Eureka

Philosophy

Research questions, physical principles and mathematical objects participate in generation together. Counterexamples should feed definition repair, with the process represented as persistent artifacts.

Architecture & control flow

1. 01

   Socratic research contract and question bank → frontier tension graph → innovation-operator scheduling.

2. 02

   The Equation Lab generates and mutates genomes within admissible/forbidden-term grammar, using surrogate traces for diagnostic signals.

3. 03

   A CoMath workspace constructs objects and conjectures, recording proof strategies, counterexample attempts and definition patches.

4. 04

   A domain–math–physics–equation–theorem–idea–refutation bridge yields harvestable clusters; the CLI subsequently invokes Aurora.

Architecture outline derived from this version’s control flow.

Inputs & outputs

Inputs

User direction, field/subfield, mode configuration, operator and term grammars, and seeded priors/tensions.

Outputs

discovery_package.json, questions and insights, equation/object/definition/conjecture/bridge IDs, and a CoMath working paper with JSONL records.

Implemented components

• A registry of 74 typed operators, Pareto-UCB/MAP-Elites scheduling structures, genome mutation, workspace/schema persistence, bridge cycles and idea harvesting.

Implementation & evidence scope

The equation model is explicitly a deterministic simulation surrogate, not physical PDE/ODE validation. Default tensions and priors are template seeds; the default conjecture path forces none_found and does not establish domain counterexample coverage. The subsequent 5.3 audit identified incomplete discovery-to-Aurora payload and verdict closure.

Code & bundled material

The introduction draws on bundled notes, changelogs and central code. Software tests, synthetic diagnostics and scientific effectiveness use different evidence standards.