Commitment Normative State Join

Abstract

Commitment memory obstructs endpoint reduction and forces the joint normative readout.

Theorem 1.1 (Commitment memory requires the joint normative state).

$$\begin{gathered} \forall History,PhysicalState,Policy:\mathrm{Type}, \\ endpoint:History\to PhysicalState,committedPermissions:History\to \mathrm{Set}(Policy), \\ first,second:History, \\ (endpoint(first)=endpoint(second)\wedge committedPermissions(first)\ne committedPermissions(second))\Rightarrow \\ (\neg (\exists statePermissions:PhysicalState\to \mathrm{Set}(Policy),committedPermissions=\mathrm{compose}(statePermissions,endpoint))\wedge \\ \forall NormativeState:\mathrm{Type},normativeState:History\to NormativeState, \\ \mathrm{Refines}(endpoint,normativeState)\wedge \mathrm{Refines}(committedPermissions,normativeState)\Rightarrow \mathrm{Refines}(\mathrm{conceptJoin}(endpoint,committedPermissions),normativeState)). \end{gathered}$$

Proof. Machine-checked in Lean as D5/S3/ConceptDynamics/NormativeStructure/CommitmentNormativeStateJoin.commitment_normative_state_join (✓ std3). ∎

Source. Repository-derived.

Commentary.

The physical endpoint and committed-permission ledger are independent readouts on the same history carrier. Two histories share an endpoint but have different committed permissions.

The first public conclusion denies every permission readout that factors through physical state alone. The second quantifies over every candidate normative state retaining both source readouts and makes it refine their canonical conceptJoin.

The obstruction and universal join clauses are imported family results; no endpoint, ledger, candidate state, or target relation is defined from the conclusions.

References

• Truth anchor: D5/S3/ConceptDynamics/NormativeStructure/CommitmentNormativeStateJoin.commitment_normative_state_join
• Dependency: D5/S3/ConceptDynamics/ConceptJoinUniversal
• Dependency: D5/S3/ConceptDynamics/NormativeStructure/CommitmentNormativeMemory