II.
Domain JSON
Structured · livedomain:mathematics
Mathematics json
Inspect the normalized record payload exactly as the atlas UI reads it.
{
"id": "domain:mathematics",
"_kind": "Domain",
"_file": "domain/domains/science-domains.yaml",
"_cluster": "domain",
"attributes": {
"displayName": "Mathematics",
"description": "Pure and applied mathematics spanning algebra, analysis, topology, number\ntheory, combinatorics, probability, statistics, and numerical methods.\nIncludes optimization, operations research, and mathematical logic. Provides\nthe foundational language for physics, computer science, economics, and\nmachine learning — and is increasingly relevant to formal verification and\nAI reasoning research.\n"
},
"outgoingEdges": [
{
"from": "domain:mathematics",
"to": "specialization:computational-mathematics",
"kind": "contains"
},
{
"from": "domain:mathematics",
"to": "specialization:statistical-methods",
"kind": "contains"
}
],
"incomingEdges": [
{
"from": "benchmark:olympiad-bench",
"to": "domain:mathematics",
"kind": "applies_to",
"attributes": {}
},
{
"from": "benchmark:gsm-symbolic",
"to": "domain:mathematics",
"kind": "applies_to",
"attributes": {}
},
{
"from": "benchmark:hle",
"to": "domain:mathematics",
"kind": "applies_to",
"attributes": {}
},
{
"from": "benchmark:frontier-math",
"to": "domain:mathematics",
"kind": "applies_to",
"attributes": {}
},
{
"from": "language:agda",
"to": "domain:mathematics",
"kind": "applies_to",
"attributes": {}
},
{
"from": "language:coq",
"to": "domain:mathematics",
"kind": "applies_to",
"attributes": {}
},
{
"from": "language:fortran",
"to": "domain:mathematics",
"kind": "applies_to",
"attributes": {}
},
{
"from": "language:idris",
"to": "domain:mathematics",
"kind": "applies_to",
"attributes": {}
},
{
"from": "language:lean",
"to": "domain:mathematics",
"kind": "applies_to",
"attributes": {}
},
{
"from": "specialization:mathematics",
"to": "domain:mathematics",
"kind": "specializes"
},
{
"from": "specialization:computational-mathematics",
"to": "domain:mathematics",
"kind": "specializes"
},
{
"from": "specialization:statistical-methods",
"to": "domain:mathematics",
"kind": "specializes"
},
{
"from": "workflow:experiment-design",
"to": "domain:mathematics",
"kind": "applies_to_domain"
},
{
"from": "lib-agent:mathematics--algebraist",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--bayesian-statistician",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--conjecture-analyst",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--discrete-optimization-expert",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--experimental-design-expert",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--literature-reviewer",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--mathematical-modeler",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--mathematics-writer",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--numerical-analyst",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--optimization-expert",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--pde-expert",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--proof-strategist",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--reproducibility-engineer",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--statistical-modeler",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--symbolic-computation-expert",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--theorem-prover-expert",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-agent:mathematics--uq-specialist",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--algorithm-complexity-analysis",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--bayesian-inference-workflow",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--benchmark-validation",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--conjecture-exploration",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--convex-analysis-verification",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--experimental-design-planning",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--hypothesis-testing-framework",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--latex-document-generation",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--mathematical-literature-review",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--mathematical-notation-standardization",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--matrix-computation-optimization",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--model-formulation-workflow",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--model-validation-framework",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--numerical-stability-analysis",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--optimization-problem-formulation",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--pde-solver-selection",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--proof-writing-assistance",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--reproducible-computation-setup",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--sensitivity-analysis-optimization",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--statistical-model-selection",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--symbolic-integration-differentiation",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--symbolic-simplification",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--theorem-proof-verification",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-process:mathematics--uncertainty-quantification",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--arxiv-search-interface",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--benchmark-suite-manager",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--combinatorial-enumeration",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--computational-environment-manager",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--convex-optimization-solver",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--coq-proof-assistant",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--counterexample-generator",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--derivative-free-optimization",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--diagram-generator",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--floating-point-analysis",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--graph-algorithm-library",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--interpolation-approximation",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--isabelle-hol-interface",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--latex-math-formatter",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--lean-proof-assistant",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--math-notation-validator",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--mathematica-wolfram-interface",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--mathscinet-interface",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--maxima-cas-interface",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--mcmc-diagnostics",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--mixed-integer-optimization",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--monte-carlo-simulation",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--multiple-testing-correction",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--nonlinear-optimization-solver",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--numerical-linear-algebra-toolkit",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--ode-solver-library",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--pde-solver-library",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--polynomial-chaos-expansion",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--power-sample-size-calculator",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--proof-structure-analyzer",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--pymc-probabilistic-programming",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--robust-statistics-toolkit",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--sage-math-interface",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--sensitivity-analysis-toolkit",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--sensitivity-analysis-uq",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--special-functions-library",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--stan-bayesian-modeling",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--sympy-computer-algebra",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
},
{
"from": "lib-skill:mathematics--zbmath-interface",
"to": "domain:mathematics",
"kind": "lib_applies_to_domain",
"attributes": {
"weight": 1
}
}
]
}