#!/usr/bin/env python3
"""
η(χ) Field Efficiency Priority Alert — Targeted P0 Directive

Issues a specific P0 CRITICAL alert requiring the swarm to prove or refute
the Field Efficiency equation η(χ) — a child equation of Φ_universal.
"""

import sys
import json
import sqlite3
from datetime import datetime, timezone
from pathlib import Path
from typing import Dict, Any

sys.path.insert(0, str(Path(__file__).parent.parent.parent / "4-Infrastructure" / "infra"))
from lean_unified_shim import SwarmAPISystem


def issue_eta_alert() -> Dict[str, Any]:
    """
    Issue P0 CRITICAL alert specifically for η(χ) verification.
    This equation depends on Φ_universal being proven first.
    """
    
    api = SwarmAPISystem()
    timestamp = datetime.now(timezone.utc).isoformat()
    
    alert_content = """
╔══════════════════════════════════════════════════════════════════════════════╗
║                   η(χ) FIELD EFFICIENCY P0 CRITICAL ALERT                    ║
╚══════════════════════════════════════════════════════════════════════════════╝

TARGET: EQUATION #0.1 — η(χ) Field Efficiency (Child of Φ_universal)
STATUS: 🚧 P0 CRITICAL — CONJECTURE (DEPENDENT ON #0)
DATE: {timestamp}
DEPENDENCY: EQUATION #0 (Φ_universal) must be proven first

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
THE EQUATION
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

                   I · ln N
    η(χ) = ───────────────────────────
           H(χ) + αK(χ) + β∫₀ᵀ S(χ,t)dt

Where:
  • I = information content (constructive)
  • ln N = log of node cardinality
  • H(χ) = Hamiltonian/Energy at state χ (destructive)
  • K(χ) = Curvature term at state χ (geometric penalty)
  • S(χ,t) = Entropy density over time (temporal accumulation)
  • α, β = weighting coefficients
  • T = time horizon

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
CRITICAL FINDINGS
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

⚠ MISSING: This equation was NOT in MATH_MODEL_MAP-42126.md
⚠ DEPENDENCY: Cannot be proven until Φ_universal (EQUATION #0) is proven
⚠ APPLICATION: Blocks Field Solver and Compression Optimization
⚠ STATUS: Documented but UNPROVEN (conjecture status)

This is a SPECIALIZED FORM of Φ_universal for single-state efficiency measurement.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
PARENT-CHILD RELATIONSHIP
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Φ_universal (EQUATION #0) = Σ χ η(χ) · cost(χ)
         ↑
         └─► η(χ) (EQUATION #0.1) = I·lnN / cost(χ)

Where cost(χ) = H(χ) + αK(χ) + β∫₀ᵀ S(χ,t)dt

SEQUENCE REQUIREMENT:
  1. Prove Φ_universal first (EQUATION #0)
  2. Then derive η(χ) as specialization
  3. Finally prove bounds: 0 ≤ η(χ) ≤ 1

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
REQUIRED PROOFS (Triumvirate Assignment)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

BUILDER → manifold_reg (ADD clock)
────────────────────────────────────
□ Implement fieldEfficiency in Lean (Q16_16)
□ Define structure FieldEfficiencyParams
□ Implement temporal integral ∫₀ᵀ S(χ,t)dt in Q16_16
□ Handle division-by-zero edge cases

WARDEN → stark_trace & warden_valid (SUBTRACT clock)
──────────────────────────────────────────────────────
□ Prove 0 ≤ η(χ) ≤ 1 (bounded efficiency)
□ Verify convexity properties
□ Check behavior at extrema (χ→0, χ→∞, T→0, T→∞)
□ Validate dimensional consistency
□ Confirm numerical stability in Q16_16

JUDGE → heatsink_halt (PAUSE clock)
───────────────────────────────────
□ Adjudicate dependency on Φ_universal proof
□ Verify parent-child relationship formally
□ Confirm no 'sorry' in committed code
□ Approve or reject for Field Solver deployment

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
DEPENDENT SYSTEMS (Blocked Pending Proof)
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

PRIORITY 1: Field Solver (RISC-V opcodes)
  → Optimization target = maximize η(χ)
  → Cannot optimize without proven bounds

PRIORITY 2: Compression Mechanics
  → Efficiency metric = achieved η(χ)
  → Cannot compare codecs without normalized metric

PRIORITY 3: Swarm Competition Scoring
  → Agent score = η(agent_state)
  → Cannot rank agents without valid metric

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
LEAN SPECIFICATION TEMPLATE
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

namespace Semantics.FieldEfficiency

open Semantics.Q16_16

structure FieldEfficiencyParams where
  I : Q16_16          -- Information content
  N : Nat             -- Node cardinality
  H : Q16_16          -- Hamiltonian/Energy
  K : Q16_16          -- Curvature term
  S : Nat → Q16_16    -- Entropy density (discretized)
  alpha : Q16_16      -- Curvature weight
  beta : Q16_16       -- Entropy weight
  T : Nat             -- Time horizon (discretized)

def integrateEntropy 
  (S : Nat → Q16_16) (T : Nat) : Q16_16 :=
  -- Discrete approximation of ∫₀ᵀ S(χ,t)dt
  ∑ t in range T, S t

def fieldEfficiency (params : FieldEfficiencyParams) : Option Q16_16 :=
  let numerator := params.I * lnQ16 params.N
  let integral := integrateEntropy params.S params.T
  let denominator := params.H + params.alpha*params.K + params.beta*integral
  
  -- Handle division by zero
  if denominator = 0 then none
  else some (numerator / denominator)

-- Required proofs (after Φ_universal is proven)
theorem fieldEfficiencyBounded (params : FieldEfficiencyParams)
  (h : fieldEfficiency params ≠ none)
  (h_cost : params.H + params.alpha*params.K + 
            params.beta*(integrateEntropy params.S params.T) > 0)
  (h_info : params.I * lnQ16 params.N ≤ 
            params.H + params.alpha*params.K + 
            params.beta*(integrateEntropy params.S params.T)) :
  fieldEfficiency params ≤ some 1 := by
  sorry -- BLOCKED: Requires Φ_universal proof first

theorem fieldEfficiencyNonNegative (params : FieldEfficiencyParams)
  (h : fieldEfficiency params ≠ none) :
  fieldEfficiency params ≥ some 0 := by
  sorry -- BLOCKED: Requires Φ_universal proof first

-- Correspondence with parent equation
theorem fieldEfficiencyCorrespondsToUniversal 
  (univ : UniversalFieldParams) (chi : State)
  (eff : FieldEfficiencyParams)
  (h_equiv : eff.I * lnQ16 eff.N = Φ_constructive univ chi)
  (h_cost : eff.H + eff.alpha*eff.K + 
            eff.beta*(integrateEntropy eff.S eff.T) = Φ_destructive univ chi) :
  fieldEfficiency eff = etaFromUniversal (phiUniversal univ) chi := by
  sorry -- BLOCKED: Requires phiUniversal definition

end Semantics.FieldEfficiency

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
BLOCKED STATUS
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

This alert is DEPENDENT on EQUATION #0 (Φ_universal).

SWARM PROTOCOL:
  1. Complete Φ_universal proof (EQUATION #0)
  2. Then unlock η(χ) proofs (EQUATION #0.1)
  3. Both must pass Triumvirate consensus

DO NOT attempt η(χ) proofs until Φ_universal is complete.
The dependency chain must be respected.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

SWARM DIRECTIVE: PROVE PARENT FIRST. THEN PROVE CHILD.

η(χ) is the efficiency lens through which all optimization occurs.
Without it, the Field Solver, Compression, and Swarm Scoring are ad-hoc.
""".format(timestamp=timestamp)

    # Store in priority_alerts table
    if api.conn:
        cursor = api.conn.cursor()
        
        cursor.execute("""
            CREATE TABLE IF NOT EXISTS priority_alerts (
                entity_id TEXT PRIMARY KEY,
                subject TEXT,
                name TEXT,
                statement TEXT,
                proof_status TEXT,
                formal_status TEXT,
                priority TEXT,
                requires_immediate_action BOOLEAN,
                depends_on TEXT,
                created_at TEXT
            )
        """)
        
        cursor.execute("""
            INSERT OR REPLACE INTO priority_alerts 
            (entity_id, subject, name, statement, proof_status, formal_status,
             priority, requires_immediate_action, depends_on, created_at)
            VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?, ?)
        """, (
            f'ETA_EFFICIENCY_P0_{timestamp.replace(":", "_")}',
            'critical_audit',
            '[P0] η(χ) Field Efficiency Verification Required',
            alert_content,
            'conjecture',
            'blocked_by_dependency',
            'P0',
            True,
            'PHI_UNIVERSAL_P0',  # Depends on Φ_universal
            timestamp
        ))
        
        api.conn.commit()
        
        return {
            'success': True,
            'alert_type': 'η(χ) Field Efficiency P0 Critical',
            'timestamp': timestamp,
            'equation': 'η(χ) = I·lnN / (H(χ) + αK(χ) + β∫₀ᵀ S(χ,t)dt)',
            'depends_on': 'EQUATION #0 (Φ_universal)',
            'status': 'BLOCKED_PENDING_PARENT_PROOF'
        }
    else:
        return {
            'success': False,
            'error': 'Database not connected',
            'alert_printed': True
        }


def main():
    print("="*70)
    print("η(χ) FIELD EFFICIENCY TARGETED ALERT")
    print("="*70)
    print()
    
    result = issue_eta_alert()
    
    if result['success']:
        print(f"[✓] {result['alert_type']}")
        print(f"    Timestamp: {result['timestamp']}")
        print(f"    Equation: {result['equation']}")
        print(f"    Status: {result['status']}")
        print(f"    Depends on: {result['depends_on']}")
        print()
        print("="*70)
        print("The swarm has been notified of η(χ) verification requirement.")
        print()
        print("⚠ IMPORTANT: This is BLOCKED until Φ_universal is proven.")
        print("   Sequence: #0 (Φ_universal) → #0.1 (η(χ))")
        print("="*70)
    else:
        print(f"[✗] Error: {result.get('error', 'Unknown')}")
        if result.get('alert_printed'):
            print("Alert content logged to console.")
    
    return result


if __name__ == '__main__':
    main()