mirror of
https://github.com/allaunthefox/Research-Stack.git
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291 lines
13 KiB
Python
291 lines
13 KiB
Python
#!/usr/bin/env python3
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"""
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η(χ) Field Efficiency Priority Alert — Targeted P0 Directive
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Issues a specific P0 CRITICAL alert requiring the swarm to prove or refute
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the Field Efficiency equation η(χ) — a child equation of Φ_universal.
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"""
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import sys
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import json
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import sqlite3
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from datetime import datetime, timezone
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from pathlib import Path
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from typing import Dict, Any
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sys.path.insert(0, str(Path(__file__).parent.parent.parent / "4-Infrastructure" / "infra"))
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from lean_unified_shim import SwarmAPISystem
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def issue_eta_alert() -> Dict[str, Any]:
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"""
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Issue P0 CRITICAL alert specifically for η(χ) verification.
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This equation depends on Φ_universal being proven first.
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"""
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api = SwarmAPISystem()
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timestamp = datetime.now(timezone.utc).isoformat()
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alert_content = """
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╔══════════════════════════════════════════════════════════════════════════════╗
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║ η(χ) FIELD EFFICIENCY P0 CRITICAL ALERT ║
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╚══════════════════════════════════════════════════════════════════════════════╝
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TARGET: EQUATION #0.1 — η(χ) Field Efficiency (Child of Φ_universal)
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STATUS: 🚧 P0 CRITICAL — CONJECTURE (DEPENDENT ON #0)
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DATE: {timestamp}
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DEPENDENCY: EQUATION #0 (Φ_universal) must be proven first
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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THE EQUATION
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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I · ln N
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η(χ) = ───────────────────────────
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H(χ) + αK(χ) + β∫₀ᵀ S(χ,t)dt
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Where:
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• I = information content (constructive)
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• ln N = log of node cardinality
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• H(χ) = Hamiltonian/Energy at state χ (destructive)
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• K(χ) = Curvature term at state χ (geometric penalty)
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• S(χ,t) = Entropy density over time (temporal accumulation)
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• α, β = weighting coefficients
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• T = time horizon
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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CRITICAL FINDINGS
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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⚠ MISSING: This equation was NOT in MATH_MODEL_MAP-42126.md
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⚠ DEPENDENCY: Cannot be proven until Φ_universal (EQUATION #0) is proven
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⚠ APPLICATION: Blocks Field Solver and Compression Optimization
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⚠ STATUS: Documented but UNPROVEN (conjecture status)
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This is a SPECIALIZED FORM of Φ_universal for single-state efficiency measurement.
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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PARENT-CHILD RELATIONSHIP
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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Φ_universal (EQUATION #0) = Σ χ η(χ) · cost(χ)
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↑
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└─► η(χ) (EQUATION #0.1) = I·lnN / cost(χ)
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Where cost(χ) = H(χ) + αK(χ) + β∫₀ᵀ S(χ,t)dt
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SEQUENCE REQUIREMENT:
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1. Prove Φ_universal first (EQUATION #0)
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2. Then derive η(χ) as specialization
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3. Finally prove bounds: 0 ≤ η(χ) ≤ 1
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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REQUIRED PROOFS (Triumvirate Assignment)
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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BUILDER → manifold_reg (ADD clock)
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────────────────────────────────────
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□ Implement fieldEfficiency in Lean (Q16_16)
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□ Define structure FieldEfficiencyParams
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□ Implement temporal integral ∫₀ᵀ S(χ,t)dt in Q16_16
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□ Handle division-by-zero edge cases
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WARDEN → stark_trace & warden_valid (SUBTRACT clock)
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──────────────────────────────────────────────────────
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□ Prove 0 ≤ η(χ) ≤ 1 (bounded efficiency)
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□ Verify convexity properties
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□ Check behavior at extrema (χ→0, χ→∞, T→0, T→∞)
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□ Validate dimensional consistency
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□ Confirm numerical stability in Q16_16
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JUDGE → heatsink_halt (PAUSE clock)
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───────────────────────────────────
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□ Adjudicate dependency on Φ_universal proof
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□ Verify parent-child relationship formally
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□ Confirm no 'sorry' in committed code
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□ Approve or reject for Field Solver deployment
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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DEPENDENT SYSTEMS (Blocked Pending Proof)
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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PRIORITY 1: Field Solver (RISC-V opcodes)
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→ Optimization target = maximize η(χ)
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→ Cannot optimize without proven bounds
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PRIORITY 2: Compression Mechanics
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→ Efficiency metric = achieved η(χ)
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→ Cannot compare codecs without normalized metric
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PRIORITY 3: Swarm Competition Scoring
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→ Agent score = η(agent_state)
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→ Cannot rank agents without valid metric
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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LEAN SPECIFICATION TEMPLATE
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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namespace Semantics.FieldEfficiency
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open Semantics.Q16_16
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structure FieldEfficiencyParams where
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I : Q16_16 -- Information content
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N : Nat -- Node cardinality
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H : Q16_16 -- Hamiltonian/Energy
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K : Q16_16 -- Curvature term
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S : Nat → Q16_16 -- Entropy density (discretized)
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alpha : Q16_16 -- Curvature weight
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beta : Q16_16 -- Entropy weight
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T : Nat -- Time horizon (discretized)
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def integrateEntropy
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(S : Nat → Q16_16) (T : Nat) : Q16_16 :=
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-- Discrete approximation of ∫₀ᵀ S(χ,t)dt
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∑ t in range T, S t
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def fieldEfficiency (params : FieldEfficiencyParams) : Option Q16_16 :=
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let numerator := params.I * lnQ16 params.N
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let integral := integrateEntropy params.S params.T
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let denominator := params.H + params.alpha*params.K + params.beta*integral
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-- Handle division by zero
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if denominator = 0 then none
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else some (numerator / denominator)
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-- Required proofs (after Φ_universal is proven)
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theorem fieldEfficiencyBounded (params : FieldEfficiencyParams)
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(h : fieldEfficiency params ≠ none)
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(h_cost : params.H + params.alpha*params.K +
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params.beta*(integrateEntropy params.S params.T) > 0)
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(h_info : params.I * lnQ16 params.N ≤
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params.H + params.alpha*params.K +
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params.beta*(integrateEntropy params.S params.T)) :
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fieldEfficiency params ≤ some 1 := by
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sorry -- BLOCKED: Requires Φ_universal proof first
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theorem fieldEfficiencyNonNegative (params : FieldEfficiencyParams)
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(h : fieldEfficiency params ≠ none) :
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fieldEfficiency params ≥ some 0 := by
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sorry -- BLOCKED: Requires Φ_universal proof first
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-- Correspondence with parent equation
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theorem fieldEfficiencyCorrespondsToUniversal
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(univ : UniversalFieldParams) (chi : State)
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(eff : FieldEfficiencyParams)
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(h_equiv : eff.I * lnQ16 eff.N = Φ_constructive univ chi)
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(h_cost : eff.H + eff.alpha*eff.K +
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eff.beta*(integrateEntropy eff.S eff.T) = Φ_destructive univ chi) :
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fieldEfficiency eff = etaFromUniversal (phiUniversal univ) chi := by
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sorry -- BLOCKED: Requires phiUniversal definition
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end Semantics.FieldEfficiency
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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BLOCKED STATUS
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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This alert is DEPENDENT on EQUATION #0 (Φ_universal).
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SWARM PROTOCOL:
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1. Complete Φ_universal proof (EQUATION #0)
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2. Then unlock η(χ) proofs (EQUATION #0.1)
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3. Both must pass Triumvirate consensus
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DO NOT attempt η(χ) proofs until Φ_universal is complete.
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The dependency chain must be respected.
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━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
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SWARM DIRECTIVE: PROVE PARENT FIRST. THEN PROVE CHILD.
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η(χ) is the efficiency lens through which all optimization occurs.
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Without it, the Field Solver, Compression, and Swarm Scoring are ad-hoc.
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""".format(timestamp=timestamp)
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# Store in priority_alerts table
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if api.conn:
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cursor = api.conn.cursor()
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cursor.execute("""
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CREATE TABLE IF NOT EXISTS priority_alerts (
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entity_id TEXT PRIMARY KEY,
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subject TEXT,
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name TEXT,
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statement TEXT,
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proof_status TEXT,
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formal_status TEXT,
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priority TEXT,
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requires_immediate_action BOOLEAN,
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depends_on TEXT,
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created_at TEXT
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)
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""")
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cursor.execute("""
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INSERT OR REPLACE INTO priority_alerts
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(entity_id, subject, name, statement, proof_status, formal_status,
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priority, requires_immediate_action, depends_on, created_at)
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VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?, ?)
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""", (
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f'ETA_EFFICIENCY_P0_{timestamp.replace(":", "_")}',
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'critical_audit',
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'[P0] η(χ) Field Efficiency Verification Required',
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alert_content,
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'conjecture',
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'blocked_by_dependency',
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'P0',
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True,
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'PHI_UNIVERSAL_P0', # Depends on Φ_universal
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timestamp
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))
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api.conn.commit()
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return {
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'success': True,
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'alert_type': 'η(χ) Field Efficiency P0 Critical',
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'timestamp': timestamp,
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'equation': 'η(χ) = I·lnN / (H(χ) + αK(χ) + β∫₀ᵀ S(χ,t)dt)',
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'depends_on': 'EQUATION #0 (Φ_universal)',
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'status': 'BLOCKED_PENDING_PARENT_PROOF'
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}
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else:
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return {
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'success': False,
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'error': 'Database not connected',
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'alert_printed': True
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}
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def main():
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print("="*70)
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print("η(χ) FIELD EFFICIENCY TARGETED ALERT")
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print("="*70)
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print()
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result = issue_eta_alert()
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if result['success']:
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print(f"[✓] {result['alert_type']}")
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print(f" Timestamp: {result['timestamp']}")
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print(f" Equation: {result['equation']}")
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print(f" Status: {result['status']}")
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print(f" Depends on: {result['depends_on']}")
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print()
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print("="*70)
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print("The swarm has been notified of η(χ) verification requirement.")
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print()
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print("⚠ IMPORTANT: This is BLOCKED until Φ_universal is proven.")
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print(" Sequence: #0 (Φ_universal) → #0.1 (η(χ))")
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print("="*70)
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else:
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print(f"[✗] Error: {result.get('error', 'Unknown')}")
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if result.get('alert_printed'):
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print("Alert content logged to console.")
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return result
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if __name__ == '__main__':
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main()
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