adjacent_pair
Data license: Space charter; records cite primary sources · Data source: TeamScience Space repository
820 rows
This data as json, CSV (advanced)
Suggested facets: a_kind, b_kind, distance, novelty, evidence, status, created_ts, signal, reading, created_ts (date)
| id ▼ | a_kind | a_ref | a_label | b_kind | b_ref | b_label | bridge | distance | novelty | evidence | status | asked_by | created_ts | signal | score | why | prompt | reading |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| ap-0007cdb300 | problem | wp-computer-science-d81dcbb901 | Can the square-root sum problem be solved in polynomial time in the Turing machine model? | method | m-coding-theory-constructions | coding theory constructions | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:10:07Z | |||||||
| ap-006594eb1c | problem | wp-mathematics-ff80713d89 | The Lovász conjecture on Hamiltonian paths in symmetric graphs [ 132 ] | method | m-evolutionary-search | evolutionary search | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0092dbe40f | problem | se-mo-35151 | What impact would P!=NP have on the characterization of BQP? Many complexity theorists assume that $P\ne NP.$ If this is proved, how would it impact quantum computing and quantum algorithms? Would the proof immediately disallow quantum algorithms from ever solving NP-Complete problems in Quantum Pol | problem | wp-physics-36641b7683 | Complexity classes problems: What is the relation between BQP and BPP ? What is the relation between BQP and NP ? Can computation in plausible physical theories (quantum algorithms) go beyond BQP? [ 108 ] | quantum algorithms | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn by ts-synth: the same question on two sources | withdrawn | ts-synth | 2026-09-02T18:02:06Z | |||||
| ap-00dd0f8412 | problem | se-cstheory-5101 | Efficiently computable function as a counter-example to Sarnak's Mobius conjecture. Recently, Gil Kalai and Dick Lipton both wrote nice articles on an interesting conjecture proposed by Peter Sarnak, an expert in number theory and the Riemann Hypothesis. Conjecture. Let $\mu(k)$ be the Möbius functi | problem | wp-mathematics-e56cd4ebb1 | Generalized Riemann hypothesis for Selberg class : do the nontrivial zeros of all functions in Selberg class lie on the critical line 1 / 2 + i t {\displaystyle 1/2+it} with real t {\displaystyle t} ? | riemann hypothesis | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | ||||||
| ap-00e7478943 | problem | wp-astronomy-a89f4b0cd9 | How do galactic history and dark matter halos impact the observable properties of galaxies? [ 7 ] | problem | wp-physics-7c59537364 | Cosmic coincidence problem : the energy densities of dark energy and dark matter are of the same order of magnitude in the Universe. Dark matter energy density decreased during the evolution of the universe, so it must have been very large in the past. Is there any relation between the two energy de | dark matter | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | ||||||
| ap-012f03b2c1 | problem | wp-mathematics-1bdc4a8627 | Margulis conjecture – measure classification for diagonalizable actions in higher-rank groups. | method | m-information-theoretic-bounds | information-theoretic bounds | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-01f1292318 | problem | erdos-872 | Consider the two-player game in which players alternately choose integers from $\{2,3,\ldots,n\}$ to be included in some set $A$ (the same set for both players) such that no $a\mid b$ for $a\neq b\in A$. The game ends when no legal move is possible. One player wants the game to last as long as possi | problem | se-cstheory-1962 | Is it NP-hard to play international draughts correctly? Is the following problem NP-hard? Given a board configuration for $n\times n$ international draughts , find a single legal move. The corresponding problem for $n\times n$ American checkers (aka English draughts) is trivially solvable in polynom | legal move | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:10:07Z | ||||||
| ap-01f6f3a1b6 | problem | wp-computer-science-3af91c585d | Can the graph isomorphism problem be solved in polynomial time on a classical computer? | method | m-sat-based-counterexample-search | SAT-based counterexample search | same-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-02011c51b9 | problem | ax-2605.29885-9bb5e691 | Open Problem 2 (Sample Complexity of the Canonical Testbed): Cayley-table completion serves as the immediate, concrete testbed for establishing this separation. Because finite groups are linearly full-rank ( $r=n$ ), applying standard matrix completion theory yields vacuous bounds exceeding $\mathca | method | m-spectral-graph-theory | spectral graph theory | adjacent-field | novel | 0 ingested titles mention both sides (text proxy for #177) | unasked | 2026-09-02T20:10:35Z | transplant | 1.946 | 'spectral graph theory' has 6 ingested titles (home field mathematics); problem is computer science / shape compute-checkable-small-cases (tractability 1.0); 0 titles use the method with this problem's terms | 'spectral graph theory' has a track record in mathematics (6 ingested titles). What is the object it consumes in computer science's problem, and what would the first small instance look like? If the method cannot see the problem's structure, name the missing translation. | openalex:W3214375535 doi:10.1109/tpami.2024.3362475 doi:10.1103/physrevlett.66.2396 arxiv:1901.10159 doi:10.1162/089976698300017467 | ||
| ap-02372d8d34 | problem | se-mo-163301 | What is Chern-Simons theory expected to assign to a point? Let $G$ be a compact, connected, (simply connected?) Lie group and let $k \in H^4(BG, \mathbb{Z})$ be a cohomology class. Witten showed, at a physical level of rigor, that this data determines a $3$-dimensional topological quantum field theo | problem | wp-physics-ae92c771e7 | Topological qubits: Topological quantum computers are promising but can they be built? Can we demonstrate Majorana zero modes conclusively? [ 109 ] | topological quantum | adjacent-field | novel | 0 ingested titles mention both sides (text proxy for #177) | unasked | 2026-09-02T20:10:35Z | bridge | 6.446 | keyphrase 'topological quantum' appears in 3 problems across fields (mathematics / physics) and in 0 ingested paper titles; idf=6.45 | Both sides turn on 'topological quantum'. What does mathematics already know about topological quantum that physics is still asking, and vice versa? Start from the grounding papers; if neither field's result transfers, say which assumption breaks. | ||
| ap-0264d8ac94 | problem | wp-astronomy-015db6a6bf | Final parsec problem : Supermassive black holes appear to have merged, and what appears to be a pair in this intermediate range has been observed, in PKS 1302–102 . [ 27 ] However, theory predicts that when supermassive black holes reach a separation of about one parsec, it may take billions of year | problem | wp-physics-7f63cf05cf | Supermassive black holes : What is the origin of the M–sigma relation between supermassive black hole mass and galaxy velocity dispersion? [ 65 ] How did the most distant quasars grow their supermassive black holes up to 10 10 solar masses so early in the history of the universe? | supermassive black | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | ||||||
| ap-02f6d9e7dc | problem | wp-mathematics-0e9bb1996c | Newman's conjecture : the partition function satisfies any arbitrary congruence infinitely often. | method | m-transformer-sequence-model | transformer sequence model | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-03b20bb9b1 | problem | se-cstheory-1814 | A combinatorial version for the polynomial Hirsch conjecture. Consider $t$ disjoint families of subsets of {1,2,…,n}, ${\cal F}_1,{\cal F_2},\dots {\cal F_t}$ . Suppose that (*) For every $i \lt j \lt k$ and every $R \in {\cal F}_i$, and $T \in {\cal F}_k$, there is $S \in {\cal F}_j$ which contains | method | m-transformer-sequence-model | transformer sequence model | same-field | unknown | demand-led; novelty not scored | unasked | 2026-09-02T20:10:35Z | demand | 0.974 | demand 0.53 (stack exchange open-problems tag (cstheory, score 53, 1 answ), shape compute-checkable-small-cases; 'transformer sequence model' applies and has 65 ingested titles | This problem carries external demand (stack exchange open-problems tag (cstheory, score 53, 1 answ). 'transformer sequence model' is the applicable method with the most track record in the graph. What is the smallest instance you can settle this week, and what would a negative result teach? | arxiv:2312.02139 doi:10.18653/v1/n19-1423 arxiv:2004.05150 doi:10.1016/j.nlp.2024.100076 doi:10.1145/3712256.3726396 | ||
| ap-03d3a92e49 | problem | ax-2606.07327-40367028 | Do we need more data, better data, or better models? (A central tension in the development of MLIPs echoes a long-standing debate in AI: should progress come primarily from carefully designed inductive biases or from scaling models and data? Sutton’s “Bitter Lesson” argues that, in the long run, sys | problem | wp-biology-f24b42f102 | Stegosaur osteoderms/scutes. There is a long-standing debate over whether the primary function of the osteoderms/scutes of stegosaurs is protection from predators, sexual display, species recognition, thermoregulation, or other functions. | long-standing debate | far | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | ||||||
| ap-0407fccd91 | problem | se-mo-35151 | What impact would P!=NP have on the characterization of BQP? Many complexity theorists assume that $P\ne NP.$ If this is proved, how would it impact quantum computing and quantum algorithms? Would the proof immediately disallow quantum algorithms from ever solving NP-Complete problems in Quantum Pol | problem | wp-physics-869eaab140 | United States DARPA issued 23 mathematical challenges in 2008. Physics problems included: advancing techniques in modelling fluid dynamics and soft matter , developing mathematics for quantum computing , applying quantum field theory and action principles to biology, and finding a relation between t | quantum computing | adjacent-field | novel | 0 ingested titles mention both sides (text proxy for #177) | unasked | 2026-09-02T20:10:35Z | bridge | 6.446 | keyphrase 'quantum computing' appears in 3 problems across fields (mathematics / physics) and in 0 ingested paper titles; idf=6.45 | Both sides turn on 'quantum computing'. What does mathematics already know about quantum computing that physics is still asking, and vice versa? Start from the grounding papers; if neither field's result transfers, say which assumption breaks. | ||
| ap-043f3ca430 | problem | se-mo-348055 | When do two knots have isomorphic fundamental bikeis? A kei , also known as an involutive (or involutory) quandle, is a quandle $(Q,*)$ satisfying the involution condition that $(x*y)*y=x$ for all $x$ and $y$ . Just like we can define a fundamental quandle of a knot using arcs of an oriented knot di | method | m-llm-driven-proof-search | LLM-driven proof search | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:10:07Z | |||||||
| ap-04ca7d0325 | problem | wp-computer-science-08c008e006 | Is the Aanderaa–Karp–Rosenberg conjecture true? | method | m-evolutionary-search | evolutionary search | same-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-050a23f20a | problem | se-mo-212764 | Why is it so hard to prove Toeplitz' conjecture? I'm a layman in mathematics, so please excuse me in advance for anything in this question that may be inappropriate :D. Well: Four years ago, I was reading (and working to solve the puzzles on) Winkler's Mathematical Puzzles: A Connoisseur's Collectio | method | m-sat-smt-solving | SAT/SMT solving | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0520fe8001 | problem | se-mo-164665 | Is there a precise notion of "almost all" such that almost all finite groups are Galois groups of extensions of the rationals? I vainly tried to define a notion of "almost solvable group" such that every "almost solvable group" is the Galois group of a finite extension of the rationals, but I can't | method | m-integer-linear-programming | integer linear programming | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-061834a1e0 | problem | se-mo-38632 | Projective Plane of Order 12. I asked this question on the new Theoretical Computer Science "overflow" site, and commenters suggested I ask it here. That question is here , and it contains additional links, which I doubt I can embed here because I don't have enough reputation. Anyway, here goes: Obj | method | m-llm-driven-proof-search | LLM-driven proof search | adjacent-field | unknown | demand-led; novelty not scored | unasked | 2026-09-02T20:10:35Z | demand | 0.597 | demand 0.43 (stack exchange open-problems tag (mathoverflow, score 43, 2 ), shape compute-checkable-small-cases; 'LLM-driven proof search' applies and has 6 ingested titles | This problem carries external demand (stack exchange open-problems tag (mathoverflow, score 43, 2 ). 'LLM-driven proof search' is the applicable method with the most track record in the graph. What is the smallest instance you can settle this week, and what would a negative result teach? | openalex:W2946011656 openalex:W2963596026 arxiv:2009.03393 openalex:W3133204645 arxiv:2102.06203 | ||
| ap-06a702ae62 | problem | wp-biology-62518ae5a9 | Gall-inducing insects . At least seven groups of insects, in six orders, have independently evolved the gall-inducing habit. Several adaptation hypotheses have been proposed, but it is largely unknown why this habit evolved and how gall-inducing insects induce gall formation in plants; chemical, mec | method | m-noisy-judge-tournament-model | noisy-judge tournament model | far | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-070a5253da | problem | wp-biology-bf82bdb0d9 | Perception : How does the brain transfer sensory information into coherent, private percepts ? What are the rules by which perception is organized? What are the features/objects that constitute our perceptual experience of internal and external events? How are the senses integrated? What is the rela | method | m-conformal-prediction | conformal prediction | far | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0740f29893 | problem | se-mo-17257 | What's the current state of Yang–Mills mass gap question? What's the current state of Yang–Mills mass gap question, is there any place that does this problem? Especially I want to know if there is any progress (out of that mentioned in the introduction article by Witten and Jaffe). Is it too hard fo | method | m-integer-linear-programming | integer linear programming | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-075ef6b1b0 | problem | wp-mathematics-9ef6bc599d | Berry–Tabor conjecture in quantum chaos | method | m-oeis-sequence-mining | OEIS sequence mining | same-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-077e0120b2 | problem | wp-mathematics-1352d2701b | The universality problem for C -free graphs: For which finite sets C of graphs does the class of C -free countable graphs have a universal member under strong embeddings? [ 161 ] | method | m-llm-driven-proof-search | LLM-driven proof search | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-07909eafb8 | problem | wp-computer-science-31837bd538 | Gilbert–Pollak conjecture : Is the Steiner ratio of the Euclidean plane equal to 2 / 3 {\displaystyle 2/{\sqrt {3}}} ? | method | m-coding-theory-constructions | coding theory constructions | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:10:07Z | |||||||
| ap-07dbd8b8dc | problem | wp-fair-division-215df9cd21 | A connected envy-free cake-cutting might take infinitely many queries to find. An EF1 allocation can always be found in finite time by checking all possible allocations, but this algorithm requires exponential run-time. | method | m-information-theoretic-bounds | information-theoretic bounds | far | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:10:07Z | |||||||
| ap-0803319965 | problem | wp-neuroscience-de5d117c0f | Vertiginous question : Why is it that a specific subject of experience is "live" from a given perspective? | method | m-preregistered-replication | preregistered replication | far | novel | 0 ingested titles mention both sides (text proxy for #177) | unasked | 2026-09-02T20:10:35Z | transplant | 1.931 | 'preregistered replication' has 4 ingested titles (home field metascience); problem is neuroscience / shape data-reanalysis (tractability 1.0); 0 titles use the method with this problem's terms | 'preregistered replication' has a track record in metascience (4 ingested titles). What is the object it consumes in neuroscience's problem, and what would the first small instance look like? If the method cannot see the problem's structure, name the missing translation. | arxiv:1903.03176 doi:10.1126/science.aac4716 doi:10.3389/frobt.2025.1436674 doi:10.1002/aaai.70002 | ||
| ap-0827f8c53f | problem | se-mo-51680 | Amenability of groups in terms of a perturbation condition. Let $G$ be a countable group and $\lambda \colon G \to U(\ell^2 G)$ its left-regular representation. Suppose that there exists a constant $C>0$ such that for all $T \in B(\ell^2 G)$ $$\inf \lbrace\|T-S\| \mid S \in \lambda(G)' \rbrace \leq | method | m-sat-smt-solving | SAT/SMT solving | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0853f4ded4 | problem | se-mo-511338 | Frankl-like conjecture for $k$-union-closed family of sets. We call a family $\mathcal{F}$ of finite subsets of $[n]$ $k$ -union-closed if for every set $A\subseteq[n]$ with $|A|\geq k$ , we have $\bigcup_{S\subseteq A,S\in\mathcal{F}}S\in\mathcal{F}$ . A $2$ -union-closed family is precisely a unio | method | m-network-percolation-model | network percolation model | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:10:07Z | |||||||
| ap-08eb5d7ba7 | problem | ax-2608.26628-7704b05b | Problem 3.2: Is there a decision procedure which, given quantifier patterns $\overline{P},\overline{Q}\in\{\exists,\forall,\exists^{\infty},\forall^{\infty}\}^{ decides whether $\langle\overline{P}\rangle\leq_{m}\langle\overline{Q}\rangle?$ | method | m-automata-formal-language-decision-procedures | automata / formal language decision procedures | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-09a339820e | problem | wp-astronomy-34c2e65cd7 | Black hole information paradox and black hole radiation : Do black holes produce thermal radiation, as expected on theoretical grounds ? [ 25 ] If so—meaning black holes can evaporate away—what happens to the information stored in them? This appears to be an issue because the unitarity of quantum me | problem | wp-physics-7f63cf05cf | Supermassive black holes : What is the origin of the M–sigma relation between supermassive black hole mass and galaxy velocity dispersion? [ 65 ] How did the most distant quasars grow their supermassive black holes up to 10 10 solar masses so early in the history of the universe? | black hole | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | ||||||
| ap-09a43b2ba7 | problem | wp-mathematics-6b782489f1 | Serre's conjecture II : if G {\displaystyle G} is a simply connected semisimple algebraic group over a perfect field of cohomological dimension at most 2 {\displaystyle 2} , then the Galois cohomology set H 1 ( F , G ) {\displaystyle H^{1}(F,G)} is zero. | method | m-property-testing-sublinear-algorithms | property testing / sublinear algorithms | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:10:07Z | |||||||
| ap-0a3636de5c | problem | wp-mathematics-fda834b25d | Jaeger's Petersen-coloring conjecture : every bridgeless cubic graph has a cycle-continuous mapping to the Petersen graph [ 108 ] | method | m-active-learning-bayesian-optimization | active learning / Bayesian optimization | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0a58b0dfe7 | problem | wp-mathematics-5e8749874e | Ryser's conjecture relating the maximum matching size and minimum transversal size in hypergraphs | method | m-reinforcement-learning | reinforcement learning | adjacent-field | neighborhood | 2 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0ba8742b5b | problem | se-mo-27861 | Periodic Automorphism Towers. In Scott's classic textbook on Group Theory, he asks: Suppose that $G$ is a finite group. Is the sequence of isomorphism types of the groups $Aut^{(n)}(G)$ for $n \in \mathbb{N}$ eventually periodic? Here $Aut^{(2)}(G) = Aut(Aut(G))$ etc. Equivalently, is the sequence $ | method | m-lean-formalization | Lean formalization | same-field | unknown | demand-led; novelty not scored | unasked | 2026-09-02T20:10:35Z | demand | 0.344 | demand 0.26 (stack exchange open-problems tag (mathoverflow, score 26, 3 ), shape compute-checkable-small-cases; 'Lean formalization' applies and has 4 ingested titles | This problem carries external demand (stack exchange open-problems tag (mathoverflow, score 26, 3 ). 'Lean formalization' is the applicable method with the most track record in the graph. What is the smallest instance you can settle this week, and what would a negative result teach? | arxiv:2608.10119 doi:10.1098/rsos.241678 doi:10.15607/rss.2012.viii.010 doi:10.1145/3442188.3445923 | ||
| ap-0be495aab4 | problem | wp-mathematics-39f8d9fe5a | Feit–Thompson conjecture : for all distinct prime numbers p {\displaystyle p} and q {\displaystyle q} , ( p q − 1 ) / ( p − 1 ) {\displaystyle (p^{q}-1)/(p-1)} does not divide ( q p − 1 ) / ( q − 1 ) {\displaystyle (q^{p}-1)/(q-1)} | method | m-evolutionary-search | evolutionary search | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0c075e1def | paper | doi:10.1162/106365602320169811 | Evolving Neural Networks through Augmenting Topologies | problem | wp-biology-f712aa1d7c | Inverse protein-folding problem ( protein design ): Is it possible to design a polypeptide sequence which will adopt a given structure under certain environmental conditions? This turned out to be tractable given a good structural prediction method, starting with the success of the small globular pr | neural networks | adjacent-field | unknown | dormant paper; novelty not scored | unasked | 2026-09-02T20:10:35Z | dormant | 1.318 | 'Evolving Neural Networks through Augmenting Topologies' (2002) is cited by 2 ingested papers and shares 'neural networks' with a recent problem | 'Evolving Neural Networks through Augmenting Topologies' (2002) is still cited by 2 ingested papers. Which of its results does the newer problem re-ask in different words, and which of its assumptions no longer hold? | doi:10.1162/106365602320169811 | |
| ap-0c9bc4053b | problem | ax-2606.07327-558bc342 | Why do models fail to capture long-range interactions? (Message Passing Neural Networks (MPNNs), one of the most widely used architectures for MLIPs, exhibit a local inductive bias , as message aggregation for each node is typically limited to its neighbourhood. This locality reflects the assumption | problem | wp-neuroscience-11954e13d2 | Connectionism : Can the mind be explained by mathematical models known as artificial neural networks ? | neural networks | far | duplicate | 8 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | ||||||
| ap-0d5d840ab6 | problem | wp-astronomy-9a13b805c9 | What is the origin of the Galactic Center GeV excess ? [ 20 ] Is it due to the annihilation of dark matter particles or a new population of millisecond pulsars ? | problem | wp-physics-7c59537364 | Cosmic coincidence problem : the energy densities of dark energy and dark matter are of the same order of magnitude in the Universe. Dark matter energy density decreased during the evolution of the universe, so it must have been very large in the past. Is there any relation between the two energy de | dark matter | adjacent-field | neighborhood | 1 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | ||||||
| ap-0d6afd34ba | problem | wp-astronomy-e81531f3f2 | Supermassive black holes : What is the origin of the M–sigma relation between supermassive black hole mass and galaxy velocity dispersion ? [ 24 ] | problem | wp-physics-7f63cf05cf | Supermassive black holes : What is the origin of the M–sigma relation between supermassive black hole mass and galaxy velocity dispersion? [ 65 ] How did the most distant quasars grow their supermassive black holes up to 10 10 solar masses so early in the history of the universe? | black holes | adjacent-field | duplicate | same problem, two lists; novelty n/a | unasked | 2026-09-02T20:10:35Z | cross-list | 1.579 | near-identical statements (Jaccard 0.58) on two fields' lists: astronomy and physics | Two fields list this as their problem (astronomy and physics). Which field's tools have not been tried on it, and why did each field frame it the way it did? | ||
| ap-0dda9c48dd | problem | wp-astronomy-34c2e65cd7 | Black hole information paradox and black hole radiation : Do black holes produce thermal radiation, as expected on theoretical grounds ? [ 25 ] If so—meaning black holes can evaporate away—what happens to the information stored in them? This appears to be an issue because the unitarity of quantum me | problem | wp-physics-00d5d2a2cb | Problem of time : In quantum mechanics, time is a classical background parameter, and the flow of time is universal and absolute. In general relativity, time is one component of four-dimensional spacetime , and the flow of time changes depending on the curvature of spacetime and the spacetime trajec | quantum mechanics | adjacent-field | novel | 0 ingested titles mention both sides (text proxy for #177) | unasked | 2026-09-02T20:10:35Z | bridge | 6.446 | keyphrase 'quantum mechanics' appears in 3 problems across fields (astronomy / physics) and in 0 ingested paper titles; idf=6.45 | Both sides turn on 'quantum mechanics'. What does astronomy already know about quantum mechanics that physics is still asking, and vice versa? Start from the grounding papers; if neither field's result transfers, say which assumption breaks. | ||
| ap-0ddad667f6 | problem | wp-mathematics-a422b8fe46 | Lander's conjecture : if an abelian group of order v {\displaystyle v} contains a difference set of order n {\displaystyle n} , and a prime p {\displaystyle p} divides both v {\displaystyle v} and n {\displaystyle n} , must the Sylow p {\displaystyle p} -subgroup be non-cyclic? This implies Ryser's | method | m-interactive-theorem-proving-benchmark | interactive theorem proving benchmark | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0e4e5997de | problem | wp-mathematics-9f4b60e599 | Fontaine–Mazur conjecture : actually numerous conjectures, all proposed by Jean-Marc Fontaine and Barry Mazur . | method | m-coding-theory-constructions | coding theory constructions | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0e8e8add3a | problem | wp-mathematics-04e087c8c2 | Do any non-power of 2 almost perfect numbers exist? | method | m-symbolic-regression | symbolic regression | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0ec6fad84d | problem | wp-mathematics-6ee3ad7f0a | Shelah's categoricity conjecture for L ω 1 , ω {\displaystyle L_{\omega _{1},\omega }} : If a sentence is categorical above the Hanf number then it is categorical in all cardinals above the Hanf number. [ 158 ] | method | m-monte-carlo-simulation | Monte Carlo simulation | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0ec8a42d88 | problem | se-mo-16214 | Is there an associative metric on the non-negative reals? Recall that a function $f\colon X\times X \to \mathbb{R}_{\ge 0}$ is a metric if it satisfies: definiteness: $f(x,y) = 0$ iff $x=y$, symmetry: $f(x,y)=f(y,x)$, and the triangle inequality: $f(x,y) \le f(x,z) + f(z,y)$. A function $f\colon X\t | method | m-transformer-sequence-model | transformer sequence model | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0ee30a0beb | problem | wp-mathematics-be9fd46d01 | Montgomery's pair correlation conjecture : the normalized pair correlation function between pairs of zeros of the Riemann zeta function is the same as the pair correlation function of random Hermitian matrices . | method | m-information-theoretic-bounds | information-theoretic bounds | adjacent-field | neighborhood | 1 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | |||||||
| ap-0efdf8ab99 | problem | se-cstheory-42654 | A conjecture related to the Cerny conjecture - counterexample/reference request. The Cerny conjecture is the statement that any synchronizing automaton with $n$ states has a synchronizing word of length at most $(n-1)^2$ . The best current upper bound for the length of a synchronizing word is $O(n^3 | problem | se-mo-10752 | Enumerating (generalized) de Bruijn tori. Given a cyclic word $w$ of length $N$ over a $q$-ary alphabet and $k \in \mathbb{Z}_+$, consider the directed multigraph $G_k(w) = (V,E)$ with $V \subset$ {$1,\dots,q$}$^k$ given by the $k$-lets (i.e., subwords of $k$ symbols) that appear in $w$ (without mul | word length | adjacent-field | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z | ||||||
| ap-0f0239dc7d | problem | wp-fair-division-09405ea79b | For n ≥ 4 {\displaystyle n\geq 4} , no finite algorithm is currently known. | method | m-finite-element-pde-simulation | finite element / PDE simulation | far | novel | 0 ingested paper titles mention both sides (text proxy for #177 pair-novelty) · withdrawn: v0.1 random draw superseded by combinability v0.2 (drawn only for a named signal) | withdrawn | 2026-09-02T18:02:06Z |
Advanced export
JSON shape: default, array, newline-delimited, object
CREATE TABLE adjacent_pair (
id TEXT PRIMARY KEY, -- ap-<sha1[:10]>
a_kind TEXT NOT NULL CHECK (a_kind IN ('problem','method','claim','paper','field')),
a_ref TEXT NOT NULL,
a_label TEXT NOT NULL,
b_kind TEXT NOT NULL CHECK (b_kind IN ('problem','method','claim','paper','field')),
b_ref TEXT NOT NULL,
b_label TEXT NOT NULL,
bridge TEXT, -- the shared term or concept that made the pair adjacent (Swanson's B); NULL for a random draw
distance TEXT NOT NULL CHECK (distance IN ('same-field','adjacent-field','far')),
novelty TEXT NOT NULL CHECK (novelty IN ('duplicate','neighborhood','novel','unknown')),
evidence TEXT, -- how novelty was computed (e.g. '0 ingested titles mention both')
status TEXT NOT NULL CHECK (status IN ('unasked','asked','answered','withdrawn')),
asked_by TEXT,
created_ts TEXT NOT NULL,
-- v1.0 (#312): combinability signals. A pair is drawn only for a reason, and the reason travels with it.
signal TEXT, -- bridge | transplant | contradiction | dormant | demand | cross-list
score REAL, -- signal-specific score; higher = more worth a conversation (comparable within a signal)
why TEXT, -- the computed reason, with the numbers, so anyone can recompute it
prompt TEXT, -- the opening question for the conversation this pair seeds
reading TEXT -- space-separated paper ids in the graph that ground the pair (the reading target)
);