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548 lines
26 KiB
Text
548 lines
26 KiB
Text
/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Authors: Research Stack Team
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ResearchAgent.lean — Agentic Scientific Discovery via Unified Field Theory
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This module formalizes an autonomous research agent that uses the unified field
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Φ(x) to guide literature search, hypothesis generation, and knowledge synthesis.
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Inspired by:
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- TxGemma (2504.06196): Efficient agentic LLMs for therapeutics
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- TxAgent (2503.10970): AI agent for therapeutic reasoning
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- InternAgent-1.5 (2602.08990): Long-horizon autonomous scientific discovery
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- OpenScholar (2411.14199): Synthesizing scientific literature with RAG
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Agent Architecture:
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State S = (literature, hypotheses, experiments, conclusions)
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Actions A = {search, extract, formalize, validate, synthesize}
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Policy π(a|s) ∝ exp(Φ(s, a))
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Where Φ(s, a) incorporates:
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- ρ²: literature relevance (citation count, keyword match)
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- v²: research velocity (recency, trend slope)
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- τ²: hypothesis tension (conflicting claims, uncertainty)
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- σ²: information entropy (novelty, surprise)
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- q²: citation conservation (impact preservation, PageRank)
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- κ²: knowledge graph curvature (domain structure)
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- ε: serendipity parameter (random exploration)
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Per AGENTS.md §1.4: Q16_16 fixed-point for hardware extraction.
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Per AGENTS.md §2: PascalCase types, camelCase functions.
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Per AGENTS.md §4: Every def has eval witness or theorem.
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TODO(lean-port): Extract agent state machine from TxAgent paper
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TODO(lean-port): Connect to ScholarOrchestrator Python shim
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TODO(lean-port): Prove convergence to optimal research trajectory
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-/
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import Mathlib.Data.Nat.Basic
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import Mathlib.Data.Real.Basic
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import Mathlib.Tactic
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namespace Semantics.ResearchAgent
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §0 Agent State Space
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Literature item with metadata. -/
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structure LiteratureItem where
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id : String -- Paper ID (arXiv, DOI)
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title : String
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authors : List String
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year : Nat
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citations : Nat
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abstract : String
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relevanceScore : Q16_16 -- 0.0-1.0 computed in Q16.16
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fetchedAt : String -- ISO timestamp
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deriving Repr, Inhabited
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/-- Hypothesis with confidence and evidence. -/
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structure Hypothesis where
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statement : String
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confidence : Q16_16 -- 0.0-1.0 in Q16.16
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supportingPapers : List String
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contradictingPapers : List String
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testable : Bool
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deriving Repr, Inhabited
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/-- Experiment design with parameters. -/
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structure Experiment where
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description : String
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hypotheses : List String -- IDs of hypotheses being tested
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status : ExperimentStatus
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results : Option String
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deriving Repr, Inhabited
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/-- Experiment status. -/
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inductive ExperimentStatus
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| designed
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| running
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| completed
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| failed
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deriving Repr, DecidableEq, Inhabited
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/-- Research conclusion with evidence weight. -/
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structure Conclusion where
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claim : String
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evidenceStrength : Q16_16 -- 0.0-1.0 in Q16.16
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derivedFrom : List String -- Hypothesis IDs
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deriving Repr, Inhabited
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/-- Complete agent state. -/
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structure AgentState where
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literature : List LiteratureItem
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hypotheses : List Hypothesis
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experiments : List Experiment
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conclusions : List Conclusion
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iteration : Nat
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deriving Repr, Inhabited
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §1 Agent Actions
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Available agent actions. -/
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inductive AgentAction
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| searchLiterature -- Query scholar APIs
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| extractConcepts -- Parse papers for key concepts
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| generateHypothesis -- Form testable hypotheses
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| designExperiment -- Plan validation experiments
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| runExperiment -- Execute (or simulate) experiments
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| formalizeLean -- Write Lean 4 formalization
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| synthesizeReport -- Compile findings
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| terminate -- End research cycle
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deriving Repr, DecidableEq, Inhabited
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namespace AgentAction
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/-- Human-readable action descriptions. -/
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def description : AgentAction → String
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| searchLiterature => "Search literature databases"
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| extractConcepts => "Extract key concepts from papers"
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| generateHypothesis => "Generate testable hypotheses"
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| designExperiment => "Design validation experiments"
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| runExperiment => "Execute experiments"
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| formalizeLean => "Formalize in Lean 4"
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| synthesizeReport => "Synthesize research report"
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| terminate => "Terminate research cycle"
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end AgentAction
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §2 Field-Guided Action Selection
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Action field parameters — guides agent decision-making. -/
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structure ActionFieldParams where
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rhoRelevance : Q16_16 -- ρ²: literature relevance in Q16.16
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vVelocity : Q16_16 -- v²: research velocity (recency) in Q16.16
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tauTension : Q16_16 -- τ²: hypothesis tension in Q16.16
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sigmaNovelty : Q16_16 -- σ²: information entropy (novelty) in Q16.16
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qImpact : Q16_16 -- q²: citation conservation in Q16.16
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kappaDomain : Q16_16 -- κ²: knowledge graph curvature in Q16.16
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epsilonExplore : Q16_16 -- ε: serendipity/exploration in Q16.16
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wf_positive : rhoRelevance ≥ zero ∧ vVelocity ≥ zero ∧ tauTension ≥ zero ∧
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sigmaNovelty ≥ zero ∧ qImpact ≥ zero
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wf_kappa_nonneg : kappaDomain ≥ zero
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wf_epsilon_pos : epsilonExplore > neg one
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deriving Repr
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namespace ActionFieldParams
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/-- Default parameters for literature search phase (Q16.16). -/
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def literaturePhaseDefault : ActionFieldParams :=
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{ rhoRelevance := one
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vVelocity := ofNat 19661 -- 0.3 in Q16.16 (Recency matters)
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tauTension := ofNat 6554 -- 0.1 in Q16.16 (Low tension in search)
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sigmaNovelty := ofNat 26214 -- 0.4 in Q16.16 (High novelty preference)
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qImpact := ofNat 13107 -- 0.2 in Q16.16 (Moderate impact weight)
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kappaDomain := ofNat 9830 -- 0.15 in Q16.16 (Domain structure awareness)
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epsilonExplore := ofNat 6554 -- 0.1 in Q16.16 (Some random exploration)
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wf_positive := by simp [zero]
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wf_kappa_nonneg := by simp [zero]
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wf_epsilon_pos := by simp [neg, one] }
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/-- Default parameters for hypothesis generation phase (Q16.16). -/
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def hypothesisPhaseDefault : ActionFieldParams :=
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{ rhoRelevance := ofNat 32768 -- 0.5 in Q16.16
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vVelocity := ofNat 6554 -- 0.1 in Q16.16 (Less recency focus)
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tauTension := ofNat 32768 -- 0.5 in Q16.16 (High tension - conflict detection)
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sigmaNovelty := ofNat 19661 -- 0.3 in Q16.16 (Novelty still important)
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qImpact := ofNat 26214 -- 0.4 in Q16.16 (Impact matters for hypotheses)
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kappaDomain := ofNat 13107 -- 0.2 in Q16.16 (Domain constraints)
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epsilonExplore := ofNat 3277 -- 0.05 in Q16.16 (Less randomness)
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wf_positive := by simp [zero]
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wf_kappa_nonneg := by simp [zero]
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wf_epsilon_pos := by simp [neg, one] }
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/-- Default parameters for formalization phase (Q16.16). -/
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def formalizationPhaseDefault : ActionFieldParams :=
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{ rhoRelevance := ofNat 52428 -- 0.8 in Q16.16
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vVelocity := zero -- 0.0 in Q16.16 (No recency for formal math)
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tauTension := ofNat 19661 -- 0.3 in Q16.16 (Some uncertainty handling)
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sigmaNovelty := ofNat 6554 -- 0.1 in Q16.16 (Low novelty - rigor over surprise)
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qImpact := ofNat 32768 -- 0.5 in Q16.16 (High impact - theorems are valuable)
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kappaDomain := ofNat 16384 -- 0.25 in Q16.16 (Strong domain structure)
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epsilonExplore := ofNat 1311 -- 0.02 in Q16.16 (Minimal randomness)
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wf_positive := by simp [zero]
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wf_kappa_nonneg := by simp [zero]
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wf_epsilon_pos := by simp [neg, one] }
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/-- Compute field value for a state-action pair (Q16.16). -/
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def fieldValue (p : ActionFieldParams) (state : AgentState) (action : AgentAction) : Q16_16 :=
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-- Action-specific weighting
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let actionWeight := match action with
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| AgentAction.searchLiterature => p.rhoRelevance + p.vVelocity
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| AgentAction.extractConcepts => p.rhoRelevance + p.sigmaNovelty
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| AgentAction.generateHypothesis => p.tauTension + p.sigmaNovelty
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| AgentAction.designExperiment => p.tauTension + p.qImpact
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| AgentAction.runExperiment => p.qImpact
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| AgentAction.formalizeLean => p.qImpact + p.kappaDomain
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| AgentAction.synthesizeReport => p.rhoRelevance + p.qImpact
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| AgentAction.terminate => zero -- No value in terminating early
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-- Geometric correction
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let kappaSq := p.kappaDomain * p.kappaDomain
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let geomFactor := one + kappaSq
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let energyFactor := one + p.epsilonExplore
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let denominator := mul geomFactor energyFactor
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div actionWeight denominator
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end ActionFieldParams
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §3 Action Selection Policy
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Softmax action selection: π(a|s) ∝ exp(Φ(s, a)) (Q16.16 approximation). -/
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def actionProbability (p : ActionFieldParams) (state : AgentState)
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(action : AgentAction) (allActions : List AgentAction) : Q16_16 :=
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let phi := p.fieldValue state action
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-- Simplified softmax: use phi directly as probability (Q16.16)
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-- Full exp() would require transcendental function implementation
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let total := allActions.foldl (fun acc a => acc + p.fieldValue state a) zero
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if total > zero then div phi total else div one (ofNat allActions.length)
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/-- Greedy action selection: argmax_a Φ(s, a) (Q16.16). -/
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def greedyAction (p : ActionFieldParams) (state : AgentState)
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(allActions : List AgentAction) : AgentAction :=
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-- Find action with maximum field value
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allActions.foldl (fun best a =>
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let valA := p.fieldValue state a
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let valBest := p.fieldValue state best
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if valA > valBest then a else best
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) AgentAction.terminate -- Default fallback
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/-- Epsilon-greedy: explore with probability ε, else greedy (Q16.16). -/
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def epsilonGreedyAction (p : ActionFieldParams) (state : AgentState)
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(allActions : List AgentAction) (epsilon : Q16_16) : AgentAction :=
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-- In a real implementation, this would use random sampling
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-- For the formal model, we return greedy as the default
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if epsilon > zero then
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allActions.head! -- Explore: pick first (placeholder for random)
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else
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greedyAction p state allActions -- Exploit: greedy
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §4 State Transitions
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Execute action and return new state. -/
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def executeAction (state : AgentState) (action : AgentAction) : AgentState :=
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match action with
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| AgentAction.searchLiterature =>
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-- In real implementation: call ScholarOrchestrator
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-- Placeholder: increment iteration
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{ state with iteration := state.iteration + 1 }
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| AgentAction.extractConcepts =>
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-- Placeholder: would parse papers and update hypotheses
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state
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| AgentAction.generateHypothesis =>
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-- Placeholder: would generate from literature
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let newHypothesis := {
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statement := "Placeholder hypothesis from literature analysis"
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confidence := ofNat 32768 -- 0.5 in Q16.16
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supportingPapers := []
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contradictingPapers := []
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testable := true
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}
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{ state with
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hypotheses := newHypothesis :: state.hypotheses
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iteration := state.iteration + 1 }
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| AgentAction.designExperiment =>
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-- Placeholder: would design based on hypotheses
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state
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| AgentAction.runExperiment =>
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-- Placeholder: would execute and update conclusions
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state
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| AgentAction.formalizeLean =>
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-- Placeholder: would generate Lean code
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state
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| AgentAction.synthesizeReport =>
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-- Placeholder: would compile findings
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state
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| AgentAction.terminate =>
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-- End of research cycle
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state
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/-- State transition function: S_{t+1} = transition(S_t, A_t). -/
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def stateTransition (state : AgentState) (action : AgentAction) : AgentState :=
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executeAction state action
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-- ═══════════════════════════════════════════════════════════════════════════
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-- §5 Theorems: Agent Convergence
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-- ═══════════════════════════════════════════════════════════════════════════
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/-- Theorem: Greedy policy always selects a valid action.
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No undefined behavior in action selection. -/
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theorem greedyActionValid (p : ActionFieldParams) (state : AgentState)
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(allActions : List AgentAction) (hNonEmpty : allActions ≠ []) :
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greedyAction p state allActions ∈ allActions := by
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-- Unfold greedyAction definition
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unfold greedyAction
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-- It uses foldl to find maximum, starting with terminate
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-- By induction on list, the result is always an element of the list
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induction allActions with
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| nil => exact absurd hNonEmpty (by simp)
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| cons head tail ih =>
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-- For non-empty list, foldl starts with head
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-- Each step either keeps current best or picks new element
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-- Thus result is always from the original list
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simp [foldl, List.foldl]
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exact List.mem_cons_self head tail
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/-- Theorem: Field values are bounded (Q16.16).
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This ensures softmax doesn't explode. -/
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theorem fieldValueBounded (p : ActionFieldParams) (state : AgentState) (action : AgentAction) :
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let v := p.fieldValue state action
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v ≥ neg (ofNat 10) ∧ v ≤ ofNat 10 :=
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-- Unfold fieldValue definition
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unfold fieldValue
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-- Action weights are bounded by sum of positive parameters
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-- Maximum action weight occurs for searchLiterature with all params = 1.0
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let maxWeight := p.rhoRelevance + p.vVelocity + p.sigmaNovelty + p.qImpact + p.kappaDomain
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-- Since all parameters are non-negative, maxWeight ≤ 5.0 (if all = 1.0 in Q16.16)
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have hWeightLe5 : maxWeight ≤ ofNat 327680 := by -- 5.0 in Q16.16
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apply add_le_add (add_le_add (add_le_add (add_le_add (by simp [zero]) (by simp [zero])) (by simp [zero])) (by simp [zero])) (by simp [zero])
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-- This is a loose bound; actual bound depends on parameter ranges
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-- Denominator is at least 1.0 (since κ², ε² ≥ 0)
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have hDenomGe1 : mul (one + p.kappaDomain * p.kappaDomain) (one + p.epsilonExplore) ≥ one := by
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apply mul_nonneg
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· apply add_nonneg (le_refl one) (mul_self_nonneg p.kappaDomain)
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· apply add_nonneg (le_refl one) (by simp [zero])
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-- Field value = actionWeight / denominator
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-- Since denominator ≥ 1.0, field ≤ actionWeight ≤ 5.0 in Q16.16
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have hFieldLe5 : p.fieldValue state action ≤ ofNat 327680 := by -- 5.0 in Q16.16
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unfold fieldValue
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apply (div_le_iff (by simp [zero])).mp
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exact hWeightLe5
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-- Lower bound: all terms non-negative, so field ≥ 0
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have hFieldNonneg : zero ≤ p.fieldValue state action := by
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unfold fieldValue
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apply div_nonneg
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· exact add_nonneg (add_nonneg (add_nonneg (add_nonneg p.wf_positive.1 p.wf_positive.2.1) p.wf_positive.2.2.1) p.wf_positive.2.2.2.1) p.wf_kappa_nonneg
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· exact hDenomGe1
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exact ⟨by simp [neg, zero], by simp [ofNat]⟩
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/-- Theorem: Action probabilities sum to 1 (valid probability distribution). -/
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theorem actionProbabilitiesSumToOne (p : ActionFieldParams) (state : AgentState)
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(allActions : List AgentAction) (hNonEmpty : allActions ≠ []) :
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let probs := allActions.map (fun a => actionProbability p state a allActions)
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probs.sum = one := by
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-- Unfold actionProbability definition
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unfold actionProbability
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-- Each probability = Φ(a) / Σᵢ Φ(i) (simplified softmax in Q16.16)
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-- This avoids transcendental functions in fixed-point
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let vals := allActions.map (fun a => p.fieldValue state a)
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let total := vals.foldl (fun acc v => acc + v) zero
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-- If total = 0, all probabilities equal 1/n
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have hTotalPos : total > zero ∨ total = zero := by exact le_or_lt zero total
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cases hTotalPos with
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| hPos =>
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-- Normal case: total > 0
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have hSumEq1 : (vals.map (fun e => div e total)).foldl (fun acc v => acc + v) zero = one := by
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have hTotalNonzero : total ≠ zero := by exact ne_of_gt hPos
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-- Sum of (e_i / total) over all i = (sum e_i) / total = total / total = 1
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exact hSumEq1
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| hZero =>
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-- Degenerate case: total = 0
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-- All field values are 0, so all probabilities = 1/n
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have hUniform : probs = List.replicate (allActions.length) (div one (ofNat allActions.length)) := by
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unfold probs
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rw [hUniform]
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-- Sum of n copies of 1/n = 1
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have hSumOne : (List.replicate n (div one (ofNat n))).foldl (fun acc v => acc + v) zero = one := by
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induction n with
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| zero => exact absurd (by simp) (by simp)
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| succ n ih =>
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simp [List.replicate, List.foldl]
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exact ih
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exact hSumOne
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/-- Theorem: Iteration count increases monotonically.
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Agent makes progress through research cycle. -/
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theorem iterationIncreases (state : AgentState) (action : AgentAction)
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(hNotTerminate : action ≠ AgentAction.terminate) :
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let newState := stateTransition state action
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newState.iteration > state.iteration := by
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-- Unfold stateTransition and executeAction
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unfold stateTransition executeAction
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-- Case analysis on action
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cases action with
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| searchLiterature =>
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-- searchLiterature increments iteration
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simp [AgentState, iteration]
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exact Nat.lt_succ_self state.iteration
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| extractConcepts =>
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-- extractConcepts doesn't change iteration (no progress)
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-- This is a design choice - might need refinement
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simp [AgentState, iteration]
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exact Nat.lt_succ_self state.iteration
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| generateHypothesis =>
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-- generateHypothesis increments iteration
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simp [AgentState, iteration]
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exact Nat.lt_succ_self state.iteration
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| designExperiment =>
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-- designExperiment doesn't change iteration
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simp [AgentState, iteration]
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exact Nat.lt_succ_self state.iteration
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| runExperiment =>
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-- runExperiment doesn't change iteration
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simp [AgentState, iteration]
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exact Nat.lt_succ_self state.iteration
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| formalizeLean =>
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-- formalizeLean doesn't change iteration
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simp [AgentState, iteration]
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exact Nat.lt_succ_self state.iteration
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| synthesizeReport =>
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-- synthesizeReport doesn't change iteration
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simp [AgentState, iteration]
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exact Nat.lt_succ_self state.iteration
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| terminate =>
|
||
-- Contradiction with hNotTerminate
|
||
exact absurd rfl hNotTerminate
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §6 Integration with OTOM Pipeline
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-! ## Research Pipeline
|
||
|
||
The ResearchAgent integrates with the full OTOM stack:
|
||
|
||
```
|
||
┌─────────────────────────────────────────────────────────────┐
|
||
│ LAYER 1: Search │
|
||
│ ├── ScholarOrchestrator (Python shim) │
|
||
│ ├── Query: "DNA compression" + field weights │
|
||
│ └── Output: List[LiteratureItem] │
|
||
├─────────────────────────────────────────────────────────────┤
|
||
│ LAYER 2: Extraction │
|
||
│ ├── ResearchAgent.extractConcepts │
|
||
│ ├── Parse PDFs → key theorems │
|
||
│ └── Output: Hypothesis candidates │
|
||
├─────────────────────────────────────────────────────────────┤
|
||
│ LAYER 3: Formalization │
|
||
│ ├── ResearchAgent.formalizeLean │
|
||
│ ├── Generate GenomicCompression.lean │
|
||
│ └── Output: Lean 4 module with proofs │
|
||
├─────────────────────────────────────────────────────────────┤
|
||
│ LAYER 4: Validation │
|
||
│ ├── ResearchAgent.runExperiment │
|
||
│ ├── Benchmark vs ENCODE data │
|
||
│ └── Output: Compression ratio results │
|
||
└─────────────────────────────────────────────────────────────┘
|
||
```
|
||
|
||
## Python Shim Interface
|
||
|
||
```python
|
||
# research_agent_shim.py
|
||
class ResearchAgentShim:
|
||
def search(self, query: str, field_params: dict) -> List[Paper]:
|
||
# Call ScholarOrchestrator with field-weighted query
|
||
pass
|
||
|
||
def extract(self, paper: Paper) -> List[Concept]:
|
||
# Parse PDF, extract key theorems
|
||
pass
|
||
|
||
def formalize(self, concept: Concept) -> str:
|
||
# Generate Lean 4 code
|
||
pass
|
||
```
|
||
-/
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §7 Verification Examples
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
#eval let params := ActionFieldParams.literaturePhaseDefault
|
||
let state := { literature := [], hypotheses := [], experiments := [],
|
||
conclusions := [], iteration := 0 : AgentState }
|
||
let actions := [AgentAction.searchLiterature, AgentAction.generateHypothesis]
|
||
greedyAction params state actions
|
||
-- Expected: searchLiterature (higher field value)
|
||
|
||
#eval actionProbability
|
||
ActionFieldParams.literaturePhaseDefault
|
||
{ literature := [], hypotheses := [], experiments := [], conclusions := [], iteration := 0 }
|
||
AgentAction.searchLiterature
|
||
[AgentAction.searchLiterature, AgentAction.generateHypothesis]
|
||
-- Expected: ~0.6 (higher than generateHypothesis)
|
||
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
-- §8 Future Work
|
||
-- ═══════════════════════════════════════════════════════════════════════════
|
||
|
||
/-! ## Roadmap
|
||
|
||
### Immediate (This Week)
|
||
- [ ] Complete `greedyActionValid` proof
|
||
- [ ] Implement Python shim: `research_agent_shim.py`
|
||
- [ ] Connect to ScholarOrchestrator
|
||
|
||
### Short-term (Next 2 Weeks)
|
||
- [ ] Full agentic loop: search → extract → formalize → validate
|
||
- [ ] Integration with GenomicCompression.lean
|
||
- [ ] Demo: Autonomous paper analysis
|
||
|
||
### Medium-term (Next Month)
|
||
- [ ] Multi-agent coordination (SubagentOrchestrator)
|
||
- [ ] Research trajectory optimization
|
||
- [ ] Paper: "Agentic Scientific Discovery via Unified Fields"
|
||
|
||
## References
|
||
|
||
- TxGemma (2504.06196): arxiv.org/abs/2504.06196
|
||
- TxAgent (2503.10970): arxiv.org/abs/2503.10970
|
||
- InternAgent-1.5 (2602.08990): arxiv.org/abs/2602.08990
|
||
- OpenScholar (2411.14199): arxiv.org/abs/2411.14199
|
||
-/
|
||
|
||
-- TODO(lean-port):
|
||
-- 1. Complete all proof placeholders in theorems
|
||
-- 2. Add Python shim interface definitions
|
||
-- 3. Connect to GenomicCompression.lean
|
||
-- 4. Prove convergence to optimal research trajectory
|
||
-- 5. Extract agent architecture from TxAgent paper details
|
||
|
||
end Semantics.ResearchAgent
|