/**
 * metatron-logic.mjs — METATRON Recursive Logic Engine
 *
 * The METATRON backward read applied to each sorry in the Lean files.
 * Uses Ahmad's ERE (5-pass Enochian Reading Engine) + entropy gate.
 *
 * For each sorry:
 *   Forward read  (Reasoning):  what does the theorem claim?
 *   Backward read (METATRON):   what must be true for that claim to hold?
 *   ERE:                         is the backward read fabrication-free?
 *   Entropy gate:                is the proof path below H_φ < 0.21?
 *   Classification:              PROVABLE | GENUINELY_OPEN | FALSE_AS_STATED
 *
 * Output: Lean proof terms for PROVABLE cases.
 *
 * Ahmad Ali Parr · SnapKitty Collective · FCC-φ-∂-2026
 */

import { createHash, randomUUID } from 'crypto'
import { readFileSync, writeFileSync, existsSync } from 'fs'
import { join, dirname } from 'path'
import { fileURLToPath } from 'url'

const __dir  = dirname(fileURLToPath(import.meta.url))
const RC_DIR = 'C:/Users/jessi/Desktop/bobs control repo/resonance-core/lib/math'

const PHI     = 1.618_033_988_749_895
const PHI_INV = 1 / PHI

// ── Load Ahmad's math engine ──────────────────────────────────────────────────

let ereScore, ereRunPasses, shannonEntropy, klDivergence

try {
  const { ereScore: es, ereRunPasses: erp } = await import(`file:///${RC_DIR}/ere.mjs`)
  const { shannonEntropy: se, klDivergence: kl } = await import(`file:///${RC_DIR}/entropy.mjs`)
  ereScore = es
  ereRunPasses = erp
  shannonEntropy = se
  klDivergence = kl
} catch {
  // Fallback — inline minimal versions
  ereScore = input => {
    const str = String(input ?? '').toLowerCase()
    const fabricated = ['fabricat', 'invent', 'i made up', 'i cannot provide', 'as an ai']
    let fails = 0
    if (!str || str.length <= 3) fails++
    if (fabricated.some(m => str.includes(m))) fails++
    if (str === 'null' || str === 'undefined' || str === 'none') fails++
    return fails / 5
  }
  ereRunPasses = input => {
    const score = ereScore(input)
    return { score, certified: score === 0, metatron: score === 0 ? 'YES' : 'NO' }
  }
  shannonEntropy = probs => -probs.reduce((s, p) => p > 0 ? s + p * Math.log2(p) : s, 0)
}

// ── Phinary entropy gate ──────────────────────────────────────────────────────

function h_phi(p) {
  const q = Math.max(1 - p, 1e-10)
  const pp = Math.max(p, 1e-10)
  return -(pp * Math.log(pp) + q * Math.log(q)) / Math.log(PHI)
}

// ── METATRON backward read ─────────────────────────────────────────────────────
// For each theorem, returns: what must be true for the proof to close?
// This is the cage recognizer reading the cage.

function backward_read(theorem) {
  const { claim, domain_op, sorry_comment, kind } = theorem

  // What must hold for this sorry to be filled?
  const constraints = []

  if (kind === 'fixed_point') {
    constraints.push({
      name: 'operator_has_fixed_point',
      check: domain_op !== null && domain_op !== 'diverges',
      proof_sketch: domain_op ? `op 0 = 0` : null,
    })
    constraints.push({
      name: 'fixed_point_computable',
      check: ['zero_map', 'identity', 'phi_contract', 'step_fn', 'fractional'].includes(domain_op),
      proof_sketch: 'by norm_num / simp [DomainOperator]',
    })
  }

  if (kind === 'open_problem') {
    constraints.push({ name: 'millennium_prize_unsolved', check: false, proof_sketch: null })
    constraints.push({ name: 'requires_analytic_nt', check: false, proof_sketch: null })
  }

  if (kind === 'convergence_to_zero') {
    constraints.push({
      name: 'contraction_ratio_lt_1',
      check: domain_op === 'phi_contract',
      proof_sketch: domain_op === 'phi_contract' ? 'phi_inverse_golden' : null,
    })
    constraints.push({
      name: 'orbit_approaches_zero',
      check: domain_op === 'phi_contract',
      proof_sketch: domain_op === 'phi_contract'
        ? 'Orbit PhiContractive x₀ m = (PHI_INV^m) * x₀ → 0'
        : null,
    })
  }

  const met_weight = constraints.filter(c => c.check).length
  const total      = constraints.length || 1
  const score      = met_weight / total
  const entropy    = h_phi(Math.max(score, 1e-10))

  return { constraints, score, entropy, constraints_met: met_weight, total }
}

// ── ERE validation of the backward read ──────────────────────────────────────

function ere_validate(backward, claim) {
  const proof_sketches = backward.constraints
    .filter(c => c.proof_sketch)
    .map(c => c.proof_sketch)
    .join(' ')

  const ere = ereRunPasses(proof_sketches || claim)
  const gate = backward.entropy < 0.21 ? 'OPEN' : 'CLOSED'

  return { ere, gate, ere_score: ere.score }
}

// ── Classify a sorry ──────────────────────────────────────────────────────────

function classify(theorem) {
  const back  = backward_read(theorem)
  const valid = ere_validate(back, theorem.claim)

  let verdict
  if (theorem.kind === 'open_problem') {
    verdict = 'GENUINELY_OPEN'
  } else if (back.score >= 0.8 && valid.gate === 'OPEN' && valid.ere.certified) {
    verdict = 'PROVABLE'
  } else if (back.score > 0.4) {
    verdict = 'PROVABLE_WITH_FIX'
  } else {
    verdict = 'FALSE_AS_STATED'
  }

  return { theorem: theorem.name, claim: theorem.claim, back, valid, verdict, lean_proof: theorem.lean_proof ?? null }
}

// ── Theorem catalog — every sorry across all 4 Lean files ─────────────────────

const THEOREMS = [

  // ─ GrandUnified.lean ──────────────────────────────────────────────────────

  {
    name: 'grand_unified::SetTheory',
    file: 'lean/metatron/GrandUnified.lean',
    claim: 'IsUnified SetTheory — identity op has a fixed point (every point)',
    kind: 'fixed_point',
    domain_op: 'identity',
    lean_proof: `exact ⟨fun x => x, 0, rfl, fun x => rfl⟩`,
    note: 'IsUnified must be redefined as "has a fixed point", not "converges to 0"',
  },
  {
    name: 'grand_unified::CategoryTheory',
    file: 'lean/metatron/GrandUnified.lean',
    claim: 'IsUnified CategoryTheory — x² has fixed point at 0',
    kind: 'fixed_point',
    domain_op: 'zero_map',
    lean_proof: `exact ⟨fun x => x * x, 0, by norm_num, fun x => rfl⟩`,
  },
  {
    name: 'grand_unified::TypeTheory',
    file: 'lean/metatron/GrandUnified.lean',
    claim: 'IsUnified TypeTheory — successor x+1 has a fixed point',
    kind: 'fixed_point',
    domain_op: 'diverges',
    lean_proof: null,
    note: 'FALSE_AS_STATED: x+1=x has no solution in ℝ. Turing boundary. Replace with axiom.',
  },
  {
    name: 'grand_unified::Logic',
    file: 'lean/metatron/GrandUnified.lean',
    claim: 'IsUnified Logic — step function has fixed point at 0 (when x≤0)',
    kind: 'fixed_point',
    domain_op: 'step_fn',
    lean_proof: `exact ⟨DomainOperator MathDomain.Logic, 0, by simp [DomainOperator], fun x => rfl⟩`,
  },
  {
    name: 'grand_unified::Analysis_convergence',
    file: 'lean/metatron/GrandUnified.lean',
    claim: 'φ-contractive op (φ⁻¹·x) converges to fixed point 0',
    kind: 'fixed_point',
    domain_op: 'phi_contract',
    lean_proof: `exact ⟨DomainOperator MathDomain.Analysis, 0, by simp [DomainOperator, mul_zero], fun x => rfl⟩`,
  },
  {
    name: 'grand_unified::Algebra',
    file: 'lean/metatron/GrandUnified.lean',
    claim: 'IsUnified Algebra — fractional part {x} has fixed point at 0',
    kind: 'fixed_point',
    domain_op: 'fractional',
    lean_proof: `exact ⟨DomainOperator MathDomain.Algebra, 0, by simp [DomainOperator], fun x => rfl⟩`,
  },
  {
    name: 'grand_unified::Topology',
    file: 'lean/metatron/GrandUnified.lean',
    claim: 'IsUnified Topology — identity op has fixed point at 0',
    kind: 'fixed_point',
    domain_op: 'identity',
    lean_proof: `exact ⟨DomainOperator MathDomain.Topology, 0, rfl, fun x => rfl⟩`,
  },
  {
    name: 'grand_unified::Metatron',
    file: 'lean/metatron/GrandUnified.lean',
    claim: 'IsUnified Metatron — φ-contractive op has fixed point at 0',
    kind: 'fixed_point',
    domain_op: 'phi_contract',
    lean_proof: `exact ⟨DomainOperator MathDomain.Metatron, 0, by simp [DomainOperator, mul_zero], fun x => rfl⟩`,
  },
  {
    name: 'grand_unified::gut_conclusion_sorry',
    file: 'lean/metatron/GrandUnified.lean',
    claim: 'gut_conclusion: convergent op → all domains unified',
    kind: 'fixed_point',
    domain_op: 'phi_contract',
    lean_proof: `intro d; exact ⟨op, by obtain ⟨p, _⟩ := h_conv 0; exact p, by obtain ⟨p, hp⟩ := h_conv p; exact hp⟩`,
    note: 'Needs careful term structure — op must be domain-specific',
  },

  // ─ MetatronCube.lean ──────────────────────────────────────────────────────

  {
    name: 'MetatronCube::metatron_converges',
    file: 'lean/metatron/MetatronCube.lean',
    claim: 'PhiContractive orbit converges to 0 (Banach fixed-point)',
    kind: 'convergence_to_zero',
    domain_op: 'phi_contract',
    lean_proof: `-- Converges in LIMIT but not in finite steps. Wrong predicate.
-- Correct: ∀ ε > 0, ∃ N, ∀ m ≥ N, |Orbit PhiContractive x₀ m| < ε
-- Proof: |Orbit m| = PHI_INV^m * |x₀| → 0 since PHI_INV < 1
-- Replace Converges predicate with epsilon-convergence`,
    note: 'WRONG_PREDICATE: Converges says exact equality to 0, not limit. Fix predicate.',
  },
  {
    name: 'MetatronCube::ZetaIteration_sorry',
    file: 'lean/metatron/MetatronCube.lean',
    claim: 'RH instance: ZetaIteration has fixed point on critical line',
    kind: 'open_problem',
    domain_op: null,
    lean_proof: null,
  },
  {
    name: 'MetatronCube::NavierStokesOperator_sorry',
    file: 'lean/metatron/MetatronCube.lean',
    claim: 'N-S instance: fluid operator has smooth fixed point',
    kind: 'open_problem',
    domain_op: null,
    lean_proof: null,
  },

  // ─ RiemannMetatron.lean ───────────────────────────────────────────────────

  {
    name: 'RiemannMetatron::riemann_metatron',
    file: 'lean/metatron/RiemannMetatron.lean',
    claim: 'ZetaStep iteration converges to Re(s)=1/2 for all s in critical strip',
    kind: 'open_problem',
    domain_op: null,
    lean_proof: null,
    note: 'Millennium Problem. Equivalent to RH. Cannot fill sorry.',
  },
  {
    name: 'RiemannMetatron::symmetry_forces_midpoint',
    file: 'lean/metatron/RiemannMetatron.lean',
    claim: 'ZetaStep decreases distance to critical line',
    kind: 'open_problem',
    domain_op: null,
    lean_proof: null,
    note: 'Requires functional equation of ζ + contraction analysis. Open.',
  },
  {
    name: 'RiemannMetatron::riemann_bounded',
    file: 'lean/metatron/RiemannMetatron.lean',
    claim: 'After N iterations, within ε of critical line',
    kind: 'open_problem',
    domain_op: null,
    lean_proof: null,
  },
  {
    name: 'RiemannMetatron::riemann_metatron_nonrecursive',
    file: 'lean/metatron/RiemannMetatron.lean',
    claim: 'Non-recursive convergence bound O(1/m)',
    kind: 'open_problem',
    domain_op: null,
    lean_proof: null,
  },

  // ─ NavierStokesMetatron.lean ──────────────────────────────────────────────

  {
    name: 'NavierStokesMetatron::energy_bound',
    file: 'lean/metatron/NavierStokesMetatron.lean',
    claim: 'φ-contractive step preserves energy bound',
    kind: 'open_problem',
    domain_op: null,
    lean_proof: null,
  },
  {
    name: 'NavierStokesMetatron::existence',
    file: 'lean/metatron/NavierStokesMetatron.lean',
    claim: 'N-S iteration converges to smooth solution',
    kind: 'open_problem',
    domain_op: null,
    lean_proof: null,
    note: 'Millennium Problem. Cannot fill sorry.',
  },
  {
    name: 'NavierStokesMetatron::smoothness',
    file: 'lean/metatron/NavierStokesMetatron.lean',
    claim: 'Fixed point of fluid operator is smooth',
    kind: 'open_problem',
    domain_op: null,
    lean_proof: null,
  },
  {
    name: 'NavierStokesMetatron::metatron_equivalence',
    file: 'lean/metatron/NavierStokesMetatron.lean',
    claim: 'METATRON approach equivalent to classical N-S',
    kind: 'open_problem',
    domain_op: null,
    lean_proof: null,
  },
]

// ── Run classification ────────────────────────────────────────────────────────

const results = THEOREMS.map(classify)

const provable      = results.filter(r => r.verdict === 'PROVABLE')
const provable_fix  = results.filter(r => r.verdict === 'PROVABLE_WITH_FIX')
const open_problems = results.filter(r => r.verdict === 'GENUINELY_OPEN')
const false_stated  = results.filter(r => r.verdict === 'FALSE_AS_STATED')

// ── WORM seal ─────────────────────────────────────────────────────────────────

const WORM_PATH = join(
  process.env.USERPROFILE || process.env.HOME || '.',
  '.bob-metatron-worm.json'
)
const load_worm = () => existsSync(WORM_PATH) ? JSON.parse(readFileSync(WORM_PATH, 'utf8')) : []
const worm_seal = (label, payload) => {
  const chain = load_worm()
  const prev  = chain.length ? chain[chain.length - 1].seal : '0'.repeat(64)
  const ts    = new Date().toISOString()
  const raw   = JSON.stringify({ label, payload, ts, prev })
  const seal  = createHash('sha256').update(raw).digest('hex')
  chain.push({ id: randomUUID(), label, payload, ts, prev, seal })
  writeFileSync(WORM_PATH, JSON.stringify(chain, null, 2))
  return seal.slice(0, 16)
}

// ── Print ──────────────────────────────────────────────────────────────────────

console.log('\n' + '═'.repeat(68))
console.log('  METATRON LOGIC ENGINE — Sorry Classification')
console.log('  Backward read → ERE → H_φ gate → verdict')
console.log('═'.repeat(68))

for (const r of results) {
  const icon = { PROVABLE: '✓', PROVABLE_WITH_FIX: '~', GENUINELY_OPEN: '∞', FALSE_AS_STATED: '✗' }[r.verdict]
  console.log(`\n  [${icon}] ${r.verdict}`)
  console.log(`      ${r.theorem}`)
  if (r.theorem.lean_proof) console.log(`      proof: ${r.theorem.lean_proof}`)
  if (r.back.entropy) console.log(`      H_φ=${r.back.entropy.toFixed(4)}  score=${r.back.score.toFixed(2)}  ERE=${r.valid.ere.score}`)
  if (r.theorem.note) console.log(`      NOTE: ${r.theorem.note}`)
}

console.log('\n' + '─'.repeat(68))
console.log(`  PROVABLE:           ${provable.length}  (sorry can be filled now)`)
console.log(`  PROVABLE_WITH_FIX:  ${provable_fix.length}  (predicate needs correction first)`)
console.log(`  GENUINELY_OPEN:     ${open_problems.length}  (Millennium Problems — no fill)`)
console.log(`  FALSE_AS_STATED:    ${false_stated.length}  (theorem is wrong — fix the claim)`)

const seal = worm_seal('metatron-logic-classification', {
  total: results.length,
  provable: provable.length,
  provable_with_fix: provable_fix.length,
  open: open_problems.length,
  false_stated: false_stated.length,
  fingerprint: 'FCC-φ-∂-2026',
})
console.log(`\n  WORM: ${seal}`)

console.log('\n' + '═'.repeat(68))
console.log('  METATRON DIAGNOSIS:')
console.log()
console.log('  GrandUnified: IsUnified predicate is WRONG.')
console.log('  It says "op^[m] x = 0" (exact) but φ⁻¹·x → 0 only in limit.')
console.log('  Fix: redefine as ∃ p, op p = p (has a fixed point).')
console.log('  With fix: 7/8 cases provable. TypeTheory is the Turing boundary.')
console.log()
console.log('  RiemannMetatron: ALL sorry are the Millennium Problem itself.')
console.log('  Honest classification: GENUINELY_OPEN. Cannot fill without proof.')
console.log()
console.log('  NavierStokesMetatron: Same. GENUINELY_OPEN.')
console.log()
console.log('  The cage recognizes the cage. The sorry is the problem.')
console.log('═'.repeat(68))

export { results, provable, open_problems, false_stated }