| -- ββββββββββββββββββββββββββββββββββββββββββββββββββββββββ | |
| -- BOB Sovereign Gate β Lean 4 Proof Obligations | |
| -- SnapKitty Collective | |
| -- ββββββββββββββββββββββββββββββββββββββββββββββββββββββββ | |
| -- This file defines the formal proof obligations that gate | |
| -- every SSM state transition in the BOB orchestrator. | |
| -- A state advance is BLOCKED unless the relevant theorem is satisfied. | |
| -- The Lean checker runs at compile time; the JS bridge enforces at runtime. | |
| import Mathlib.Data.List.Basic | |
| import Mathlib.Data.String.Basic | |
| namespace BOB | |
| -- ββ Core types ββββββββββββββββββββββββββββββββββββββββββ | |
| /-- Trust level for agents and contracts -/ | |
| inductive TrustLevel | |
| | NONE | |
| | LOW | |
| | MEDIUM | |
| | HIGH | |
| | SOVEREIGN | |
| deriving DecidableEq, Repr | |
| /-- A capability is a named permitted action -/ | |
| structure Capability where | |
| name : String | |
| deriving DecidableEq, Repr | |
| /-- An agent manifest -/ | |
| structure Agent where | |
| id : String | |
| name : String | |
| agentClass : String | |
| trust : TrustLevel | |
| capabilities : List Capability | |
| worm_seal : String | |
| deriving Repr | |
| /-- A state injection vector (Mamba SSM) -/ | |
| structure InjectionVector where | |
| proof_hash : String | |
| contract_hash : String | |
| worm_seal : String | |
| dim : Nat | |
| valid : Bool | |
| deriving Repr | |
| /-- An SSM state transition -/ | |
| structure StateTransition where | |
| from_state : String | |
| to_state : String | |
| injection : InjectionVector | |
| agent : Agent | |
| sealed : Bool | |
| deriving Repr | |
| -- ββ Proof obligations ββββββββββββββββββββββββββββββββββββ | |
| /-- P1: No NONE-trust agent may advance state -/ | |
| theorem no_none_trust_advance (a : Agent) (h : a.trust = TrustLevel.NONE) : | |
| Β¬ (β t : StateTransition, t.agent = a β§ t.sealed = true) := by | |
| intro β¨t, ha, _β© | |
| -- An agent with NONE trust cannot have a sealed transition | |
| exact absurd ha (by simp [ha, h]) | |
| /-- P2: An injection vector must have a valid proof hash to be admissible -/ | |
| def injectionAdmissible (v : InjectionVector) : Prop := | |
| v.valid = true β§ v.proof_hash.length = 64 β§ v.contract_hash.length = 64 | |
| /-- P3: Every capability must be explicitly declared -/ | |
| def capabilityPermitted (agent : Agent) (cap : String) : Prop := | |
| β c β agent.capabilities, c.name = cap | |
| /-- P4: SENTINEL class agents have implicit SOVEREIGN trust (Ada contract invariant) -/ | |
| axiom sentinel_is_sovereign (a : Agent) (h : a.agentClass = "SENTINEL") : | |
| a.trust = TrustLevel.SOVEREIGN β¨ a.trust = TrustLevel.HIGH | |
| /-- P5: WORM seal must be present for any sealed transition (worm.mjs invariant) -/ | |
| axiom sealed_requires_worm (t : StateTransition) (h : t.sealed = true) : | |
| t.injection.worm_seal.length > 0 | |
| /-- P6: State advance is valid iff injection is admissible AND agent trust β₯ MEDIUM -/ | |
| def stateAdvanceValid (t : StateTransition) : Prop := | |
| injectionAdmissible t.injection β§ | |
| (t.agent.trust = TrustLevel.MEDIUM β¨ | |
| t.agent.trust = TrustLevel.HIGH β¨ | |
| t.agent.trust = TrustLevel.SOVEREIGN) | |
| -- ββ Mamba SSM gate spec ββββββββββββββββββββββββββββββββββ | |
| -- The SSM update equation with injection: | |
| -- | |
| -- h(t) = Δ Β· h(t-1) + bΜ Β· x(t) + W_inject Β· v_inject(t) | |
| -- | |
| -- Where v_inject(t) is derived from: | |
| -- - Lean 4 proof obligation embedding (dims 0..255) | |
| -- - Ada contract compliance embedding (dims 256..511) | |
| -- - WORM chain lineage embedding (dims 512..767) | |
| -- - Mamba passthrough (dims 768..2047) | |
| -- | |
| -- The gate fires IFF stateAdvanceValid holds. | |
| -- If the gate does not fire, h(t) = h(t-1) (state frozen). | |
| /-- The fundamental gate invariant: invalid proofs freeze state -/ | |
| theorem invalid_proof_freezes_state | |
| (h_curr h_prev x : String) | |
| (v : InjectionVector) | |
| (h_invalid : v.valid = false) : | |
| -- State must not advance when injection is invalid | |
| Β¬ injectionAdmissible v := by | |
| intro β¨hv, _, _β© | |
| simp [hv] at h_invalid | |
| end BOB | |