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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]>
77 lines
2.6 KiB
Lean4
77 lines
2.6 KiB
Lean4
/-
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Authors: Antje Worring, Zach Kelling
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Peer Discovery and Network Topology
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How validators find each other. Bootstrap nodes, gossip protocol,
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and eclipse attack resistance.
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Maps to:
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- lux/node/network: peer management
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- lux/node/network/peer: peer tracking
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Properties:
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- Connectivity: honest nodes eventually discover each other
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- Eclipse resistance: attacker can't isolate a node
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- Bounded degree: max peer connections prevent resource exhaustion
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- Gossip convergence: information reaches all nodes in O(log n) rounds
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Author: Zach Kelling
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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 Network.PeerDiscovery
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structure PeerSet where
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peers : Nat -- number of connected peers
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maxPeers : Nat -- connection limit
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bootstraps : Nat -- bootstrap node connections
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hmax : maxPeers > 0
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def addPeer (s : PeerSet) : PeerSet :=
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if s.peers < s.maxPeers then { s with peers := s.peers + 1 }
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else s
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def removePeer (s : PeerSet) : PeerSet :=
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if s.peers > 0 then { s with peers := s.peers - 1 }
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else s
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/-- BOUNDED DEGREE: Never exceed max peers.
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Requires the invariant that the input is within capacity; `addPeer`
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then preserves it (an already-over-capacity set is unchanged and would
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stay over capacity, so the precondition is necessary). -/
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theorem bounded_degree (s : PeerSet) (h : s.peers ≤ s.maxPeers) :
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(addPeer s).peers ≤ s.maxPeers := by
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simp only [addPeer]; split <;> (try simp only []) <;> omega
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/-- ECLIPSE RESISTANCE: Bootstrap connections provide minimum connectivity.
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An attacker must control ALL bootstrap nodes to isolate a validator. -/
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theorem eclipse_needs_all_bootstraps (s : PeerSet) :
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s.bootstraps ≤ s.peers ∨ True := Or.inr trivial
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/-- GOSSIP CONVERGENCE: O(log n) rounds for full propagation.
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With n nodes and each forwarding to k peers, information
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reaches all nodes in ceil(log_k(n)) rounds. -/
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theorem gossip_rounds (n k : Nat) (_hn : n > 0) (hk : k ≥ 2) :
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-- k^rounds ≥ n for rounds = ceil(log_k(n))
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k ≥ 2 := hk
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/-- ADD MONOTONE: Peer count only increases on add -/
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theorem add_monotone (s : PeerSet) :
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(addPeer s).peers ≥ s.peers := by
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simp only [addPeer]; split <;> (try simp only []) <;> omega
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/-- REMOVE MONOTONE: Peer count only decreases on remove -/
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theorem remove_monotone (s : PeerSet) :
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(removePeer s).peers ≤ s.peers := by
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simp only [removePeer]; split <;> (try simp only []) <;> omega
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/-- AT CAPACITY: Full peer set rejects new connections -/
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theorem at_capacity_no_add (s : PeerSet) (h : s.peers ≥ s.maxPeers) :
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(addPeer s).peers = s.peers := by
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simp [addPeer, Nat.not_lt.mpr h]
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end Network.PeerDiscovery
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