Numerous standard AQFT results#20
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Introduce `IsKMSStateForFlow.exists_gns_unitary_strongContinuous`, which shows that a KMS state at inverse temperature β > 0 for a one-parameter Killing flow on a region B yields a GNS triple carrying a strongly continuous unitary group implementing the flow. The proof routes through `IsKMSState.invariant_of_pos` (KMS invariance) and the abstract `exists_gns_unitary_of_invariant_strongContinuous` construction, with the ℝ action packaged via `Multiplicative ℝ`. The corresponding blueprint theorem is added and marked `\leanok`. Blueprint: aqft-in-lean Repository: physicslib/physicslib4 Agent job: 12795f85-3d3c-4844-8791-af82c47219b0 Conversation: 8c3f8f53-54fb-4b75-a25c-1a20a5ce2abf
…ocal alge… - Introduce `eq_zero_of_commute_of_cyclic`, an abstract lemma showing that an operator commuting with a cyclically-spanning set and annihilating the cyclic vector must be zero. - Use it in `localVonNeumann_separating` to prove that, given cyclicity of Ω for R(B₁), any R ∈ R(B₂) with RΩ = 0 vanishes, leveraging curved microcausality to obtain the required commutativity. - Add the corresponding blueprint theorem with `\leanok`, dependencies on curved microcausality and the cyclic-vector definition. Blueprint: aqft-in-lean Repository: physicslib/physicslib4 Agent job: 01f5ebbc-b8cc-4e58-acc5-a20bf58d7b2f Conversation: 8c3f8f53-54fb-4b75-a25c-1a20a5ce2abf
…hesis - Introduce `eq_zero_of_commute_of_cyclic`, an abstract lemma showing that an operator commuting with a cyclic set and annihilating the cyclic vector must be zero. - Add `localVonNeumann_separating` as a Minkowski corollary: cyclicity of Ω for R(B₁) (the Reeh-Schlieder input, taken as an explicit hypothesis) implies Ω is separating for the spacelike-separated algebra R(B₂), via microcausality. - Document both results in the blueprint with a new Statistical Independence theorem node, noting that cyclicity is a hypothesis here to mirror the curved-spacetime setting where no spectrum condition is available. Blueprint: aqft-in-lean Repository: physicslib/physicslib4 Agent job: 01f5ebbc-b8cc-4e58-acc5-a20bf58d7b2f Conversation: 8c3f8f53-54fb-4b75-a25c-1a20a5ce2abf
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