RemarkRemark: AI-adaptedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Classical scalar sector and bundle limitation

Remarks

Trivial-potential classical charged-scalar Einstein–Maxwell system uses a globally defined real one-form $A$ and $F = d A$ , so it describes only the trivial-potential sector. It does not cover a connection on an arbitrary nontrivial principal $U (1)$ bundle, a scalar represented only by local sections with nontrivial transition functions, or singular currents. In this global real-potential sector $λ$ may be any real number; charge quantization belongs to a separately specified bundle representation and is not inferred here. The field $φ$ is a classical complex field, not a quantum amplitude, and no value of $ℏ$ is used.

Classical scalar sector and bundle limitation

Remarks

Depends on

Dependency tree · 2 levels

Sources