Cascade Wipeout · Lean Theorems

cascade_wipeout

OPEN sorry

CascadeWipeout.lean:52
Needs: foldl arithmetic

restaker_below_threshold

OPEN sorry

CascadeWipeout.lean:60
Depends: cascade_wipeout

correlated_worse_than_iid

OPEN sorry

RestakeWipeout.lean:38
Needs: monotonicity lemma

full_correlation_single_slash

CLOSED ✓

RestakeWipeout.lean:47
Proof: simp + ring

usde_reserve_inadequacy

OPEN sorry

SEC-012 theorem
Needs: norm_num arithmetic

EigenLayer AllocationManager._slashOperator · Contract: 0x948a420b8CC1d6BFd0B6087C2E7c344a2CD0bc39

-- CascadeWipeout.lean
-- EigenLayer Cascade Slashing Invariant
-- SEC-REPORT-ARB-006 · γ₁ = 14.134725141734693 · Day 98
-- Sorry debt: cascade_wipeout, restaker_wipeout

import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Basic

namespace CascadeWipeout

def WAD : ℕ := 10^18

/-- Operator state: maxMagnitude shared across all AVS allocations -/
structure OperatorState where
  maxMagnitude : ℕ
  encumberedMag : ℕ
  avsCount : ℕ
  deriving Repr

/-- Apply one slash: reduce maxMagnitude by slashedMag -/
def applySlash (s : OperatorState) (slashedMag : ℕ) : OperatorState :=
  { s with
    maxMagnitude := s.maxMagnitude - slashedMag
    encumberedMag := s.encumberedMag - slashedMag }

/-- Cascade: sequential slashes from n independent AVSes -/
def cascade (s : OperatorState) (slashes : List ℕ) : OperatorState :=
  slashes.foldl applySlash s

/-- Full allocation: each AVS gets WAD/n magnitude -/
def fullAllocation (n : ℕ) : List ℕ :=
  List.replicate n (WAD / n)

/-- THEOREM: Full allocation cascade → complete wipeout -/
theorem cascade_wipeout (n : ℕ) (hn : n ≥ 2) (hn_div : n ∣ WAD) :
    let slashes := fullAllocation n
    let s₀ := initialState n
    (cascade s₀ slashes).maxMagnitude = 0 := by
  simp [cascade, fullAllocation, initialState, applySlash]
  -- Requires: n * (WAD / n) = WAD (exact division, given hn_div)
  sorry -- foldl arithmetic: WAD - n*(WAD/n) = 0

end CascadeWipeout

-- RestakeWipeout.lean
-- Restaker Capital Wipeout Under Correlated Slash
-- SEC-REPORT-ARB-006 · γ₁ = 14.134725141734693 · Day 98

import Mathlib.Data.Real.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real

namespace RestakeWipeout

/-- THEOREM: At full correlation (ρ=1), single AVS slash = total wipeout path -/
theorem full_correlation_single_slash (p : RestakerPosition)
    (hc : p.correlation = 1) (hn : p.avsCount ≥ 1) :
    expectedLossCorrelated p = p.capital := by
  simp [expectedLossCorrelated, hc]
  ring -- ✓ CLOSED — no sorry

/-- THEOREM: Correlated slash expected loss ≥ IID expected loss -/
theorem correlated_worse_than_iid (p : RestakerPosition) ... := by
  sorry -- resolvable: monotonicity of correlated model over IID

end RestakeWipeout

cascade_wipeout — prove foldl of (· - WAD/n) applied n times to WAD = 0

Tactic: induction on n, simp with Nat.div_mul_cancel (from hn_div), omega for arithmetic

restaker_below_threshold — follows from cascade_wipeout (0 < threshold)

Tactic: have h := cascade_wipeout; exact Nat.lt_of_eq_of_lt h ht

correlated_worse_than_iid — IID loss ≤ correlated loss when ρ > 0

Tactic: unfold defs, gcongr, apply pow_le_one, nlinarith [hr, hc, hc1]

full_correlation_single_slash — ✓ CLOSED with simp + ring

Proof complete. No sorry debt.

usde_reserve_inadequacy — 45e6 / (5.3e9 × 0.0003) = 28.3 < 30

Tactic: intros; norm_num (pure arithmetic, closes immediately)

File	Location	Imports
CascadeWipeout.lean	/mnt/nas-diskpool/eose/lean-corpus/MeekProofs/	Mathlib.Data.List.Basic, BigOperators
RestakeWipeout.lean	/mnt/nas-diskpool/eose/lean-corpus/MeekProofs/	Mathlib.Data.Real.Basic, Pow.Real

joffe-math v2: SEC harness theorems live in MeekProofs/ alongside AlgebraTools.lean, Analysis.lean, and the broader Mathlib corpus. Build with lake build MeekProofs.CascadeWipeout.