TimeReversalOp
plain-language theorem explainer
The TimeReversalOp structure introduces the time reversal operator in the Recognition Science QFT ledger model as a placeholder asserting negation on real time. Researchers deriving CPT invariance from discrete symmetries would cite it when assembling the T component of the ledger double-entry rules. The declaration is a bare structure definition with a single trivial field and no further reduction.
Claim. The time reversal operator is the structure whose single field requires that negation holds for every real number $t$, serving as the T-symmetry component in the ledger whose entries are balanced collections of recognition events.
background
The module QFT-005 derives CPT invariance from the ledger's double-entry structure. C-symmetry follows from J(x) = J(1/x) cost duality, P-symmetry from the isotropic 3D voxel lattice, and T-symmetry from the eight-tick cycle running forward or backward. The Ledger structure requires that the sum of charges over its list of entries equals zero.
proof idea
This is a structure definition with an empty proof body. It simply declares the TimeReversalOp carrier together with the placeholder field negate that holds trivially for all real t.
why it matters
The definition supplies the T component needed for the CPT theorem targeted in the module's PRL outline. It sits downstream of the eight-tick octave (T7) and the actualization operator A that selects minimal-J configurations. Sibling declarations such as applyT and applyCPT are expected to use it to establish cost preservation under reversal.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.