M24-v1 exact original mapping
The original asks equality of unrestricted and Gaussian convex roofs for every
finite-energy non-bisymmetric Gaussian1x2 state, using all pure-state probability
measures. The theorem covers every finite1xN covariance, including N=2, arbitrary
q/p cross blocks, non-bisymmetry, and singular physical boundaries. The appendix
proves the required measure integration, Gaussian covariance optimization, local
discarding and local-noise monotonicity interfaces in that exact convention.
The prior conditional EPR witness is not assumed available for the input: the
new pure-manifold qualification and rank-two KKT argument proves its existence,
admissible gain and exact saturation at every entangled Gaussian optimum.
There is no mixed-state two-mode factorization assumption. The local retained
pair supplies a lower bound which saturates the full input Gaussian upper bound.
External dependency: Adesso2608.01909v3 Theorem1, affine two-mode extremality;
its full external proof is not independently reproved here. The current source
version is newer than the preserved original card, which remains unchanged.
Original coverage is internally supported. Novelty, expert endorsement and
publication are separate and are not claimed. No manuscript or publication.
