Hanze axioms and theorems

Finite-game interpretation of Hanze as PACT carrier, UPL adjudication, AtomGate policy, and replayable local log.

Sequent form

Γ ⊢ K @ B ⇐ W : σ

Finite-game interpretation

Avatars make bounded transitions, UPL adjudicates the moves, AtomGate maps statuses to actions, and PACT replay reconstructs the history.

Vocabulary

A1
Status closure: Σ is a fixed finite set with |Σ| = 9.
A2
Action grounding: π : Σ → 𝒜 total and functional; 𝒜 = π(Σ).

Identity

A3
Avatar uniqueness: atlas (namespace, name) is a partial map.
A4
Principal as relation: principal Avatar ⇀ Avatar, acyclic.
A5
Root finiteness: principal chain terminates ≤ max_depth.

Judgment

A6
Determinacy: every judgment produces exactly one σ ∈ Σ.
A7
Witness gating: σ = checked requires all required witnesses.
A8
Mandate witness: σ = checked requires a sufficient principal chain.
A9
Boundary containment: action operates only within B.

Log

A10
Append-only PACTLog.
A11
Sequence monotonicity.
A12
Event closure: each event carries its full judgment + action.
A13
Replay determinism: same log → same reconstructed history.

Game

A14
Termination: adjudication terminates in finite steps.
A15
Adjudication determinism: same input → same σ.

Humility

A16
Bounded warrant: σ is a claim within B, not absolute truth.

Proof obligations

T1
Status uniqueness.
T2
Policy totality.
T3
Payment safety: action = release ⇒ σ = checked.
T4
Mandate safety: σ = checked ⇒ principal chain sufficient.
T5
Replay determinism: same PACTLog → same reconstructed state.
T6
Basket atomicity: basket_action = release ⇒ all items checked.

Bounded non-claims