#!/usr/bin/env python3
"""
Φ_universal Priority Alert — Targeted P0 Directive

Issues a specific P0 CRITICAL alert requiring the swarm to prove or refute
the Universal Field equation (Φ_universal) — the foundational equation
that was MISSING from the system.
"""

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

sys.path.insert(0, '/home/allaun/Documents/Research Stack/tools')
from lean_unified_shim import SwarmAPISystem


def issue_phi_universal_alert() -> Dict[str, Any]:
    """
    Issue P0 CRITICAL alert specifically for Φ_universal verification.
    This is the targeted follow-up to the general math foundation audit.
    """
    
    api = SwarmAPISystem()
    timestamp = datetime.now(timezone.utc).isoformat()
    
    alert_content = """
╔══════════════════════════════════════════════════════════════════════════════╗
║                    Φ_UNIVERSAL P0 CRITICAL ALERT                             ║
╚══════════════════════════════════════════════════════════════════════════════╝

TARGET: EQUATION #0 — Φ_universal (Universal Field)
STATUS: 🚧 P0 CRITICAL — CONJECTURE (UNPROVEN)
DATE: {timestamp}

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

    Φ_universal = Σᵢ wᵢ·lnNᵢ - Σⱼ vⱼ·lnNⱼ  [CORRECTED: Cost form matches Landauer]
                = Σᵢ wᵢ·hᵢ/lnNᵢ - Σⱼ vⱼ·pⱼ/lnNⱼ  [Efficiency form]
    
    NOTE: Previous formulation wᵢ/lnNᵢ has been CORRECTED to wᵢ·lnNᵢ
    Landauer: E_min = k_B T ln N — Cost increases with alphabet size N

Where:
  • wᵢ = informational weight (constructive terms)
  • vⱼ = entropic weight (destructive terms)  
  • Nᵢ, Nⱼ = node cardinalities (state space sizes)
  • hᵢ = merit coefficient = qualityᵢ/lnNᵢ (efficiency per unit cost)
  • pⱼ = penalty coefficient = disorderⱼ/lnNⱼ (inefficiency measure)
  
  CORRECTION: hᵢ = 1/(lnNᵢ)² was mathematically inconsistent with Landauer

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

⚠ MISSING: This equation was NOT in MATH_MODEL_MAP-42126.md
⚠ FOUNDATION GAP: All 88+ Lean modules depend on this being correct
⚠ STATUS: Documented but UNPROVEN (conjecture status)

The Principal Investigator has identified this as a potential deep fault
in the mathematical foundations. The swarm must PROVE or REFUTE.

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

BUILDER → manifold_reg (ADD clock)
────────────────────────────────────
□ Implement phiUniversal in Lean (Q16_16 fixed-point)
□ Create structure UniversalField with all components
□ Define both forms: reciprocal-log and weighted-log

WARDEN → stark_trace & warden_valid (SUBTRACT clock)
──────────────────────────────────────────────────────
□ Prove equivalence: phiUniversalReciprocal = phiUniversalWeighted
□ Verify convergence for all N ≥ 2
□ Check numerical stability in Q16_16
□ Validate boundary conditions (N→2, N→∞)

JUDGE → heatsink_halt (PAUSE clock)
───────────────────────────────────
□ Adjudicate proof completeness
□ Verify no 'sorry' remains in committed code
□ Confirm cross-consistency with Φ_genomic
□ Approve or reject for system-wide deployment

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

• Genomic Compression (Φ_genomic specialization)
• Cognitive Load (L_I, L_E, L_G)
• AVMR Framework (field equations)
• Compression Mechanics
• Entropy-Based Routing
• All 88+ OTOM modules

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

namespace Semantics.UniversalField

open Semantics.Q16_16

structure UniversalFieldParams where
  n m : Nat  -- Dimensions
  w : Fin n → Q16_16  -- Informational weights
  v : Fin m → Q16_16  -- Entropic weights
  N : Fin n → Nat     -- Info node cardinalities
  M : Fin m → Nat     -- Entropy node cardinalities
  h : Fin n → Q16_16  -- Harmonic coefficients
  p : Fin m → Q16_16  -- Penalty coefficients

def phiUniversalReciprocal (params : UniversalFieldParams) : Q16_16 :=
  -- Σᵢ wᵢ/lnNᵢ + Σⱼ vⱼ/lnNⱼ
  sorry

def phiUniversalWeighted (params : UniversalFieldParams) : Q16_16 :=
  -- Σᵢ wᵢ lnNᵢ hᵢ - Σⱼ vⱼ lnNⱼ pⱼ
  sorry

theorem phiUniversalEquivalence (params : UniversalFieldParams) :
  phiUniversalReciprocal params = phiUniversalWeighted params := by
  sorry

theorem phiUniversalNormalization (params : UniversalFieldParams)
  (hw : ∑ i, params.w i = 1) (hv : ∑ j, params.v j = 1) :
  phiUniversalReciprocal params ≤ 1 := by
  sorry

end Semantics.UniversalField

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
SUCCESS CRITERIA
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

✓ All four theorems proven with complete formal proofs
✓ Q16_16 implementation verified numerically stable
✓ Cross-reference with Φ_genomic validated
✓ No 'sorry' in committed code
✓ Triumvirate consensus reached (Builder ✓ Warden ✓ Judge ✓)

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

SWARM DIRECTIVE: PROVE OR REFUTE. NO INTERMEDIATE STATE ACCEPTABLE.

The mathematical integrity of the entire OTOM system depends on this.
""".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,
                created_at TEXT
            )
        """)
        
        cursor.execute("""
            INSERT OR REPLACE INTO priority_alerts 
            (entity_id, subject, name, statement, proof_status, formal_status,
             priority, requires_immediate_action, created_at)
            VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?)
        """, (
            f'PHI_UNIVERSAL_P0_{timestamp.replace(":", "_")}',
            'critical_audit',
            '[P0] Φ_universal Verification Required',
            alert_content,
            'conjecture',
            'needs_formalization',
            'P0',
            True,
            timestamp
        ))
        
        api.conn.commit()
        
        return {
            'success': True,
            'alert_type': 'Φ_universal P0 Critical',
            'timestamp': timestamp,
            'equation': 'Φ_universal = Σᵢ wᵢ/lnNᵢ + Σⱼ vⱼ/lnNⱼ',
            'status': 'ALERT_INJECTED_INTO_SWARM'
        }
    else:
        return {
            'success': False,
            'error': 'Database not connected',
            'alert_printed': True
        }


def main():
    print("="*70)
    print("Φ_UNIVERSAL TARGETED ALERT")
    print("="*70)
    print()
    
    result = issue_phi_universal_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()
        print("="*70)
        print("The swarm has been notified of the specific Φ_universal")
        print("verification requirement. Triumvirate is activated.")
        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()