Maths AI — Bounded Experimental Intelligence Lab
A local laboratory for bounded hypothesis search, deterministic verification, counterexamples, and reproducible comparison against fixed baselines.
Hypothesis search
Experimental
Verification
Independent adapters only
Resource model
Bounded local runs
Capability claim
None beyond executed evidence
Legacy Simulation Build
Local simulation components and build checks
These are deterministic local simulation diagnostics, not independently verified mathematical discoveries. Verified evidence appears only in Verified Experimental Mode.
Commands verified
python main.py --ticks 5passedGenerated evolving agent/theorem simulation and dashboard.html.
python -m unittest discover maths_ai_ecosystem/testspassed9 tests passed.
python -m compileall -q maths_ai_ecosystem main.pypassedPython compile check passed.
Generated files
Latest simulation events (not verifier evidence)
Verified Experimental Mode
Evidence, not agent theatre.
This runs a bounded Python experiment with truth-table, SymPy, and deterministic graph verifiers. Only independent verifier output can become VERIFIED.
No result is shown until a Python experiment executes.
Recursive Mathematical Rewrite Cognition Engine
Mathematical intelligence emerges when symbolic structures recursively rewrite themselves under proof, stability, and abstraction constraints. Expressions rewrite, theorems rewrite, proof paths rewrite, theorem graphs rewrite, rewrite rules rewrite, and meta-theorems guide the process.
This browser loop is a visual rewrite demo only. It never verifies a theorem; use Verified Experimental Mode above for persisted, independently checkable evidence.
Theorem Graph
Live Rewrite Activity
Theorem Genome Inspector
Double Negation Elimination
Demo seed¬¬A rewrites to A in classical Boolean logic
Use truth-table equivalence for A and ¬¬A.
Rule Evolution
Meta-Cognition
Step the simulation to detect abstraction, bridge, and rule-evolution patterns.
Stability
No termination or confluence warnings.
Tick Trace
No rewrite tick has executed yet.
Math Imagination Engine v2
Latent equation dreams with validity gates
Inspired by your PyTorch sketch: structural latent encoding, parameter blending, diffusion-style mutation, rule retrieval, validity checks, proof-step imagination, geometric trajectory frames, and self-critique.
Waiting for a math imagination run
The result will include an imagined equation, retrieved transformation rules, validity notes, critique scores, trajectory frames, proof step, and latent introspection.
Human Understanding Optimizer
Create primitive parameters and result parameters, then let the loop search for the best combination. Every domain can be represented through Object, Property, Relation, Action, Time, Space, State, Flow, Information, Constraint, Observer, and Abstraction.
Create parameter
Create resulting parameter
Loop progress
0/84The loop tests parameter mixtures, scores the result parameters, keeps the strongest combination, and stops when the search budget ends.
Live visual optimization field
14 parameters / 6 result parametersParameter space
Object
Object
What exists as a thing, entity, variable, body, agent, or node.
Property
Property
What an object is like: length, mass, color, value, role, capacity, or feature.
Relation
Relation
How objects connect: equality, distance, causality, ownership, dependency, or similarity.
Action
Action
What changes: transformation, decision, operation, force, mutation, or behavior.
Time
Time
When change occurs: order, duration, rhythm, history, future, deadline, or sequence.
Space
Space
Where things exist: position, boundary, geometry, topology, field, market, or environment.
State
State
Current condition: stable, active, failed, solved, growing, constrained, or ready.
Energy / Flow
Energy / Flow
Movement and transfer: energy, money, attention, information, force, traffic, or momentum.
Information
Information
Meaning and signals: data, message, uncertainty reduction, pattern, code, or feedback.
Constraint
Constraint
Rules and limits: law, boundary, invariant, budget, assumption, condition, or proof gate.
Observer
Observer
Viewpoint and interpretation: user, scientist, model, frame, bias, measurement, or context.
Abstraction
Abstraction
Level of representation: symbol, model, theorem, class, schema, map, or compressed idea.
Pythagoras example
Relation
A concrete relation primitive: a^2 + b^2 = c^2 connects sides through invariant structure.
Visual analogy
Observer
A viewpoint bridge that helps a mind interpret formal structure as something seen.
Best combo so far
Run the loop to generate combinations and reveal the strongest understanding recipe.
Self-Evolving Internet-Learning Symbolic AI Engine
Internet gives experience. Symbolic rewriting creates structure. Testing creates truth. Memory creates growth. Meta-rules create intelligence.
RuleForge reads only approved sources, treats observations as evidence rather than truth, extracts structured claims, converts them into binary symbolic graphs, creates candidate rules, sandbox-tests them, and stores only decisions with an audit trail.
Internet Input Stream
Run a RuleForge cycle to read an approved source.
Core Loop
Extracted Knowledge
No claims extracted yet.
Symbolic Binary Graph
The 0/1 atom graph appears after extraction.
Generated Rules
No rules in this panel yet.
Sandbox Test Results
Sandbox results appear after rules are generated.
Rejected / Review Queue
No rules in this panel yet.
Active Laws
No rules in this panel yet.
Meta-Learning Layer
Meta-rules appear after sandbox decisions.
Memory + Audit
Memory fills after the first cycle.
Third-Person Strategist Watching RuleForge
MetaObserver does not create rules directly. It diagnoses RuleForge from above and recommends learning direction, experiments, mutations, retirements, and safety posture. Human approval is required before changing RuleForge behavior.
System Diagnosis
Waiting for RuleForge activity.
Next Recommended Path
Waiting for RuleForge activity.
Danger Warnings
No danger scan yet.
Breakthrough Signals
No breakthrough scan yet.
Strategy Q&A
Waiting for RuleForge activity.
Strategic Score Vector
Waiting for RuleForge activity.
Timeline of Strategic Decisions
Waiting for RuleForge activity.
Internal Cognitive Civilization
Math Agent
Generates conjectures, proofs, counterexamples, symbolic transformations, and theorem-solving strategies.
formal correctness
Logic Agent
Checks inference validity, assumptions, contradiction chains, and proof structure.
consistency
Physics Agent
Tests ideas against simulation, dimensional analysis, conservation laws, and empirical constraints.
reality fit
Critic Agent
Attacks weak assumptions, detects hallucinations, finds benchmark loopholes, and demands evidence.
falsification
Compression Agent
Turns long reasoning into compact abstractions, invariants, reusable lemmas, and concept hierarchies.
minimum description length
Explorer Agent
Searches weird intersections, mutates hypotheses, proposes new agent variants, and opens research branches.
novelty
Memory Agent
Maintains theorem graph, failed attempts, lineage, invariant database, and evolving abstraction tree.
cumulative learning
Teacher Agent
Explains discoveries back to other agents, creates curricula, and converts failures into training examples.
transfer
Fundamental Hypothesis
Intelligence is not a static model. It emerges from recursive interaction, transformation reasoning, compression, simulation, evolutionary adaptation, and structured self-correction.
Reality Is Final Judge
Persistent Memory
Theorem graph
Claims, lemmas, proof dependencies, counterexamples, and proof status.
Abstraction hierarchy
Compressed concepts arranged from concrete examples to reusable transformations.
Invariant database
Stable patterns that survive mutation, testing, and domain transfer.
Failed attempts archive
Rejected proofs, broken simulations, bad variants, and why they failed.
Concept evolution tree
How an idea changed across debate, mutation, critique, and validation.
Reasoning lineage
Which agent, prompt variant, benchmark, and proof path produced an accepted result.
Evolutionary Selection
Weak structures die
Variants that fail proofs, tests, simulations, or compression benchmarks are archived with failure reasons.
Strong structures survive
Variants that improve correctness, abstraction, transfer, and efficiency become parents for the next generation.
Version 0.1 Build Plan
0.1 Local model
Run a local LLM through Ollama or LM Studio and expose it to a TypeScript orchestration layer.
0.1 Agent society
Instantiate 8 specialized agents with independent memory and explicit evaluation roles.
0.1 Reality gate
Use Python execution, tests, symbolic checks, and theorem-prover hooks before accepting claims.
0.1 Mutation loop
Mutate prompts, heuristics, memory schemas, and abstraction methods under bounded permissions.
0.1 Selection
Rank variants by correctness, compression, transfer, proof success, and energy cost.
0.1 Lineage
Persist every accepted idea, failed attempt, proof path, mutation, and benchmark result.
Mathematical reasoning
Autonomously generate proofs, counterexamples, invariants, abstractions, and transformations.
Recursive evolution
Mutate cognitive strategies while preserving lineage, rollback, and hard validation.
Scientific emergence
Search for structures that compress reality better than brute-force prediction.