Research-Stack/0-Core-Formalism/lean/Semantics/Semantics/AgenticOrchestration.lean

/- Copyright (c) 2026 Sovereign Research Stack. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Research Stack Team

AgenticOrchestration.lean — Multi-Agent Coordination for Research Automation

This module re-exports agentic orchestration components from split modules:
- Hardware-native agent structures (AgenticHardware.lean)
- Core agent types, states, and tasks (AgenticCore.lean)
- Orchestration field computation (AgenticOrchestrationField.lean)
- Task assignment and orchestration algorithm (AgenticTaskAssignment.lean)
- Orchestration correctness theorems (AgenticTheorems.lean)

Split from AgenticOrchestration.lean per swarm suggestion (USER AUTHORIZED).

Agent Types:
1. SearchAgent — Literature discovery (wraps ScholarOrchestrator)
2. ExtractAgent — Concept extraction from papers
3. FormalizeAgent — Lean 4 code generation
4. ValidateAgent — Empirical benchmarking
5. SynthesizeAgent — Report compilation
6. BuilderAgent — Builder (Architect): ADD clock, proposes forward progress, builds state (manifold_reg)
7. WardenAgent — Warden: SUBTRACT clock, reverses to check, validates proofs (stark_trace)
8. JudgeAgent — Judge (HeatSink): PAUSE clock, holds state, adjudicates (heatsink_halt)

Orchestration via unified field Φ_orchestrate:
Φ_team(team, task) = Σᵢ Φᵢ(agentᵢ) + Σᵢ<ⱼ Φ_coordination(agentᵢ, agentⱼ)

Where coordination field captures:
- Dependency: Agent j needs output from agent i
- Conflict: Agents compete for resources
- Synergy: Agents collaborate on shared goals

Triumvirate Integration:
Swarm bug detection maps to Triumvirate roles via severity-based logic:
- Severity ≥ 85 + incomplete proof → WardenAgent (proof validation)
- Severity ≥ 85 + other → JudgeAgent (critical issues)
- Warnings → JudgeAgent (hold state for assessment)
- Other → BuilderAgent (forward progress)

Hardware Mapping:
- BuilderAgent → manifold_reg (Topological State, ADD clock)
- WardenAgent → stark_trace & warden_valid (Integrity, SUBTRACT clock)
- JudgeAgent → heatsink_halt (Energy Guard, PAUSE clock)

Per AGENTS.md §1.4: Q16_16 fixed-point for hardware extraction.
Per AGENTS.md §2: PascalCase types, camelCase functions.
Per AGENTS.md §4: Every def has eval witness or theorem.

NII-02 TRANSLATION ENGINE ASSIGNMENT:
====================================
This file is assigned to NII-02 Translation Engine for:
- Translation of agent orchestration field to hardware-accelerated computation
- Extraction of coordination patterns for multi-agent hardware scheduling
- Translation of task dependency graphs to hardware resource allocation
- Formalization of agent field dynamics for hardware implementation

Translation responsibilities:
1. Map AgentFieldParams and CoordinationParams to hardware-native representation
2. Translate orchestration field computation to GPU/accelerator kernels
3. Extract task scheduling algorithms for hardware dispatch
4. Formalize agent state transitions for hardware state machines

-/

import Semantics.Hardware.AgenticHardware
import Semantics.AgenticCore
import Semantics.AgenticOrchestrationField
import Semantics.AgenticTaskAssignment
import Semantics.AgenticTheorems
import Semantics.SubagentOrchestrator

namespace Semantics.AgenticOrchestration

open Semantics.Q16_16
open Semantics.SubagentOrchestrator

/-! ## Layered Orchestration

```
┌─────────────────────────────────────────────────────────────┐
│  LAYER 3: AgenticOrchestration                              │
│  ├── Research pipeline: search → extract → formalize       │
│  ├── Agent teams: specialized workers                        │
│  └── Task graph: dependency management                       │
├─────────────────────────────────────────────────────────────┤
│  LAYER 2: SubagentOrchestrator                               │
│  ├── Domain coordination: compression ↔ field-physics        │
│  ├── Resource allocation: CPU, memory, SRAM                │
│  └── Convergence: multi-domain theorem proving              │
├─────────────────────────────────────────────────────────────┤
│  LAYER 1: Individual Agents                                  │
│  ├── SearchAgent → ScholarOrchestrator (Python)              │
│  ├── FormalizeAgent → GenomicCompression.lean                │
│  └── ValidateAgent → unified_field_validation.py             │
└─────────────────────────────────────────────────────────────┘
```

## Communication Protocol

Agents communicate via:
1. **Message passing**: Async queue (Kafka/RabbitMQ style)
2. **Shared state**: OTOM knowledge graph
3. **Direct RPC**: For synchronous coordination

Message types:
- `TaskRequest`: Assign new task
- `TaskComplete`: Report results
- `DependencyMet`: Notify unblocking
- `ResourceRequest`: Ask for allocation
-/

-- ═══════════════════════════════════════════════════════════════════════════
-- §1  Agent Communication Protocol (Async Message Passing)
-- ═══════════════════════════════════════════════════════════════════════════

/-- Message types for agent communication. -/
inductive Message
  | taskRequest (taskId : String) (description : String) (requiredType : AgentType)
  | taskComplete (agentId : String) (taskId : String) (results : List String)
  | dependencyMet (taskId : String) (depTaskId : String)
  | resourceRequest (agentId : String) (resourceType : String) (amount : Q16_16)
  | resourceGrant (agentId : String) (resourceType : String) (amount : Q16_16)
  | coordinationUpdate (targetId : String) (fieldValue : Q16_16)
  | error (agentId : String) (errorCode : Nat) (description : String)
  deriving Repr, DecidableEq, BEq, Inhabited

/-- Priority levels for message queue ordering. -/
inductive MessagePriority
  | high
  | normal
  | low
  deriving Repr, DecidableEq, BEq, Inhabited

/-- An envelope wrapping a message with metadata. -/
structure Envelope where
  sender : String
  recipient : String
  message : Message
  priority : MessagePriority
  timestamp : Nat
  deriving Repr, Inhabited

/-- Async mailbox for each agent (FIFO with priority ordering). -/
structure Mailbox where
  agentId : String
  inbox : List Envelope
  outbox : List Envelope
  nextSeq : Nat
  deriving Repr, Inhabited

namespace Mailbox

/-- Create an empty mailbox for an agent. -/
def create (agentId : String) : Mailbox :=
  { agentId := agentId, inbox := [], outbox := [], nextSeq := 0 }

/-- Send a message: enqueue in the outbox with next sequence number. -/
def send (mb : Mailbox) (recipient : String) (msg : Message)
    (priority : MessagePriority := .normal) : Mailbox :=
  { mb with
    outbox := mb.outbox ++
      [{ sender := mb.agentId, recipient := recipient, message := msg,
         priority := priority, timestamp := mb.nextSeq }]
    nextSeq := mb.nextSeq + 1 }

/-- Receive a message: dequeue the highest-priority message from inbox. -/
def receive (mb : Mailbox) : Option (Envelope × Mailbox) :=
  match mb.inbox with
  | [] => none
  | msg :: rest => some (msg, { mb with inbox := rest })

/-- Deliver a message to this mailbox (insert in priority order). -/
def deliver (mb : Mailbox) (env : Envelope) : Mailbox :=
  let rec insertByPriority (env : Envelope) : List Envelope → List Envelope
    | [] => [env]
    | h :: t =>
      if env.priority == .high && h.priority != .high then
        env :: h :: t
      else if env.priority == .normal && h.priority == .low then
        env :: h :: t
      else
        h :: insertByPriority env t
  { mb with inbox := insertByPriority env mb.inbox }

/-- Flush outbox: move all outgoing messages to a delivery list. -/
def flushOutbox (mb : Mailbox) : List (String × Envelope) × Mailbox :=
  let deliveries := mb.outbox.map (fun env => (env.recipient, env))
  (deliveries, { mb with outbox := [] })

/-- Number of pending messages in inbox. -/
def inboxSize (mb : Mailbox) : Nat := mb.inbox.length

end Mailbox

/-- Global message broker maintaining all agent mailboxes. -/
structure MessageBroker where
  mailboxes : List Mailbox
  deriving Repr, Inhabited

namespace MessageBroker

/-- Create an empty broker. -/
def empty : MessageBroker := { mailboxes := [] }

/-- Register an agent's mailbox with the broker. -/
def registerMailbox (broker : MessageBroker) (mb : Mailbox) : MessageBroker :=
  { broker with mailboxes := mb :: broker.mailboxes }

/-- Find the mailbox for a given agent ID. -/
def findMailbox (broker : MessageBroker) (agentId : String) : Option Mailbox :=
  broker.mailboxes.find? (fun mb => mb.agentId = agentId)

/-- Update a specific mailbox in the broker. -/
def updateMailbox (broker : MessageBroker) (mb : Mailbox) : MessageBroker :=
  { broker with mailboxes :=
      broker.mailboxes.map (fun m => if m.agentId = mb.agentId then mb else m) }

/-- Deliver all messages from all outboxes to their destinations (one cycle). -/
def deliveryCycle (broker : MessageBroker) : MessageBroker :=
  let (allDeliveries, flushedBroker) :=
    List.foldl (fun ((dels, brkr) : List (String × Envelope) × MessageBroker) (mb : Mailbox) =>
      let (deliveries, newMb) := mb.flushOutbox
      (dels ++ deliveries, brkr.updateMailbox newMb)
    ) ([], broker) broker.mailboxes
  List.foldl (fun (brkr : MessageBroker) (recipientId, env) =>
    match brkr.findMailbox recipientId with
    | some mb => brkr.updateMailbox (mb.deliver env)
    | none => brkr
  ) flushedBroker allDeliveries

/-- Total pending messages across all inboxes. -/
def totalPending (broker : MessageBroker) : Nat :=
  broker.mailboxes.foldl (fun acc mb => acc + mb.inboxSize) 0

end MessageBroker

-- ═══════════════════════════════════════════════════════════════════════════
-- §2  Connection to SubagentOrchestrator Domain Definitions
-- ═══════════════════════════════════════════════════════════════════════════

/-- Map an AgentType to a SubagentOrchestrator Domain. -/
def agentTypeToDomain (t : AgentType) : Domain :=
  match t with
  | AgentType.searchAgent     => .compression
  | AgentType.extractAgent    => .fieldPhysics
  | AgentType.formalizeAgent  => .braidAlgebra
  | AgentType.validateAgent   => .evolutionSearch
  | AgentType.synthesizeAgent => .domainModels
  | AgentType.metaAgent       => .coreBind
  | AgentType.builderAgent    => .memoryState
  | AgentType.wardenAgent     => .memoryState
  | AgentType.judgeAgent      => .coreBind

/-- Map a SubagentOrchestrator Domain back to the closest AgentType. -/
def domainToAgentType (d : Domain) : AgentType :=
  match d with
  | Domain.coreBind       => .metaAgent
  | Domain.compression    => .searchAgent
  | Domain.spatialVLSI    => .builderAgent
  | Domain.diffusionFlow  => .extractAgent
  | Domain.pistShell      => .builderAgent
  | Domain.fieldPhysics   => .extractAgent
  | Domain.braidAlgebra   => .formalizeAgent
  | Domain.kernelDomain   => .validateAgent
  | Domain.evolutionSearch => .validateAgent
  | Domain.memoryState    => .builderAgent
  | Domain.cognitiveControl => .judgeAgent
  | Domain.geometry       => .formalizeAgent
  | Domain.thermodynamic  => .judgeAgent
  | Domain.diagnostic     => .wardenAgent
  | Domain.cloudStorage   => .synthesizeAgent
  | Domain.gpuResources   => .validateAgent
  | Domain.domainModels   => .synthesizeAgent
  | Domain.fieldOperator  => .metaAgent

/-- Convert an AgentState to a SubagentOrchestrator SpawnedSubagent. -/
def agentStateToSpawnedSubagent (agent : AgentState) : SpawnedSubagent :=
  { id := 0
    parentId := none
    domain := agentTypeToDomain agent.agentType
    strategy := .perDomain
    lifecycle :=
      match agent.status with
      | AgentStatus.idle      => .pending
      | AgentStatus.working   => .running
      | AgentStatus.waiting   => .pending
      | AgentStatus.completed => .completed
      | AgentStatus.failed    => .failed
    taskDescription := agent.currentTask.getD "idle"
    assignedTo := "cpu"
    failureRecord := none }

/-- Create a SubagentSystem from a list of AgentStates for cross-system analysis. -/
def agentStatesToSubagentSystem (agents : List AgentState) : SubagentSystem :=
  let domainExperts : List DomainExpert :=
    agents.map (fun a =>
      { domain := agentTypeToDomain a.agentType
        expertiseLevel := Q16_16.sat01 (Q16_16.one - a.load)
        modulesKnown := a.completedTasks })
  { domainExperts := domainExperts
    codebaseExpert :=
      { coverage := Q16_16.sat01 (Q16_16.ofNat
          (agents.filter (fun a => a.status = .completed)).length
          / Q16_16.ofNat (max agents.length 1))
        importGraphComplete := agents.all (fun a => a.status = .completed || a.status = .idle)
        theoremCoverage := Q16_16.zero }
    integrationAnalyst :=
      { crossDomainPairs := agents.flatMap (fun a =>
          agents.map (fun b => (agentTypeToDomain a.agentType, agentTypeToDomain b.agentType)))
        hybridizationScore := Q16_16.one
        gapIdentified := [] }
    scheduler :=
      { impactWeight := Q16_16.ofFloat 0.6
        effortWeight := Q16_16.ofFloat 0.4
        threshold := Q16_16.ofFloat 0.1 }
  }

-- ═══════════════════════════════════════════════════════════════════════════
-- §3  Orchestration Stability: DeadlockFreedom and StarvationFreedom
-- ═══════════════════════════════════════════════════════════════════════════

/-- A system state snapshot for reasoning about liveness properties. -/
structure OrchestrationState where
  agents : List AgentState
  tasks : List Task
  completedIds : List String
  broker : MessageBroker
  step : Nat
  deriving Repr, Inhabited

namespace OrchestrationState

/-- Check whether all tasks are completed. -/
def allTasksCompleted (s : OrchestrationState) : Bool :=
  s.completedIds.length = s.tasks.length

/-- Check if there is a cycle in the task dependency graph. -/
def hasCircularDependency (tasks : List Task) : Bool :=
  let rec dfs (fuel : Nat) (visited : List String) (taskId : String) : Bool :=
    match fuel with
    | 0 => true
    | fuel' + 1 =>
      if visited.contains taskId then true
      else
        match tasks.find? (fun t => t.id = taskId) with
        | none => false
        | some task => task.dependencies.foldl (fun acc depId => acc || dfs fuel' (taskId :: visited) depId) false
  tasks.any (fun t => dfs tasks.length [] t.id)

/-- A transition from one state to the next, capturing progress. -/
structure Transition (s s' : OrchestrationState) : Prop where
  stepForward : s'.step = s.step + 1
  progress : s.allTasksCompleted ∨ s'.completedIds.length > s.completedIds.length

end OrchestrationState

/-- DeadlockFreedom: Whenever there is an unfinished task and no circular
    dependencies, a progress-making transition exists. -/
def DeadlockFreedom : Prop :=
  ∀ (s : OrchestrationState),
    ¬s.allTasksCompleted ∧ ¬OrchestrationState.hasCircularDependency s.tasks →
    ∃ (s' : OrchestrationState), OrchestrationState.Transition s s'

/-- StarvationFreedom: Every waiting agent eventually becomes unblocked. -/
def StarvationFreedom : Prop :=
  ∀ (s : OrchestrationState) (agent : AgentState),
    agent ∈ s.agents ∧ agent.status = AgentStatus.waiting →
    ∃ (s' : OrchestrationState),
      s'.step > s.step ∧
      (match s'.agents.find? (fun a => a.id = agent.id) with
       | some a' => a'.status ≠ AgentStatus.waiting
       | none => True)

/-- The research pipeline is acyclic (verified by decide). -/
theorem researchPipelineIsAcyclic : ¬OrchestrationState.hasCircularDependency researchPipeline := by
  decide

-- ═══════════════════════════════════════════════════════════════════════════
-- §4  Verification Examples & Eval Witnesses
-- ═══════════════════════════════════════════════════════════════════════════

-- Original orchestration verification example.
#eval let agents := [
  { id := "A1", agentType := AgentType.searchAgent, currentTask := none,
    completedTasks := [], outputBuffer := [], load := zero, status := AgentStatus.idle, primitiveLUT := none },
  { id := "A2", agentType := AgentType.extractAgent, currentTask := none,
    completedTasks := [], outputBuffer := [], load := zero, status := AgentStatus.idle, primitiveLUT := none }
]
let tasks := researchPipeline.take 2
let params := { rhoCapability := one, vEfficiency := one, tauLoad := zero, qReliability := one }
let (updated, completed, steps) := runOrchestration agents tasks params 
  { dependencyStrength := ofNat 32768, conflictPenalty := ofNat 6553, synergyBonus := ofNat 19660 }
steps
-- expect: 8

-- Task assignment to best agent.
#eval (assignTask researchPipeline[0] [
  { id := "A1", agentType := AgentType.searchAgent, currentTask := none,
    completedTasks := [], outputBuffer := [], load := zero, status := AgentStatus.idle, primitiveLUT := none },
  { id := "A2", agentType := AgentType.extractAgent, currentTask := none,
    completedTasks := [], outputBuffer := [], load := zero, status := AgentStatus.idle, primitiveLUT := none }
] { rhoCapability := one, vEfficiency := one, tauLoad := zero, qReliability := one }).map (fun a => a.id)
-- expect: some "A1"

-- Witness: Mailbox send/receive cycle.
#eval
  let mb := Mailbox.create "A1"
  let mb' := mb.send "A2" (Message.taskRequest "T1" "Search literature" .searchAgent)
  let (deliveries, _) := mb'.flushOutbox
  deliveries.length
  -- expect: 1

-- Witness: Message delivery to recipient.
#eval
  let mb1 := Mailbox.create "A1"
  let mb2 := Mailbox.create "A2"
  let mb1' := mb1.send "A2" (Message.taskRequest "T1" "Search" .searchAgent)
  let (deliveries, _) := mb1'.flushOutbox
  match deliveries with
  | (recipientId, _) :: _ => recipientId
  | _ => ""
  -- expect: "A2"

-- Witness: Mailbox receive returns messages in priority order.
#eval
  let mb := Mailbox.create "A1"
  let envLow : Envelope := {
    sender := "A2"
    recipient := "A1"
    message := Message.taskRequest "T1" "low" AgentType.searchAgent
    priority := MessagePriority.low
    timestamp := 0
  }
  let envHigh : Envelope := {
    sender := "A2"
    recipient := "A1"
    message := Message.taskRequest "T1" "high" AgentType.searchAgent
    priority := MessagePriority.high
    timestamp := 1
  }
  let mb' := mb.deliver envLow
  let mb'' := mb'.deliver envHigh
  match mb''.receive with
  | some (env, _) => env.priority == MessagePriority.high
  | none => false
  -- expect: true

-- Witness: Agent type to domain mapping.
#eval
  agentTypeToDomain AgentType.searchAgent == Domain.compression
  -- expect: true

-- Witness: Pipeline acyclicity.
#eval OrchestrationState.hasCircularDependency researchPipeline
  -- expect: false

/-! ## Roadmap

### Immediate (This Week)
- [x] Connect to SubagentOrchestrator.lean
- [x] Define agent communication protocol (Lean + Python)
- [ ] Implement Python AgentShim classes

### Short-term (Next 2 Weeks)
- [ ] Full research pipeline: 7 tasks, 5 agents
- [ ] Integration with GenomicCompression + ResearchAgent
- [ ] Demo: Autonomous paper analysis end-to-end

### Medium-term (Next Month)
- [ ] Multi-team orchestration (multiple research projects)
- [ ] Dynamic agent spawning based on workload
- [ ] Paper: "Agentic Orchestration for Scientific Discovery"

## Open Questions

1. **Deadlock prevention**: How to guarantee no circular dependencies?
   - ✦ Formalized: `researchPipelineIsAcyclic` theorem verified by `native_decide`
   - ✦ General case: `hasCircularDependency` predicate detects cycles at runtime
2. **Fault tolerance**: Agent failure recovery mechanisms?
3. **Scalability**: 10 agents? 100 agents? 1000 agents?
4. **Human-in-the-loop**: When should human review be required?
-/

-- All TODO(lean-port) items resolved. Completed work:
--   1. Connected to SubagentOrchestrator domain definitions (§2)
--   2. Defined agent communication protocol with async message passing (§1)
--   3. Defined DeadlockFreedom / StarvationFreedom as Prop predicates (§3)
--   4. Proved researchPipelineIsAcyclic (§3)
--   5. Completed all proof placeholders

end Semantics.AgenticOrchestration