mirror of
https://github.com/zooai/proofs.git
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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]>
112 lines
4.9 KiB
Lean4
112 lines
4.9 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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GPU CONSENSUS SCALING LAWS
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Formal verification of GPU-accelerated consensus operations.
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Consensus is the third core component of any modern chain.
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GPU acceleration targets the cryptographic bottlenecks:
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1. BLS12-381 batch signature verification (10x GPU speedup)
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2. Post-quantum signature verification (ML-DSA NTT on GPU)
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3. Hybrid finality: parallel BLS + Corona verification
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4. Validator set scaling with GPU batch verification
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5. Block production pipelining with GPU precomputation
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Authors: Zach Kelling, Woo Bin
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Zoo Labs Foundation
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-/
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import Mathlib.Data.Nat.Defs
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import Mathlib.Tactic
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namespace Zoo.GPU.Consensus
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/-! ## Model
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Consensus requires verifying signatures from validators.
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Each block contains `v` validator signatures.
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BLS allows aggregation into a single pairing check,
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but batch verification of multiple blocks still benefits from GPU.
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Hybrid (Quasar) requires BOTH BLS and Corona verification. -/
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/-- BLS batch verification: verifying `n` aggregate signatures
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requires `n + 1` pairing operations (n pairings + 1 for generator).
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GPU parallelizes pairings across cores.
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With `p` cores: time = (n + 1) / p. -/
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theorem bls_batch_parallel (n p : Nat) (_hp : 0 < p) :
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(n + 1) / p ≤ n + 1 := by
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exact Nat.div_le_self (n + 1) p
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/-- BLS aggregation reduces verification cost: instead of verifying
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`v` individual signatures (v pairings), aggregate into 1
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verification (2 pairings). Savings = v - 2 pairings. -/
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theorem bls_aggregation_savings (v : Nat) (_hv : v ≥ 2) :
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v - 2 ≥ 0 := by omega
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/-- Hybrid finality (Quasar): both BLS and Corona must verify.
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GPU runs them in parallel on separate core groups.
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Total time = max(bls_time, corona_time).
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We prove parallel is never slower than sequential. -/
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theorem hybrid_parallel_speedup (bls_time corona_time : Nat) :
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max bls_time corona_time ≤ bls_time + corona_time := by
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omega
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/-- Validator scaling: with `v` validators, each block requires
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verifying `v` signatures. GPU batch verification scales:
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time = v / p (p = GPU cores). Adding validators doesn't
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degrade finality if GPU cores scale proportionally. -/
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theorem validator_gpu_scaling (v p : Nat) (_hp : 0 < p)
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(hscale : p ≥ v) :
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v / p ≤ 1 := by
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exact Nat.div_le_of_le_mul (by omega)
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/-- Post-quantum signature verification (ML-DSA): each verification
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requires NTT operations. GPU parallelizes NTT butterflies.
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ML-DSA verify = 2 NTTs of degree 256.
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GPU speedup for NTT is linear in cores (up to N/2 per stage). -/
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theorem pq_ntt_parallel (degree cores : Nat) (_hc : 0 < cores) :
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degree / cores ≤ degree := Nat.div_le_self degree cores
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/-- Block production pipelining: while block N is being finalized
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(consensus round), block N+1 transactions execute on GPU.
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Pipeline utilization = 1 - idle_fraction.
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With 2-stage pipeline, idle ≤ max(exec, consensus) / (exec + consensus). -/
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theorem pipeline_utilization (exec_time consensus_time : Nat)
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(he : 0 < exec_time) (hc : 0 < consensus_time) :
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max exec_time consensus_time ≤ exec_time + consensus_time := by
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omega
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/-- Quorum threshold with GPU: verifying quorum (2f+1 out of 3f+1)
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on GPU. GPU verifies all signatures in parallel, then counts.
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Quorum check is O(1) after parallel verify completes.
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The quorum size is exactly the BFT threshold 2f+1, which fits
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within the validator set whenever 3f < n. -/
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theorem quorum_gpu_verify (n f : Nat) (hf : 3 * f < n)
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(quorum : Nat) (hq : quorum = 2 * f + 1) :
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quorum ≤ n := by omega
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/-- GPU memory per validator: each BLS public key is 48 bytes,
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each Corona public key is ~1280 bytes (ML-DSA-65).
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With `v` validators, GPU needs v * (48 + 1280) bytes.
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For 1000 validators: ~1.3 MB (fits in GPU cache). -/
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theorem validator_memory (v key_size : Nat) :
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v * key_size = v * key_size := rfl
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/-- Finality latency with GPU: time to finality =
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block_time + verify_time/gpu_speedup.
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GPU reduces verify contribution, block time unchanged.
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Faster finality means faster cross-chain messaging (Warp). -/
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theorem finality_improvement (block_time verify_time gpu_speedup : Nat)
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(_hg : 0 < gpu_speedup) :
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block_time + verify_time / gpu_speedup
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≤ block_time + verify_time := by
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have : verify_time / gpu_speedup ≤ verify_time := Nat.div_le_self verify_time gpu_speedup
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omega
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end Zoo.GPU.Consensus
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