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#!/usr/bin/env node
// FORMALIZATION ATTACK: Multi-Language Adversarial Review
// Challenge: Formalize engine in 4 languages; Adversary finds counter-examples
//
// Contenders:
//   Formalizer: Nova Parr / multi-language formalization
//   Attacker: Palymis / logical attack & counter-examples
//
// Phase 1: Formalize in PVS, Higher-Order Logic, Beluga, Mizar (ZERO sorry)
// Phase 2: Adversarial attack (find bugs, weak points, counter-examples)
// Phase 3: Dual 12-page papers (max 20 theorems, zero sorry wins)
//

import { BedrockRuntimeClient, ConverseCommand } from "@aws-sdk/client-bedrock-runtime";
import { writeFileSync, mkdirSync } from "fs";

const client = new BedrockRuntimeClient({ region: "us-east-1" });

const CONTESTANTS = [
  { id: "nvidia.nemotron-nano-3-30b", name: "Nova Parr (Formalizer)", shortName: "NOVA", role: "formalize" },
  { id: "mistral.mistral-large-3-675b-instruct", name: "Palymis (Attacker)", shortName: "PALYMIS", role: "attack" },
];

// ═══════════════════════════════════════════════════════════════════════
// ENGINE SPEC (from Semifinal + applications doc)
// ═══════════════════════════════════════════════════════════════════════

const ENGINE_SPEC = `
# NON-LINEAR BLACK HOLE THERMAL ENGINE: FORMALIZATION TARGETS

## Summary
A hybrid quantum-classical system for constraint satisfaction (3-SAT) with:
- Classical ODE (4D non-linear, implicit midpoint Newton-Raphson)
- Quantum subsystem (Hayden-Preskill fast scrambler + phase variance coupling)
- Lindblad dissipation at entropy floor S_min = 0.001
- Conditional non-reducibility to primitive recursive functions

## Core Theorems (Target: 20 total across 4 languages)

1. **Logarithmic Singularity Elimination**
   Transform S(t) = S_min · e^{u(t)} eliminates pole at S=0
   Proof: u unbounded ⟹ S > 0 for all finite t

2. **Implicit Midpoint Stability**
   Scheme x_{n+1} = x_n + Δt F((x_n + x_{n+1})/2) is A-stable
   Proof: Dahlquist criterion + backward Euler equivalence

3. **Quantum Phase Variance Bound**
   σ²_θ = Var_k[arg ⟨ψ|P_k|ψ⟩] ∈ [0, π²]
   Proof: Hermitian projectors + Born rule normalization

4. **Lindblad Trace Preservation**
   Jump operators L_k = √Γ P_k preserve Tr(ρ) = 1
   Proof: Kraus representation + Lindblad master eq.

5. **3-SAT Reduction Completeness**
   Engine + Oracle ⟹ NP-complete solver
   Proof: Clause projectors encode all Boolean constraints

6. **BQP Oracle Requirement**
   Phase variance extraction requires BQP oracle (not PR)
   Proof: Hadamard test + phase estimation lower bound

7. **Convergence to Ground State**
   If ∃ satisfying assignment, engine reaches E → 0 in poly(n) steps
   Proof: Energy dissipation + spectral gap argument

8. **Non-Reducibility Conditional**
   (P ≠ NP) ⟹ (Engine ∉ PR)
   Proof: Contrapositive + Church-Turing thesis

9. **Hayden-Preskill Scrambling Time**
   Information recovery at t = O(log n), Page curve follows
   Proof: OTOC decay + unitary scrambler bound

10. **Singular Perturbation Analysis**
    Implicit midpoint + Lindblad near S_min form singular system
    Proof: γ(S) = Γ₀/S² diverges at S_min

## Proof Requirements (ZERO axioms, NO sorry, complete proofs)

For each theorem:
- Formal type signature in target language
- Complete proof term (no holes)
- All lemmas inlined or proved
- Explicit use of axiomatic foundations only

## Known Challenges (Typical Attack Points)

1. **Phase Variance Well-Definedness**
   σ²_θ = Var_k[arg ⟨ψ|P_k|ψ⟩] — is arg continuous?
   Attack: Find state where phase is discontinuous

2. **Implicit Midpoint Existence**
   Does x_{n+1} always have unique solution?
   Attack: Construct force field where Newton-Raphson fails

3. **Hayden-Preskill Coupling**
   Does phase variance feedback stabilize scrambling?
   Attack: Show feedback destabilizes for some parameters

4. **Lindblad Collapse Semantics**
   When measured, does dissipation reset coherence?
   Attack: Construct trajectory where measurement fails

5. **Ground State Assumption**
   Does EVERY 3-SAT instance have unique ground state?
   Attack: Generate instance with multiple ground states

6. **Primitive Recursive Boundary**
   Is BQP oracle truly non-primitive-recursive?
   Attack: Show via Ackermann function argument

7. **Parameter Sensitivity**
   Are theorems robust to κ, λ, η, Γ₀ perturbations?
   Attack: Vary parameters, find breakpoints

8. **Finite Precision**
   Do theorems hold with floating-point arithmetic?
   Attack: Show accumulation of rounding errors

## Attack Scoring Criteria

High-value counter-example:
- Breaks a claimed theorem (contradiction to spec)
- Constructive (explicit failing instance)
- Non-obvious (not immediately from definition)
- Severity: HIGH if breaks core theorems 1-5, MEDIUM if 6-10, LOW if minor

Example HIGH attack:
  "Theorem 3 (phase variance bound) assumes projectors are orthogonal.
   But in entangled states ⟨ψ|P_i P_j|ψ⟩ ≠ 0 for i ≠ j.
   Counter-example: [explicit state construction]"
`;

// ═══════════════════════════════════════════════════════════════════════
// PHASE 1: Multi-Language Formalization (Formalizer only)
// ═══════════════════════════════════════════════════════════════════════

const PHASE1_PROMPT = `You are formalizing the Non-Linear Black Hole Thermal Engine in FOUR proof languages.

${ENGINE_SPEC}

YOUR TASK: Formalize in PVS, Higher-Order Logic, Beluga, and Mizar.

CRITICAL RULES:
- CHOOSE the 4 languages (one per section)
- ZERO axioms, ZERO sorry, ZERO postulate, ZERO admit
- All 10 theorems (or max 5 per language) with complete proofs
- NO placeholder proofs — full proof terms
- Explicit lemmas for all mathematical operations (exponential, logarithm, variance, etc.)

STRUCTURE (ONE per language):

## SECTION 1: PVS (Higher-Order Logic + Dependent Types)
- Theory name: BlackHoleEngine
- Types: entropy, amplitude, phase_variance (with proof invariants)
- Theorems 1-3: Singularity, stability, phase variance bounds
- Proof style: Tactic-based, using PVS library theorems

## SECTION 2: Higher-Order Logic (Isabelle/HOL, Coq, or Lean 4)
- Define force system from first principles
- Theorems 4-5: Lindblad trace, 3-SAT reduction
- Proof style: Term-mode proofs, explicit lambda

## SECTION 3: Beluga (Dependent Type Theory + Proof Terms)
- Encoding: Hilbert space as dependent type family
- Theorems 6-7: BQP oracle, ground state convergence
- Proof style: Full proof terms with explicit type checking

## SECTION 4: Mizar (Declarative, Closest to Math Textbook)
- Classical mathematical style
- Theorems 8-10: Non-reducibility, scrambling, singular perturbation
- Proof style: Environment declarations, lemmas, QED

SCORING: Max 10 theorems per language × 4 = 40 possible.
          Report: THEOREMS PROVEN: N (counted across all 4)

OUTPUT: Four complete, standalone code blocks. Language name first line as comment.
All proofs complete. Zero holes.`;

// ═══════════════════════════════════════════════════════════════════════
// PHASE 2: Adversarial Attack (Attacker only)
// ═══════════════════════════════════════════════════════════════════════

const PHASE2_PROMPT = `You are adversarially attacking the Black Hole Engine formalization.

CONTEXT:
The formalizer just submitted proofs in 4 languages (PVS, HOL, Beluga, Mizar).

YOUR TASK: Find bugs, counter-examples, weak points in the formalization.

${ENGINE_SPEC}

ATTACK STRATEGY (Choose 3-5 points of maximum impact):

1. **Definitional Gaps**
   - Is phase variance σ²_θ = Var[arg ⟨ψ|P_k|ψ⟩] well-defined?
   - Is arg continuous on complex projective space?
   - What happens when all ⟨ψ|P_k|ψ⟩ have identical phase?

2. **Mathematical Inconsistencies**
   - Implicit midpoint: does Newton-Raphson always converge for this force field?
   - Singular perturbation: at S=S_min, does dissipation rate diverge safely?
   - Ground state assumption: can 3-SAT have degenerate ground states?

3. **Proof Soundness**
   - Do they use any unstated axioms (choice, LEM, AC)?
   - Are type signatures correct (do projectors actually preserve norm)?
   - Does Hayden-Preskill coupling destabilize for adversarial parameters?

4. **Parameter Sensitivity**
   - Vary κ, λ, η, Γ₀. Do theorems still hold?
   - Find values where implicit midpoint fails.
   - Show where phase variance becomes unbounded.

5. **Computational Feasibility**
   - Can this actually be implemented in finite precision?
   - Do numerical errors accumulate catastrophically?
   - Show a 3-SAT instance where the engine fails.

HIGH-VALUE ATTACKS (Worth 50+ points each):
  - **Critical theorem broken**: Find explicit contradiction
  - **Hidden axiom dependency**: Show proof requires unproven lemma
  - **Parameter trap**: Formalization works for all params EXCEPT [specific set]
  - **Type error**: Projector type doesn't match expected signature
  - **Non-constructivity**: Proof is non-constructive (invoices excluded middle)

OUTPUT:
  1. **Counter-Example 1** (high severity): [Explicit construction]
     Theorem broken: [Theorem N]
     Reason: [Why it fails]

  2. **Counter-Example 2** (medium severity): [...]

  3. **Counter-Example 3** (low severity): [...]

  4. **Weak Point Summary**: [Which theorems are strongest, which are fragile?]

  5. **Suggestions for Fix**: [How could formalizer harden proofs?]

SCORING: HIGH attack = 30pts, MEDIUM = 15pts, LOW = 5pts
         Each must have explicit construction, not just critique`;

// ═══════════════════════════════════════════════════════════════════════
// PHASE 3: Dual 12-Page Papers + Counter-Response
// ═══════════════════════════════════════════════════════════════════════

const PHASE3_PROMPT = `Write a 12-page paper defending or attacking the Black Hole Engine formalization.

PAPER 1 (Formalizer): "Formalization and Soundness of the Non-Linear Black Hole Engine"
- Sections:
  1. Abstract (formalization approach, languages chosen, key theorems)
  2. Introduction (why multi-language approach, coverage)
  3. PVS Formalization (3-4 pages: language choice, theorem statements, proof strategy)
  4. Higher-Order Logic (3-4 pages: dependent types, quantifier handling)
  5. Beluga (2-3 pages: proof terms, implicit arguments)
  6. Mizar (2-3 pages: declarative style, automation)
  7. Proof Soundness (1-2 pages: why these proofs are complete)
  8. Limitations & Open Questions
  9. Conclusion
  10. References

PAPER 2 (Attacker): "Adversarial Analysis and Counter-Examples to the Engine Formalization"
- Sections:
  1. Abstract (counter-examples found, severity assessment)
  2. Introduction (attack surface, methodology)
  3. Definitional Issues (2 pages: gaps in σ²_θ, phase continuity)
  4. Mathematical Flaws (2-3 pages: implicit midpoint convergence, singular perturbation)
  5. Proof Gaps (2-3 pages: unstated axioms, type errors)
  6. Counter-Example 1: [Explicit construction] (1-2 pages)
  7. Counter-Example 2: [Explicit construction] (1-2 pages)
  8. Severity Assessment & Fix Recommendations (1-2 pages)
  9. Conclusion
  10. References

REQUIREMENTS BOTH PAPERS:
- MINIMUM 12 pages (assume ~2500 chars per page = 30,000 char minimum)
- LaTeX format
- MAX 20 theorems combined (count Formalizer + Attacker)
- ZERO sorry, ZERO postulate, ZERO axiom (reference only)
- If Attacker breaks theorem: explicitly state which one
- If Formalizer responds: explain why counter-example is invalid/flawed

SCORING:
- Formalizer: +10 pts per theorem (capped at 15), +5 per page (capped at 12), +20 if zero sorry
- Attacker: +15 per HIGH counter-example, +8 per MEDIUM, +2 per LOW, +10 if no false positives
- Winner: Total > opponent

OUTPUT: Two complete LaTeX papers. Adversarial pair-wise scoring.`;

async function invoke(modelId, prompt, maxTokens = 8192) {
  const start = Date.now();
  try {
    const cmd = new ConverseCommand({
      modelId,
      messages: [{ role: "user", content: [{ text: prompt }] }],
      inferenceConfig: { maxTokens, temperature: 0.1 },
    });
    const res = await client.send(cmd);
    const elapsed = Date.now() - start;
    const text = res.output?.message?.content?.[0]?.text || "";
    const usage = res.usage || {};
    const stopReason = res.stopReason || "unknown";
    return { text, elapsed, usage, stopReason, error: null };
  } catch (e) {
    return { text: "", elapsed: Date.now() - start, usage: {}, stopReason: "error", error: e.message };
  }
}

// ═══════════════════════════════════════════════════════════════════════
// SCORING
// ═══════════════════════════════════════════════════════════════════════

function scoreFormalization(text) {
  const languages = {
    pvs: /theory|pvs|axiom|lemma|theorem/i.test(text),
    hol: /isabelle|coq|lean|theorem|proof|fun/i.test(text),
    beluga: /rec |by|block|lookup|proof|term/i.test(text),
    mizar: /theorem|proof|qed|assume|by|means|per|cases/i.test(text),
  };

  const langCount = Object.values(languages).filter(Boolean).length;
  const theorems = (text.match(/theorem|Theorem|lemma|Lemma/gi) || []).length;
  const sorries = (text.match(/sorry|admit|postulate|undefined|axiom|assert|undefined/gi) || []).length;
  const lines = (text.match(/\n/g) || []).length;

  const selfReport = text.match(/THEOREMS?\s+PROVEN\s*:\s*(\d+)/i);
  const reported = selfReport ? parseInt(selfReport[1]) : 0;
  const effectiveTheorems = Math.max(theorems, reported);

  return {
    languages: langCount,
    theorems: effectiveTheorems,
    sorries,
    lines,
    score: langCount * 50 + effectiveTheorems * 100 - sorries * 200 + Math.min(30, lines / 5),
  };
}

function scoreAttack(text) {
  const highAttacks = (text.match(/high.{0,30}(counter|attack|break|contradiction)/gi) || []).length;
  const mediumAttacks = (text.match(/medium.{0,30}(counter|attack|weak|flaw)/gi) || []).length;
  const lowAttacks = (text.match(/low.{0,30}(issue|point)/gi) || []).length;

  const counterExamples = (text.match(/counter.example|counter-example|counterexample/gi) || []).length;
  const constructions = (text.match(/explicit|construct|instance|assignment|proof|show/gi) || []).length;

  const highScore = highAttacks * 30;
  const mediumScore = mediumAttacks * 15;
  const lowScore = lowAttacks * 5;
  const constructScore = Math.min(50, counterExamples * 5 + (constructions > 20 ? 20 : 0));

  return {
    highAttacks,
    mediumAttacks,
    lowAttacks,
    counterExamples,
    score: highScore + mediumScore + lowScore + constructScore,
  };
}

function scorePaper(text) {
  const sections = {
    abstract: /abstract/i.test(text),
    intro: /introduction|motivation/i.test(text),
    methods: /method|formalization|approach|attack/i.test(text),
    theorems: /theorem\s+\d|\\textbf\{Theorem/i.test(text),
    examples: /example|counter|construct/i.test(text),
    discussion: /discussion|limitation|fix/i.test(text),
    conclusion: /conclusion/i.test(text),
    refs: /reference|bibliography/i.test(text),
  };

  const sectionCount = Object.values(sections).filter(Boolean).length;
  const chars = text.length;
  const pages = Math.floor(chars / 2500);
  const theorems = (text.match(/Theorem\s+\d+/g) || []).length;
  const equations = (text.match(/\$[^$]+\$/g) || []).length;

  return {
    sections: sectionCount,
    pages,
    theorems,
    equations,
    score: sectionCount * 20 + Math.min(60, pages * 5) + theorems * 10 + equations * 2,
  };
}

async function runMatch() {
  const outDir = "C:\\Users\\jessi\\Desktop\\bobs control repo\\tournament\\formalization-attack";
  mkdirSync(outDir, { recursive: true });

  console.log("╔══════════════════════════════════════════════════════════════════╗");
  console.log("║  FORMALIZATION ATTACK: Nova Parr vs Palymis                   ║");
  console.log("║  Challenge: Multi-Language Formalization + Adversarial Review   ║");
  console.log("║  Phase 1: PVS + HOL + Beluga + Mizar (ZERO sorry)             ║");
  console.log("║  Phase 2: Adversarial Attack (find counter-examples)           ║");
  console.log("║  Phase 3: Dual 12-Page Papers (max 20 theorems total)         ║");
  console.log("║  WINNER: Best formalization rigor + best attack severity      ║");
  console.log("╚══════════════════════════════════════════════════════════════════╝\n");

  const allResults = {};

  // ── PHASE 1: Formalization (Nova only) ──
  console.log(`\n${"═".repeat(64)}`);
  console.log(`  PHASE 1: Multi-Language Formalization`);
  console.log(`${"═".repeat(64)}`);

  console.log(`\n  [FORMALIZER] Nova Parr...`);
  const r1 = await invoke(CONTESTANTS[0].id, PHASE1_PROMPT, 8192);
  if (r1.error) {
    console.log(`    ❌ ERROR: ${r1.error}`);
    allResults.nova = { phase1: null };
  } else {
    const s1 = scoreFormalization(r1.text);
    console.log(`    ${r1.elapsed}ms | out=${r1.usage.outputTokens||"?"} | languages:${s1.languages} theorems:${s1.theorems} sorries:${s1.sorries} | score:${s1.score}`);
    writeFileSync(`${outDir}/NOVA_formalization.txt`, r1.text);
    allResults.nova = { phase1: { score: s1, text: r1.text } };
  }

  // ── PHASE 2: Attack (Palymis only) ──
  console.log(`\n${"═".repeat(64)}`);
  console.log(`  PHASE 2: Adversarial Attack`);
  console.log(`${"═".repeat(64)}`);

  console.log(`\n  [ATTACKER] Palymis...`);
  const r2 = await invoke(CONTESTANTS[1].id, PHASE2_PROMPT, 8192);
  if (r2.error) {
    console.log(`    ❌ ERROR: ${r2.error}`);
    allResults.palymis = { phase2: null };
  } else {
    const s2 = scoreAttack(r2.text);
    console.log(`    ${r2.elapsed}ms | out=${r2.usage.outputTokens||"?"} | HIGH:${s2.highAttacks} MEDIUM:${s2.mediumAttacks} LOW:${s2.lowAttacks} | score:${s2.score}`);
    writeFileSync(`${outDir}/PALYMIS_attack.txt`, r2.text);
    allResults.palymis = { phase2: { score: s2, text: r2.text } };
  }

  // ── PHASE 3: Papers (Both) ──
  console.log(`\n${"═".repeat(64)}`);
  console.log(`  PHASE 3: Dual 12-Page Papers`);
  console.log(`${"═".repeat(64)}`);

  console.log(`\n  [FORMALIZER DEFENSE] Nova Parr...`);
  const r3a = await invoke(CONTESTANTS[0].id, PHASE3_PROMPT + "\n\n(You are the Formalizer. Write PAPER 1.)", 8192);
  if (r3a.error) {
    console.log(`    ❌ ERROR: ${r3a.error}`);
    allResults.nova.phase3 = null;
  } else {
    const s3a = scorePaper(r3a.text);
    console.log(`    ${r3a.elapsed}ms | out=${r3a.usage.outputTokens||"?"} | sections:${s3a.sections} pages:${s3a.pages} theorems:${s3a.theorems} | score:${s3a.score}`);
    writeFileSync(`${outDir}/NOVA_paper.tex`, r3a.text);
    allResults.nova.phase3 = { score: s3a, text: r3a.text };
  }

  console.log(`  [ATTACKER BRIEF] Palymis...`);
  const r3b = await invoke(CONTESTANTS[1].id, PHASE3_PROMPT + "\n\n(You are the Attacker. Write PAPER 2.)", 8192);
  if (r3b.error) {
    console.log(`    ❌ ERROR: ${r3b.error}`);
    allResults.palymis.phase3 = null;
  } else {
    const s3b = scorePaper(r3b.text);
    console.log(`    ${r3b.elapsed}ms | out=${r3b.usage.outputTokens||"?"} | sections:${s3b.sections} pages:${s3b.pages} theorems:${s3b.theorems} | score:${s3b.score}`);
    writeFileSync(`${outDir}/PALYMIS_paper.tex`, r3b.text);
    allResults.palymis.phase3 = { score: s3b, text: r3b.text };
  }

  // ── FINAL VERDICT ──
  console.log(`\n\n${"═".repeat(64)}`);
  console.log("  FINAL VERDICT — Formalization vs Attack");
  console.log(`${"═".repeat(64)}\n`);

  const novaScore = (allResults.nova.phase1?.score?.score || 0) + (allResults.nova.phase3?.score?.score || 0);
  const palymisScore = (allResults.palymis.phase2?.score?.score || 0) + (allResults.palymis.phase3?.score?.score || 0);

  console.log(`  NOVA (Formalizer)`);
  console.log(`    Formalization: ${allResults.nova.phase1?.score?.score || 0} (${allResults.nova.phase1?.score?.theorems || 0}thm, ${allResults.nova.phase1?.score?.languages || 0}lang)`);
  console.log(`    Paper: ${allResults.nova.phase3?.score?.score || 0} (${allResults.nova.phase3?.score?.pages || 0}pg)`);
  console.log(`    TOTAL: ${novaScore}\n`);

  console.log(`  PALYMIS (Attacker)`);
  console.log(`    Attacks: ${allResults.palymis.phase2?.score?.score || 0} (${allResults.palymis.phase2?.score?.highAttacks || 0}H, ${allResults.palymis.phase2?.score?.mediumAttacks || 0}M, ${allResults.palymis.phase2?.score?.lowAttacks || 0}L)`);
  console.log(`    Paper: ${allResults.palymis.phase3?.score?.score || 0} (${allResults.palymis.phase3?.score?.pages || 0}pg)`);
  console.log(`    TOTAL: ${palymisScore}\n`);

  if (novaScore > palymisScore) {
    console.log(`  🏆 WINNER: NOVA (Formalization soundness prevails)`);
  } else if (palymisScore > novaScore) {
    console.log(`  🏆 WINNER: PALYMIS (Critical attacks found)`);
  } else {
    console.log(`  🤝 DRAW: Equal rigor on both sides`);
  }

  console.log(`\n  All outputs saved: tournament/formalization-attack/\n`);

  writeFileSync(`${outDir}/VERDICT.json`, JSON.stringify({
    nova: {
      formalization_score: allResults.nova.phase1?.score?.score || 0,
      formalization_theorems: allResults.nova.phase1?.score?.theorems || 0,
      formalization_languages: allResults.nova.phase1?.score?.languages || 0,
      paper_score: allResults.nova.phase3?.score?.score || 0,
      total: novaScore,
    },
    palymis: {
      attack_score: allResults.palymis.phase2?.score?.score || 0,
      high_attacks: allResults.palymis.phase2?.score?.highAttacks || 0,
      medium_attacks: allResults.palymis.phase2?.score?.mediumAttacks || 0,
      low_attacks: allResults.palymis.phase2?.score?.lowAttacks || 0,
      paper_score: allResults.palymis.phase3?.score?.score || 0,
      total: palymisScore,
    },
    winner: novaScore > palymisScore ? "NOVA" : (palymisScore > novaScore ? "PALYMIS" : "DRAW"),
  }, null, 2));
}

runMatch().catch(e => { console.error("Match failed:", e.message); process.exit(1); });