4% \(C3\) and 88\.9% \(C4\)\. The interpretation: prior reports on LLM\-only hypothesis generation note quantitative\-falsifier rates in the3030–50%50\\%range\[[10](https://arxiv.org/html/2608.20361#bib.bib10),[7](https://arxiv.org/html/2608.20361#bib.bib7)\]\. The factor\-of\-two improvement here is not an LLM\-capability story – the underlying proposer is the same MiniMax\-M2\.7 used in baseline comparisons; it is a*scaffold*story\. The five\-form family expander forces a numeric target, a numeric baseline and a numeric epsilon to be filled or the form is rejected at validation\. Hence the≥83%\\geq 83\\%rate is what happens when the LLM’s degrees of freedom are constrained to the falsifier schema rather than to free text\. The slight edge of C4 \(88\.9%\) reflects an upstream effect: the judge’s mechanism\-specificity axis prefers survivors that name a concrete mathematical object, and concrete objects are easier to quantify\.

![Refer to caption](https://arxiv.org/html/2608.20361v1/x3.png)Figure 9:Left: % proposals with a quantitative falsifier \(numeric comparator \+ literal threshold\)\. Right: real tokens per final idea member\. C3’s outlier cost reflects transient LLM\-provider retries, not a design flaw\.
#### Judge dimension separation\.

Figure[10](https://arxiv.org/html/2608.20361#S8.F10)shows the six\-axis score distribution over the full set of 163 cross\-domain judgments\. Survivors and rejected separate on every axis\. The two highest\-weight axes carry the strongest signal:*type agreement*\(survivor mean 0\.49 vs rejected 0\.10, a 4\.9×\\timesgap\) and*vocabulary genuineness*\(0\.46 vs 0\.10\)\. Three deeper observations follow\. First, the separation is largest on the two axes most directly tied to the categorical model \(type, vocabulary genuineness\) and smallest on*novelty value*– which is the only axis the LLM judges purely on surface fluency\. This pattern is what we would expect if the judge is genuinely doing the local preservation task rather than scoring all six axes from a single “does this look good” impression; an impression\-driven judge would show uniformly correlated axes\. Second, the rejected scores cluster near zero on type agreement and vocabulary genuineness with explicit homonymy\-risk text in the rationale – e\.g\., a rejected bridge between a circuit\-netlist paper and an equivariant image\-registration paper has only “mechanism” as a common token; on the circuit side “mechanism” refers to a numerical solver step, on the registration side to an equivariant feature transformation; the judge correctly identifies this as token\-collision rather than morphism\-collision\. This is exactly the failure mode an embedding\-similarity gate would pass through and is the reason category\-theoretic phrasing of the question matters\. Third, the separation holds on*every*axis simultaneously, which makes the aggregate threshold robust to single\-axis noise: a survivor must clear multiple structural reasons, and a rejected candidate typically loses on several axes at once, not just on one accidental low score\.

![Refer to caption](https://arxiv.org/html/2608.20361v1/x4.png)Figure 10:Six\-axis plausibility judge scores, 154 rejected \(purple boxes\) vs 9 survivors \(green boxes plus jittered dots\), drawn from the full archive of C4 cross\-domain judgments\. Survivor and rejected distributions separate on every axis; the three high\-weight axes –*type agreement*\(w=0\.30w=0\.30\),*vocabulary genuineness*\(w=0\.20w=0\.20\) and*mechanism specificity*\(w=0\.15w=0\.15\) – carry the cleanest separation, with mean gaps of at least 4×\\times\.
#### Cost\.

Wall\-clock times: 5h55min \(C1\), 1h03min \(C2\), 10h47min \(C3\), 32min \(C4\)\. Real token estimates:∼\\sim9M,∼\\sim1M,∼\\sim6M,∼\\sim0\.05M\. Token cost per final idea member:∼\\sim800 \(C1\),∼\\sim570 \(C2\),∼\\sim2,500 \(C3, quota\-contended\),∼\\sim700 \(C4\)\. The interpretation: the structural gates dominate the throttling and the LLM gates dominate the cost\. Most of the C4 saving \(32 minutes vs nearly six hours for C1\) is not from a smarter LLM but from the upstream collapse 13,951→\\to163: by the time tokens are spent, the bridge candidate set has been thinned by structural reasoning that costs essentially nothing per item\. C3’s outlier is a quota\-contention artefact, not a design pathology – a controlled rerun on a private quota brings C3 onto the C1 line\. Even with that artefact, the cost range570570–2,5002\{,\}500tokens per idea places this pipeline at least an order of magnitude below the per\-idea cost of contemporary end\-to\-end “AI scientist” systems\[[18](https://arxiv.org/html/2608.20361#bib.bib18),[13](https://arxiv.org/html/2608.20361#bib.bib13)\], which is the empirical case for structuring the gate before the generator rather than after\.

#### Sample ideas\.

Two concrete outputs ground the methodology\. Both have the same structural property: a specific target metric, a specific baseline and a specific numerical threshold to refute against\. This property is what distinguishes a falsifier\-form hypothesis from the kind of vague “X improves Y” suggestion an LLM\-only generator typically produces; it is also what makes the ideas downstream\-actionable – a human or agent can decide what to run without re\-reading the source papers\.

> Inquiry:Can ICON’s atmospheric well\-mixed assumption parameterization for lifetime estimation be transferred to CLIMBER\-X’s carbon\-flux coupling layer to improve mass\-conservation fidelity in the 10\-year carbon turnover regime? Hypothesis \(strict form\):Implementing ICON’s well\-mixed assumption parameterization for atmospheric lifetime estimation into CLIMBER\-X’s carbon\-flux coupling module will reduce the normalised RMSE of the 10\-year carbon turnover against the CLIMBER\-X baseline by at least 15% without requiring re\-running coupled GCM simulations\. Falsifier:If inserting ICON’s lifetime reconstruction parameterization into CLIMBER\-X yields normalised RMSE≥\\geqbaseline, the hypothesis is refuted\.

A within\-domain example \(C1\):

> Inquiry:Does explicit modelling of spatial affordance dynamics between physical objects and digital overlays improve parent\-child co\-engagement metrics in educational mixed\-reality robotics compared to state\-based affordance approaches? Hypothesis:A dynamic affordance graph \(DAG\) modelling real\-time object\-state transitions under multi\-agent \(parent \+ robot \+ child\) interaction will yield higher co\-engagement duration and lower disengagement events than a static affordance baseline, with effect size≥\\geq0\.4 Cohen’sddon the relevant human\-evaluation rubric\.

## 9Discussion

#### Within vs cross\.

The 86×\\timesasymmetry between within\-domain \(13,951\) and cross\-domain \(163\) mined opportunities is the most important number in the paper\. It tells us two things: first, the KG*is*clustered – the within\-domain miner has no shortage of structural depth to exploit – and second, real cross\-cluster bridges are rare*by design*: the miner requires each cross\-cluster signature to include at least one specific term and to span at least two parent domains, so that boilerplate co\-occurrences \(such as “release code” or “comprehensive evaluation”\) are filtered out before they can pose as bridges\. The 17×\\timesfunnel applied by the judge takes the 163 down to 9 – a survivor rate consistent with the prior in the analogical\-reasoning literature that genuinely structure\-preserving cross\-domain analogies are sparse\[[36](https://arxiv.org/html/2608.20361#bib.bib36),[34](https://arxiv.org/html/2608.20361#bib.bib34)\]\.

### 9\.1Why the judge must remain advisory

A natural temptation is to operate the judge as a blocking gate: a candidate that scores below threshold is silently dropped and never appears downstream\. We did not\. The argument has three parts\.

#### \(i\) SoundnessBench precedent\.

SoundnessBench\[[21](https://arxiv.org/html/2608.20361#bib.bib21)\]reconstructs 1,099 ML research proposals from ICLR submissions, labels each with reviewer soundness sub\-scores, and audits the labels against the underlying papers\. Its central finding is that current LLMs are*not*reliable as stand\-alone first\-gate soundness graders: the failure mode is not random noise but systematic miscategorisation – LLMs over\-reject proposals that name unfamiliar baselines, and over\-accept proposals that recite popular methods regardless of whether the proposed combination is sound\. Our six\-axis rubric \(§[6](https://arxiv.org/html/2608.20361#S6)\) is substantially narrower than ICLR soundness grading – we ask only about structural plausibility of a cross\-paper bridge, not about full method correctness – but the failure modes carry over\. A bridge that the LLM fails to recognise \(because the mechanism is named idiosyncratically in one of the papers\) is exactly the kind of false negative SoundnessBench warns about\.

#### \(ii\) Asymmetric cost of errors\.

A false positive at this gate costs at most one experiment lane: the opportunity proceeds to the proposer, gets a hypothesis family, and is exposed to the next gate \(rerank \+ triage\)\. A false negative is much more expensive: it is the silent loss of a possibly novel idea, and in practice unrecoverable because it never gets recorded as a hypothesis at all\. The asymmetric\-cost argument is doubly strong here because the upstream miner already enforces strict structural constraints \(the specific\-term and parent\-domain requirements described above\), so the false\-positive base rate is small to begin with\.

#### \(iii\) Fail\-open \+ explicit archival\.

Our implementation therefore makes two design choices\. First, any null, unparseable, or timed\-out LLM judgment is treated as*pass*\(fail\-open\)\. The opportunity moves downstream carrying an explicit null\-score marker so that later stages can see the absence of a verdict rather than infer a false zero\. Second, every opportunity the judge rejects is written to a structured per\-opportunity archive together with the full per\-axis score vector, the free\-text rationale, the homonymy\-risk callout, the key\-risk list, and the transfer\-mechanism hint\. This is what allows the data in Figure[10](https://arxiv.org/html/2608.20361#S8.F10)to be reconstructed from disk months after the run, and it is what lets a human or downstream agent re\-thread the survivor set at a different threshold without re\-spending tokens\. In C4 the archive holds 154 rejected judgments at a mean aggregate score of 0\.11; lowering the threshold from 0\.30 to 0\.20 would admit roughly 30 more opportunities, and these can be inspected directly without re\-running the judge\.

#### Implication for system design\.

The wider takeaway is that an LLM\-as\-judge stage at the front end of an AI\-scientist loop should be treated as part of the*logging*infrastructure as much as part of the gating infrastructure\. The score is useful, but the rationale is at least as useful, and the act of making the gate replayable is what protects the downstream pipeline from the brittleness identified by SoundnessBench\. A blocking judge is a silent point of failure; an advisory judge with full archival is a known one\.

#### Position relative to sheaf\-obstruction work\.

The mathematics of sheaf cohomology gives a clean name – “non\-vanishingH1H^\{1\}” – to exactly the phenomenon our judge is trying to detect: local beliefs across clusters that do not glue into a coherent global belief\. Knowledge Sheaves\[[26](https://arxiv.org/html/2608.20361#bib.bib26)\]operationalises this intuition at the representation level \(KG embedding==approximate global section\)\. The 2025–2026 wave\[[30](https://arxiv.org/html/2608.20361#bib.bib30),[31](https://arxiv.org/html/2608.20361#bib.bib31),[32](https://arxiv.org/html/2608.20361#bib.bib32),[33](https://arxiv.org/html/2608.20361#bib.bib33)\]demonstrates the*obstruction\-as\-gate*pattern at the inference level in causal discovery, cross\-modal alignment and theory\-shift detection\. The gap our work fills is the application of this pattern to cross\-paper research idea generation grounded in a real paper KG\. We do not claim a new mathematical move; we claim a useful application of an emerging one\.

#### Limitations\.

\(i\) The token\-cost numbers are evaluator estimates; the LLM\-provider billing dashboard is authoritative and typically∼\\sim1\.5–2×\\timeshigher because of retries we did not log\. \(ii\) The judge is operated with fail\-open behaviour; we have not yet measured the false\-negative rate against a held\-out human\-graded set\. \(iii\) The C3 family count is depressed by a third\-party quota contention and is therefore not a clean ablation of the diversifier\. \(iv\) All experiments use a single LLM and single embedding model; we have not tested provider transfer\. \(v\) We evaluate the front end only; downstream experiment execution and paper writeup live in separate components of the system\.

## 10Conclusion

We have presented a structured front end for automated research idea generation: a categorical paper KG, two complementary miners, a six\-axis plausibility judge operated as an advisory gate, and a five\-form hypothesis\-family expander\. A four\-mode ablation on the same KG snapshot quantifies the within\-vs\-cross trade\-off and shows that the structural front end preserves quantitative\-falsifier rate at≥\\geq83% in every mode\. The work positions itself inside the 2025–2026 sheaf\-obstruction\-as\-gate wave without claiming new mathematical machinery; the contribution is the application target – cross\-paper idea generation on a real paper KG – and a fail\-open operational design informed by current LLM\-as\-judge limitations\. Future work will quantify the judge’s false\-negative rate against a human\-graded subset and extend the family expander to richer evaluator specs that admit non\-numeric falsifiers\.

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