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zooqueenandHanzo Dev
ac9676a47a
The formal/lean library (53 files — a separate formalization from lean/) had ~110 type-check errors across 38 files and had never had its Mathlib oleans built. It now verifies at 0 errors under the project's strict setting: `lake env lean -D autoImplicit=false`, all 53 files. Fixed the same families as the sibling lean/ tree (the content is diverged, so each was repaired directly): - Crypto (BLS/FROST/Corona/Hybrid/threshold/FHE/Verkle): omega needs in-scope structure invariants; Nat-division bounds; noncomputable over opaque verifiers; Fin n index → Nat; deriving Inhabited. - DeFi (AMM/staking/fees/flashloan/HFT/router): constant-product invariant and fee bounds via Nat.div_mul_le_self / Nat.div_le_of_le_mul; dead tactics. - Protocol/Consensus/Warp/Bridge: BFT quorum theorems tightened to n=3f+1; pipe-projection parse fixes; split-after-simp; dead tactics; built the Consensus/Safety + ThresholdProof dependency oleans from clean source. - Network/Compute/Trust/Build: record-projection opacity (unfold+split), foldl-min monotonicity, BEq parse parens. - autoImplicit=false: declared previously auto-bound variables (explicit binders / variable blocks); the lakefile sets autoImplicit:=false. Integrity: no sorry/admit/native_decide; no proof-by-assumption axiom cheats. Statement changes only tightened false/trivial draft theorems to true invariants. Remaining axioms are trusted-base only (opaque crypto primitives, protocol modeling / honesty-static, build determinism). Co-authored-by: Hanzo Dev <[email protected]>
122 lines
4.7 KiB
Lean4
122 lines
4.7 KiB
Lean4
/-
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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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unfold submitAttestation; split <;> simp
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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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unfold submitAttestation; split <;> simp
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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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unfold submitAttestation
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split <;> split <;> (simp_all; try omega)
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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 [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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