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zooqueenandHanzo Dev
d3bff5e2dc
The lean/ proof library (88 files) had ~180 type-check errors across ~45 files plus 31 proof-by-assumption axiom cheats. It now type-checks cleanly under Lean 4.14.0 + Mathlib, with every theorem genuinely proven from definitions. Errors fixed: - Stale Mathlib imports: Data.Nat.Basic / Data.Int.Basic were removed this rev -> Data.Nat.Defs / Data.Int.Defs (57 files). - Shared AI/Agent/Governance/Contract/DeFi/Ecology draft files: same proof-rot as the zoo-labs sibling library (now reconciled): omega missing in-scope bounds, dead tactics after simp, simp over-reduction, doc-comment placement, reserved-word binders, deriving Repr on Finset-bearing structs, noncomputable defs over opaque primitives. - Consensus/Liveness: collapsed a 74-error cascade (undefined shared state model inlined from Safety.lean; the |>. pipe-projection vs comparison parse trap on 14 lines rewritten to explicit dot projection). - Crypto (BLS/FROST/Corona/Hybrid/threshold/FHE), Consensus, Protocol, Warp, Trust, GPU, Compute, Network, DeFi: brought structure invariants into scope for omega, Nat-division bounds via Nat.div_le_of_le_mul / Nat.div_mul_le_self, noncomputable over opaque crypto ops, deriving Inhabited for index access. Integrity: - Removed all 31 `theorem X := X_ax` cheats (axiom asserting the identical statement) and proved each from definitions; removed the UNSOUND content_addressed axiom (hash-injectivity over a struct with free fields). - Quorum-intersection theorems (BFT/Quasar/Flare/Warp/BLS/GPU/Bridge): the draft hypothesis 3f<n is insufficient (n unbounded above makes them false); tightened to the optimal-resilience invariant n=3f+1 / 2t>n. Statement intent preserved. - Net axiom change: -35 / +1 (the one addition, honesty_static, is a fixed-validator-set modeling assumption matching sibling files). - Remaining axioms are trusted-base only: opaque crypto primitives (groups, pairings, hardness, hashes, FHE encrypt/decrypt, BLS soundness, forward secrecy, Fisher-Yates uniformity) and protocol modeling assumptions. No sorry/admit/native_decide. Verified all theorems trace to [propext, Classical.choice, Quot.sound] plus those primitives. Co-authored-by: Hanzo Dev <[email protected]>
124 lines
4.8 KiB
Lean4
124 lines
4.8 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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Cross-Chain Compute Verification
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Proves that AI compute can be safely distributed across N chains
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simultaneously, with purely accretive rewards based on proven
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compute used.
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Inspired by OpenAI Compute Protocol + Bittensor subnet model,
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adapted for Lux multi-chain architecture.
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Maps to:
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- lux/node: multi-chain VM execution
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- zoo/ZIPs/ZIP-002-poai.md: Proof of AI consensus
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- hanzo/engine: inference serving across chains
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Properties:
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- Safety: compute on chain_i doesn't affect chain_j
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- Accretive: rewards only increase with proven compute
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- Conservation: total rewards ≤ total compute value
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- Composability: N chains compose safely
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Data.List.Basic
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import Mathlib.Data.Finset.Basic
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import Mathlib.Tactic
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namespace Compute.CrossChain
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/-- A chain identifier -/
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structure ChainId where
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id : Nat
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deriving DecidableEq, Repr
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/-- Compute attestation from a single chain -/
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structure ComputeAttestation where
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chain : ChainId
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computeUnits : Nat -- normalized compute (GPU-hours equivalent)
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resultHash : Nat -- Merkle root of outputs
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teeValid : Bool -- TEE attestation verified
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timestamp : Nat
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/-- Cross-chain compute state for a single provider -/
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structure ProviderState where
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totalCompute : Nat -- cumulative compute across all chains
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totalRewards : Nat -- cumulative rewards earned
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attestations : List ComputeAttestation
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activeChains : List ChainId -- chains currently computing on
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/-- Reward function: compute → reward (monotone, sublinear) -/
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def computeReward (computeUnits : Nat) (rewardRate : Nat) : Nat :=
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computeUnits * rewardRate / 1000 -- basis points
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/-- Submit attestation from one chain -/
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def submitAttestation (s : ProviderState) (a : ComputeAttestation) : ProviderState :=
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if a.teeValid then
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{ s with
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totalCompute := s.totalCompute + a.computeUnits
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totalRewards := s.totalRewards + computeReward a.computeUnits 100
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attestations := a :: s.attestations
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activeChains := if s.activeChains.contains a.chain then s.activeChains
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else a.chain :: s.activeChains }
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else s -- invalid TEE attestation rejected
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-- ═══════════════════════════════════════════════════════════════
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-- SAFETY THEOREMS
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-- ═══════════════════════════════════════════════════════════════
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/-- CHAIN ISOLATION: Submitting compute on chain_i doesn't reduce
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existing compute from chain_j -/
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theorem chain_isolation (s : ProviderState) (a : ComputeAttestation) :
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(submitAttestation s a).totalCompute ≥ s.totalCompute := by
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simp only [submitAttestation]; split <;> (try simp only []) <;> omega
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/-- ACCRETIVE ONLY: Rewards only increase, never decrease -/
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theorem rewards_accretive (s : ProviderState) (a : ComputeAttestation) :
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(submitAttestation s a).totalRewards ≥ s.totalRewards := by
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simp only [submitAttestation]; split <;> (try simp only []) <;> omega
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/-- INVALID TEE REJECTED: Without valid TEE, state unchanged -/
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theorem invalid_tee_rejected (s : ProviderState) (a : ComputeAttestation)
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(h : a.teeValid = false) :
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submitAttestation s a = s := by
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simp [submitAttestation, h]
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/-- CONSERVATION: rewards never exceed compute value -/
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theorem reward_bounded (computeUnits rewardRate : Nat) :
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computeReward computeUnits rewardRate ≤ computeUnits * rewardRate := by
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simp [computeReward]
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exact Nat.div_le_self _ _
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/-- N-CHAIN COMPOSABILITY: Processing attestations from N chains
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in sequence is equivalent to processing them in any order
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(because addition is commutative) -/
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theorem multi_chain_commutative (s : ProviderState)
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(a1 a2 : ComputeAttestation) :
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(submitAttestation (submitAttestation s a1) a2).totalCompute =
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(submitAttestation (submitAttestation s a2) a1).totalCompute := by
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simp only [submitAttestation]
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split <;> split <;> simp only [Nat.add_right_comm, Nat.add_assoc]
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/-- MONOTONE CHAIN COUNT: active chains only grows -/
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theorem chains_monotone (s : ProviderState) (a : ComputeAttestation) :
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(submitAttestation s a).activeChains.length ≥ s.activeChains.length := by
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simp only [submitAttestation]
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split
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· split <;> simp [List.length_cons]
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· exact Nat.le_refl _
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/-- ZERO COMPUTE = ZERO REWARDS -/
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theorem zero_compute_zero_reward (rate : Nat) :
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computeReward 0 rate = 0 := by
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simp [computeReward]
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/-- EMPTY PROVIDER: initial state has zero everything -/
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def emptyProvider : ProviderState :=
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{ totalCompute := 0, totalRewards := 0, attestations := [], activeChains := [] }
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theorem empty_provider_zero : emptyProvider.totalCompute = 0 := rfl
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end Compute.CrossChain
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