A PUBLIC OVERVIEW
Start from a goal and continue with evidence
Daedalus connects research goals, exploration, tools, evidence checks and review in a continuing process. This diagram presents the responsibilities and relationships at a conceptual level.
RESEARCH STAGE
Research goals
Identify a question worth answering and the understanding or value it could bring.
RESEARCH STAGE
Idea exploration
Find structural connections across fields and propose representations, mechanisms and directions.
RESEARCH STAGE
Research tools
Develop capabilities for observing, comparing and testing the decisive questions.
RESEARCH STAGE
Evidence checks
Use observations and counterexamples to clarify conditions and remaining gaps.
RESEARCH STAGE
Research review
Assess correctness, novelty and scientific value separately, then identify the next work.
RESEARCH STAGE
Continued development
Preserve useful branches and tools so new evidence can drive revision, extension and stronger questions.
Start with a question worth answering
Research exploration begins with a question that remains unresolved and is worth pursuing. Daedalus looks for ways to make progress: phenomena that need explanation, conditions that limit existing methods, and observations that could change our understanding. An idea earns value by enabling clearer judgments, stronger explanations or further inquiry. The system connects questions, methods and checks so that an abstract proposal can develop into a concrete direction. A question may change as exploration proceeds, while its connection to a meaningful research need stays clear.
Look for structural connections across fields
Fields may use different terminology while facing similar relationships, constraints or forms of organization. Daedalus explores whether those connections can offer a new approach to the current problem. What survives the transfer? Which conditions must be added? Why should a method work in the new setting? Analogy can inspire a proposal; structural transfer also requires an explicit correspondence and a test. Progress comes from the explanations, observations or tools that correspondence enables. A failed transfer can still reveal what the target problem is missing.
Change the representation to reveal hidden mechanisms
Research can stall when its current representation hides a decisive distinction. A phenomenon can be reorganized around relationships, states, processes or interactions, allowing previously entangled explanations to become distinguishable. Daedalus explores these changes while asking what becomes observable and which original conditions remain. A useful representation helps researchers pose a more discriminating question and design a check that can answer it. Its contribution must return to the research object and improve understanding or action.
Build tools for the research question
An idea needs a way to meet evidence. Daedalus includes tool building in exploration so that a proposal's key elements can be computed, compared or checked. Existing capabilities provide a starting point, while new tool requirements make unresolved gaps concrete. A research tool should produce inspectable observations, support a clear judgment and define the scope of its result. Even when a direction falls short, a tool developed along the way may support later inquiry and leave a capability worth developing.
OPEN MATHEMATICAL FOUNDATIONS
The mathematical tool layer.
These public mathematical foundations illustrate what a research tool can help examine. The examples explain uses and ideas, rather than a project-specific recipe or implementation.
01 / MATHEMATICS
Beta-weighted expectations
E[f(X)] = ∫ f(x) w(x) dx
A standard probability distribution can turn uncertain behaviour into a weighted expectation. This offers a way to reason about how outcomes vary over an interval, with the weighting and assumptions stated explicitly.
02 / MATHEMATICS
Markov stationary analysis
πP = π · ∑ πᵢ = 1
When a question involves transitions between states, stationary analysis examines their long-run relationships. Balance and normalization are familiar mathematical checks for the proposed description.
03 / MATHEMATICS
Symbolic and numerical checks
f(x) ≡ g(x)
Symbolic reasoning and numerical evaluation serve different purposes: a derivation explains a relationship, while calculation can reveal inconsistencies in a stated case. Used together, they help researchers inspect a mathematical formulation.
Explore freely and let checks guide the next step
Free exploration makes room for ambitious mechanisms, unfamiliar connections and new questions. Rigorous inquiry gives those proposals clear conditions and testable content. Daedalus connects the two: an idea enters exploration, then computation, comparison, counterexamples and review clarify its boundaries. Results guide whether to revise an assumption, seek another observation, develop a tool or pursue another route. Creativity has room to grow while remaining accountable to evidence. Each round should clarify the question or make its next test more meaningful.
Judge correctness, novelty and scientific value separately
A result may be correct under its stated conditions without introducing a new method. An original proposal may still leave an important problem untouched. Daedalus treats technical correctness, methodological novelty and scientific value as distinct judgments. Checks ask whether a proposal holds; novelty asks how it differs from existing work; value asks whether it changes understanding, improves research decisions or opens an important question. Each needs its own evidence and may be resolved at a different stage. This distinction makes both progress and the next evidence need clearer.
Let failure produce the next piece of research
Failure can reveal a method's conditions, a representation's blind spot or an unresolved part of a question. Daedalus asks what the failure establishes: an incorrect judgment, insufficient evidence or a tool unable to perform the decisive check. Each calls for different work. Useful observations and capabilities are preserved, while the exposed gap becomes a more concrete question. A failure is productive when it reduces uncertainty or enables a stronger test, allowing inquiry to continue beyond an unsuccessful attempt.
Keep branches available for continued development
A research direction's value may take time to emerge. A branch that is difficult to test today may become important after a new observation or tool. A local advance may support a different question. Daedalus preserves connections among branches so that ideas can be extended, revised or recombined. Specific questions and evidence gaps guide continuation, with opportunities to revisit different directions. Keeping several routes available supports comparison, reveals complementary contributions and allows priorities to change as conditions change.
The exploration stage within AutoResearch
Within AutoResearch, Daedalus develops research questions and ideas: turn goals into candidate directions, find connections across fields, identify tools to build, and continue in response to checks and review. It supplies the broader workflow with clear questions, actionable proposals and explicit evidence needs. These can guide subsequent observations, comparisons and revisions of the goal. Its role is to make automated exploration accumulate useful research content while maintaining the connection among questions, methods and evidence.
Evolve while preserving human research judgment
Daedalus extends exploration from organizing existing information and actions toward constructing representations, tools and research questions. That evolution needs continued evaluation: does a new capability help research, work on new problems and justify further effort? Researchers contribute domain context, judge importance and decide what evidence supports the next step. The system broadens exploration, offers candidates and clarifies gaps; human experience calibrates value and meaning. Together they develop directions around clear, testable and worthwhile scientific goals.
THE NEXT QUESTION