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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]>
98 lines
2.9 KiB
Lean4
98 lines
2.9 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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Quasar Protocol Formal Model
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Models protocol/quasar/ -- BLS+Corona hybrid quantum consensus.
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Quasar is the finality engine. It collects blocks from all chains
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and produces quantum-final aggregate blocks with dual signatures:
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- BLS (classical, fast): 96-byte aggregated signatures
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- Corona (post-quantum, larger): ~4KB lattice-based threshold signatures
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Maps to:
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- quasar/bls.go: BLS signature aggregation (quorum = 2f+1)
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- quasar/core.go: Quasar struct, chain buffers, quantum finality
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- quasar/engine.go: Engine implementation
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- quasar/horizon.go: Event horizon (pending blocks)
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Properties:
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- BLS aggregation correctness: agg_verify(agg_sig, agg_pk, msg) iff all individual sigs valid
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- Quorum threshold: 2f+1 signatures required for finality
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- Dual signature: quantum block has both BLS and Corona sigs
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- Epoch monotonicity: quantum height only increases
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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 Protocol.Quasar
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/-- Signature types -/
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structure BLSSig where
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bytes : List UInt8
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valid : Bool
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structure CoronaSig where
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bytes : List UInt8
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valid : Bool
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/-- Quasar signature = BLS + Corona (models quasar.QuasarSig) -/
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structure QuasarSig where
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bls : BLSSig
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corona : CoronaSig
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/-- Quantum block (models quasar.QuantumBlock) -/
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structure QuantumBlock where
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height : Nat
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sourceBlocks : List Nat -- block hashes
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signature : QuasarSig
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/-- Quasar state -/
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structure QuasarState where
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quantumHeight : Nat
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finalized : List QuantumBlock
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/-- BLS aggregation: aggregate of valid sigs is valid -/
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axiom bls_aggregation_sound :
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∀ (sigs : List BLSSig),
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(∀ s ∈ sigs, s.valid = true) →
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sigs ≠ [] →
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-- Aggregated signature is valid (bilinear pairing property)
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∃ (agg : BLSSig), agg.valid = true
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/-- Quantum height is monotonically increasing -/
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def addBlock (s : QuasarState) (b : QuantumBlock)
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(_h : b.height > s.quantumHeight) : QuasarState :=
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{ quantumHeight := b.height
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, finalized := b :: s.finalized }
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theorem height_monotone (s : QuasarState) (b : QuantumBlock)
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(h : b.height > s.quantumHeight) :
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(addBlock s b h).quantumHeight > s.quantumHeight := by
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simp [addBlock]
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exact h
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/-- Quorum intersection for BLS signatures:
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Two quorums of 2f+1 from n=3f+1 validators share f+1 members.
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At least one shared member is honest. -/
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theorem bls_quorum_intersection
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(n f : Nat) (hn : n ≤ 3 * f + 1)
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(q1 q2 : Nat)
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(hq1 : q1 ≥ 2 * f + 1) (hq2 : q2 ≥ 2 * f + 1) :
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q1 + q2 > n := by
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omega
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/-- Dual signature validity: both components must be valid -/
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def isValidQuantumSig (qs : QuasarSig) : Bool :=
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qs.bls.valid && qs.corona.valid
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/-- A finalized block has both BLS and Corona valid -/
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theorem quantum_finality_requires_both
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(qs : QuasarSig) (h : isValidQuantumSig qs = true) :
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qs.bls.valid = true ∧ qs.corona.valid = true := by
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simp [isValidQuantumSig] at h
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exact h
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end Protocol.Quasar
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